%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU373+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 10:44:11 AM UTC 2026
% Result : Theorem 12.77s 2.32s
% Output : CNFRefutation 12.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 119
% Syntax : Number of formulae : 1344 ( 680 unt; 0 typ; 0 def)
% Number of atoms : 8996 (2631 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 17379 (3550 ~;2620 |; 144 &;10705 @)
% ( 66 <=>; 294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 222 ( 219 usr; 9 con; 0-6 aty)
% Number of variables : 3033 ( 0 ^;3015 !; 18 ?;3033 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_1_0_filter_1,type,
a_1_0_filter_1: $i > $i ).
thf(tp_a_2_2_lattice3,type,
a_2_2_lattice3: $i > $i > $i ).
thf(tp_a_2_3_lattice3,type,
a_2_3_lattice3: $i > $i > $i ).
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_apply_as_element,type,
apply_as_element: $i > $i > $i > $i > $i ).
thf(tp_apply_binary,type,
apply_binary: $i > $i > $i > $i ).
thf(tp_apply_binary_as_element,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_apply_netmap,type,
apply_netmap: $i > $i > $i > $i ).
thf(tp_apply_on_structs,type,
apply_on_structs: $i > $i > $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_below,type,
below: $i > $i > $i > $o ).
thf(tp_below_refl,type,
below_refl: $i > $i > $i > $o ).
thf(tp_bijective,type,
bijective: $i > $i > $i > $o ).
thf(tp_boole_POSet,type,
boole_POSet: $i > $i ).
thf(tp_boole_lattice,type,
boole_lattice: $i > $i ).
thf(tp_boolean_lattstr,type,
boolean_lattstr: $i > $o ).
thf(tp_bottom_of_relstr,type,
bottom_of_relstr: $i > $i ).
thf(tp_bottom_of_semilattstr,type,
bottom_of_semilattstr: $i > $i ).
thf(tp_bounded_lattstr,type,
bounded_lattstr: $i > $o ).
thf(tp_bounded_relstr,type,
bounded_relstr: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_cast_to_el_of_LattPOSet,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(tp_cast_to_el_of_lattice,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_centered,type,
centered: $i > $o ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_closed_subsets,type,
closed_subsets: $i > $i > $o ).
thf(tp_compact_top_space,type,
compact_top_space: $i > $o ).
thf(tp_complemented_lattstr,type,
complemented_lattstr: $i > $o ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_complete_latt_str,type,
complete_latt_str: $i > $o ).
thf(tp_complete_relstr,type,
complete_relstr: $i > $o ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_directed_subset,type,
directed_subset: $i > $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_distributive_lattstr,type,
distributive_lattstr: $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_carrier_subset,type,
empty_carrier_subset: $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_equipotent,type,
equipotent: $i > $i > $o ).
thf(tp_ex_inf_of_relstr_set,type,
ex_inf_of_relstr_set: $i > $i > $o ).
thf(tp_ex_sup_of_relstr_set,type,
ex_sup_of_relstr_set: $i > $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_full_subrelstr,type,
full_subrelstr: $i > $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_as_relation_of,type,
identity_as_relation_of: $i > $i ).
thf(tp_identity_on_carrier,type,
identity_on_carrier: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_incl_POSet,type,
incl_POSet: $i > $i ).
thf(tp_inclusion_order,type,
inclusion_order: $i > $i ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_interior,type,
interior: $i > $i > $i ).
thf(tp_is_a_cover_of_carrier,type,
is_a_cover_of_carrier: $i > $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_eventually_in,type,
is_eventually_in: $i > $i > $i > $o ).
thf(tp_is_often_in,type,
is_often_in: $i > $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_join,type,
join: $i > $i > $i > $i ).
thf(tp_join_absorbing,type,
join_absorbing: $i > $o ).
thf(tp_join_associative,type,
join_associative: $i > $o ).
thf(tp_join_commut,type,
join_commut: $i > $i > $i > $i ).
thf(tp_join_commutative,type,
join_commutative: $i > $o ).
thf(tp_join_of_latt_set,type,
join_of_latt_set: $i > $i > $i ).
thf(tp_join_on_relstr,type,
join_on_relstr: $i > $i > $i ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_k10_filter_1,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(tp_k1_pcomps_1,type,
k1_pcomps_1: $i > $i ).
thf(tp_k2_lattice3,type,
k2_lattice3: $i > $i ).
thf(tp_k8_filter_1,type,
k8_filter_1: $i > $i > $i ).
thf(tp_latt_element_smaller,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(tp_latt_set_smaller,type,
latt_set_smaller: $i > $i > $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_latt_str_of,type,
latt_str_of: $i > $i > $i > $i ).
thf(tp_lattice,type,
lattice: $i > $o ).
thf(tp_lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
thf(tp_lower_bounded_semilattstr,type,
lower_bounded_semilattstr: $i > $o ).
thf(tp_meet,type,
meet: $i > $i > $i > $i ).
thf(tp_meet_absorbing,type,
meet_absorbing: $i > $o ).
thf(tp_meet_associative,type,
meet_associative: $i > $o ).
thf(tp_meet_commut,type,
meet_commut: $i > $i > $i > $i ).
thf(tp_meet_commutative,type,
meet_commutative: $i > $o ).
thf(tp_meet_of_latt_set,type,
meet_of_latt_set: $i > $i > $i ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_meet_on_relstr,type,
meet_on_relstr: $i > $i > $i ).
thf(tp_meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_modular_lattstr,type,
modular_lattstr: $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_net_str,type,
net_str: $i > $i > $o ).
thf(tp_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_restr_as_relation_of,type,
relation_dom_restr_as_relation_of: $i > $i > $i > $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_of_lattice,type,
relation_of_lattice: $i > $i ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_restriction_as_relation_of,type,
relation_restriction_as_relation_of: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_relstr_element_smaller,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(tp_relstr_set_smaller,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(tp_sK10_SY242,type,
sK10_SY242: $i > $i ).
thf(tp_sK11_SY337,type,
sK11_SY337: $i > $i > $i ).
thf(tp_sK12_SY348,type,
sK12_SY348: $i > $i > $i ).
thf(tp_sK13_SY335,type,
sK13_SY335: $i > $i > $i ).
thf(tp_sK14_SY369,type,
sK14_SY369: $i > $i > $i ).
thf(tp_sK15_SY377,type,
sK15_SY377: $i > $i > $i ).
thf(tp_sK16_SY374,type,
sK16_SY374: $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_SY224,type,
sK5_SY224: $i > $i ).
thf(tp_sK6_SY282,type,
sK6_SY282: $i > $i ).
thf(tp_sK7_SY326,type,
sK7_SY326: $i ).
thf(tp_sK8_SY301,type,
sK8_SY301: $i > $i ).
thf(tp_sK9_SY287,type,
sK9_SY287: $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_subnetstr,type,
subnetstr: $i > $i > $i > $o ).
thf(tp_subrelstr,type,
subrelstr: $i > $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_subset_intersection2,type,
subset_intersection2: $i > $i > $i > $i ).
thf(tp_subset_union2,type,
subset_union2: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_symmetric,type,
symmetric: $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_L_join,type,
the_L_join: $i > $i ).
thf(tp_the_L_meet,type,
the_L_meet: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_mapping,type,
the_mapping: $i > $i > $i ).
thf(tp_the_topology,type,
the_topology: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_trivial_carrier,type,
trivial_carrier: $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_pair_as_carrier_subset,type,
unordered_pair_as_carrier_subset: $i > $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_upper_bounded_relstr,type,
upper_bounded_relstr: $i > $o ).
thf(tp_upper_bounded_semilattstr,type,
upper_bounded_semilattstr: $i > $o ).
thf(tp_v1_binop_1,type,
v1_binop_1: $i > $i > $o ).
thf(tp_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_partfun1,type,
v1_partfun1: $i > $i > $i > $o ).
thf(tp_v1_rat_1,type,
v1_rat_1: $i > $o ).
thf(tp_v1_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(tp_with_infima_relstr,type,
with_infima_relstr: $i > $o ).
thf(tp_with_suprema_relstr,type,
with_suprema_relstr: $i > $o ).
thf(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(38,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(73,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(177,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(194,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_yellow_6) ).
thf(222,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(223,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(229,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(231,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( net_str @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
thf(236,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(237,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(240,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(241,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(242,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(243,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(244,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(245,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(246,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(264,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(267,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(268,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(275,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
thf(276,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( element @ ( apply_netmap @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_waybel_0) ).
thf(278,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(280,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(283,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_0) ).
thf(286,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(288,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(291,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(292,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(293,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(298,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(301,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(303,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(307,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(308,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(309,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(310,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(312,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(313,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(316,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(317,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(319,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(322,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(331,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( net_str @ C @ A )
=> ( ( subnetstr @ C @ A @ B )
<=> ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_yellow_6) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(375,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(376,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(390,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier_subset @ A )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(391,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(407,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(430,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_0) ).
thf(442,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_grcat_1) ).
thf(444,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( unordered_pair_as_carrier_subset @ A @ B @ C )
= ( unordered_pair_as_carrier_subset @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(513,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(521,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i,D: $i] :
( ( subset @ C @ D )
=> ( ( ( is_eventually_in @ A @ B @ C )
=> ( is_eventually_in @ A @ B @ D ) )
& ( ( is_often_in @ A @ B @ C )
=> ( is_often_in @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_waybel_0) ).
thf(523,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
thf(526,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(534,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(548,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(582,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(586,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(593,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(598,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(602,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(603,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(605,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(616,axiom,
! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(622,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ( ( related_reflexive @ ( boole_POSet @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow_1) ).
thf(623,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(625,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/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
thf(629,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(639,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_wellord1) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_wellord1) ).
thf(660,axiom,
! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_1) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(669,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(692,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(698,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
thf(702,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(748,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(754,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(758,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l29_wellord1) ).
thf(764,conjecture,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( subset @ ( the_carrier @ C ) @ ( the_carrier @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_yellow_6) ).
thf(765,negated_conjecture,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( subset @ ( the_carrier @ C ) @ ( the_carrier @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[764]) ).
thf(766,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( subset @ ( the_carrier @ C ) @ ( the_carrier @ B ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[765]) ).
thf(767,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(768,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(769,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(770,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(771,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(772,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(773,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(774,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(775,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(776,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(777,plain,
$true = $true,
inference(unfold_def,[status(thm)],[229]) ).
thf(778,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)],[231]) ).
thf(779,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( net_str @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(780,plain,
$true = $true,
inference(unfold_def,[status(thm)],[236]) ).
thf(781,plain,
$true = $true,
inference(unfold_def,[status(thm)],[237]) ).
thf(782,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(783,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(784,plain,
$true = $true,
inference(unfold_def,[status(thm)],[242]) ).
thf(785,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(786,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(787,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(788,plain,
$true = $true,
inference(unfold_def,[status(thm)],[246]) ).
thf(789,plain,
$true = $true,
inference(unfold_def,[status(thm)],[264]) ).
thf(790,plain,
$true = $true,
inference(unfold_def,[status(thm)],[267]) ).
thf(791,plain,
$true = $true,
inference(unfold_def,[status(thm)],[268]) ).
thf(792,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(793,plain,
$true = $true,
inference(unfold_def,[status(thm)],[276]) ).
thf(794,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( element @ ( apply_netmap @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(795,plain,
$true = $true,
inference(unfold_def,[status(thm)],[278]) ).
thf(796,plain,
$true = $true,
inference(unfold_def,[status(thm)],[280]) ).
thf(797,plain,
$true = $true,
inference(unfold_def,[status(thm)],[283]) ).
thf(798,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(799,plain,
$true = $true,
inference(unfold_def,[status(thm)],[286]) ).
thf(800,plain,
$true = $true,
inference(unfold_def,[status(thm)],[288]) ).
thf(801,plain,
$true = $true,
inference(unfold_def,[status(thm)],[291]) ).
thf(802,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(803,plain,
$true = $true,
inference(unfold_def,[status(thm)],[293]) ).
thf(804,plain,
$true = $true,
inference(unfold_def,[status(thm)],[298]) ).
thf(805,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(806,plain,
$true = $true,
inference(unfold_def,[status(thm)],[301]) ).
thf(807,plain,
$true = $true,
inference(unfold_def,[status(thm)],[303]) ).
thf(808,plain,
$true = $true,
inference(unfold_def,[status(thm)],[307]) ).
thf(809,plain,
$true = $true,
inference(unfold_def,[status(thm)],[308]) ).
thf(810,plain,
$true = $true,
inference(unfold_def,[status(thm)],[309]) ).
thf(811,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(812,plain,
$true = $true,
inference(unfold_def,[status(thm)],[312]) ).
thf(813,plain,
$true = $true,
inference(unfold_def,[status(thm)],[313]) ).
thf(814,plain,
$true = $true,
inference(unfold_def,[status(thm)],[316]) ).
thf(815,plain,
$true = $true,
inference(unfold_def,[status(thm)],[317]) ).
thf(816,plain,
$true = $true,
inference(unfold_def,[status(thm)],[319]) ).
thf(817,plain,
$true = $true,
inference(unfold_def,[status(thm)],[322]) ).
thf(818,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( net_str @ C @ A )
=> ( ( subnetstr @ C @ A @ B )
<=> ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(819,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(820,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(821,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(822,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(823,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier_subset @ A )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(824,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(825,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(826,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(827,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(828,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(829,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(830,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(831,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( unordered_pair_as_carrier_subset @ A @ B @ C )
= ( unordered_pair_as_carrier_subset @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(832,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(833,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(834,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(835,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i,D: $i] :
( ( subset @ C @ D )
=> ( ( ( is_eventually_in @ A @ B @ C )
=> ( is_eventually_in @ A @ B @ D ) )
& ( ( is_often_in @ A @ B @ C )
=> ( is_often_in @ A @ B @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(836,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(837,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(838,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(839,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(840,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(841,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(842,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(843,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(844,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(845,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(846,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(847,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(848,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(849,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(850,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(851,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(852,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ( ( related_reflexive @ ( boole_POSet @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(853,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(854,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)],[625]) ).
thf(855,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(856,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(857,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(858,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(859,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(860,plain,
( ( ! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(861,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(862,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(863,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(864,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(865,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(866,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(867,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(868,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(869,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(870,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(871,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(872,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(873,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(874,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(875,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(876,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[707]) ).
thf(877,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(878,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(879,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[747]) ).
thf(880,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[748]) ).
thf(881,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[751]) ).
thf(882,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[754]) ).
thf(883,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[756]) ).
thf(884,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[758]) ).
thf(885,plain,
( ( ( one_sorted_str @ sK1_A )
=> ! [SY205: $i] :
( ( net_str @ SY205 @ sK1_A )
=> ! [SY206: $i] :
( ( subnetstr @ SY206 @ sK1_A @ SY205 )
=> ( subset @ ( the_carrier @ SY206 ) @ ( the_carrier @ SY205 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[766]) ).
thf(886,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[885]) ).
thf(887,plain,
( ( ! [SY205: $i] :
( ( net_str @ SY205 @ sK1_A )
=> ! [SY206: $i] :
( ( subnetstr @ SY206 @ sK1_A @ SY205 )
=> ( subset @ ( the_carrier @ SY206 ) @ ( the_carrier @ SY205 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[885]) ).
thf(888,plain,
( ( ~ ! [SY205: $i] :
( ( net_str @ SY205 @ sK1_A )
=> ! [SY206: $i] :
( ( subnetstr @ SY206 @ sK1_A @ SY205 )
=> ( subset @ ( the_carrier @ SY206 ) @ ( the_carrier @ SY205 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[887]) ).
thf(889,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(890,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(891,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(892,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(893,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(894,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(895,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(896,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(897,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(898,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(899,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(900,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(901,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(902,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(903,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(904,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(905,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(906,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(907,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(908,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(909,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(910,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(911,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(912,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(913,plain,
( ( ! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(914,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(915,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(916,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(917,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(918,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(919,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)],[854]) ).
thf(920,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(921,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ( ( related_reflexive @ ( boole_POSet @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(922,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(923,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(924,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(925,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(926,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(927,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(928,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(929,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(930,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(931,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(932,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(933,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(934,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(935,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(936,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(937,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(938,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i,D: $i] :
( ( subset @ C @ D )
=> ( ( ( is_eventually_in @ A @ B @ C )
=> ( is_eventually_in @ A @ B @ D ) )
& ( ( is_often_in @ A @ B @ C )
=> ( is_often_in @ A @ B @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(939,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(940,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(941,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(942,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( unordered_pair_as_carrier_subset @ A @ B @ C )
= ( unordered_pair_as_carrier_subset @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(943,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(944,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(945,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(946,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(947,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(948,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(949,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(950,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier_subset @ A )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(951,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(952,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(953,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(954,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(955,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( net_str @ C @ A )
=> ( ( subnetstr @ C @ A @ B )
<=> ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(956,plain,
$true = $true,
inference(copy,[status(thm)],[817]) ).
thf(957,plain,
$true = $true,
inference(copy,[status(thm)],[816]) ).
thf(958,plain,
$true = $true,
inference(copy,[status(thm)],[815]) ).
thf(959,plain,
$true = $true,
inference(copy,[status(thm)],[814]) ).
thf(960,plain,
$true = $true,
inference(copy,[status(thm)],[813]) ).
thf(961,plain,
$true = $true,
inference(copy,[status(thm)],[812]) ).
thf(962,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(963,plain,
$true = $true,
inference(copy,[status(thm)],[810]) ).
thf(964,plain,
$true = $true,
inference(copy,[status(thm)],[809]) ).
thf(965,plain,
$true = $true,
inference(copy,[status(thm)],[808]) ).
thf(966,plain,
$true = $true,
inference(copy,[status(thm)],[807]) ).
thf(967,plain,
$true = $true,
inference(copy,[status(thm)],[806]) ).
thf(968,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(969,plain,
$true = $true,
inference(copy,[status(thm)],[804]) ).
thf(970,plain,
$true = $true,
inference(copy,[status(thm)],[803]) ).
thf(971,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(972,plain,
$true = $true,
inference(copy,[status(thm)],[801]) ).
thf(973,plain,
$true = $true,
inference(copy,[status(thm)],[800]) ).
thf(974,plain,
$true = $true,
inference(copy,[status(thm)],[799]) ).
thf(975,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(976,plain,
$true = $true,
inference(copy,[status(thm)],[797]) ).
thf(977,plain,
$true = $true,
inference(copy,[status(thm)],[796]) ).
thf(978,plain,
$true = $true,
inference(copy,[status(thm)],[795]) ).
thf(979,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( element @ ( apply_netmap @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(980,plain,
$true = $true,
inference(copy,[status(thm)],[793]) ).
thf(981,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(982,plain,
$true = $true,
inference(copy,[status(thm)],[791]) ).
thf(983,plain,
$true = $true,
inference(copy,[status(thm)],[790]) ).
thf(984,plain,
$true = $true,
inference(copy,[status(thm)],[789]) ).
thf(985,plain,
$true = $true,
inference(copy,[status(thm)],[788]) ).
thf(986,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(987,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(988,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(989,plain,
$true = $true,
inference(copy,[status(thm)],[784]) ).
thf(990,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(991,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(992,plain,
$true = $true,
inference(copy,[status(thm)],[781]) ).
thf(993,plain,
$true = $true,
inference(copy,[status(thm)],[780]) ).
thf(994,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( net_str @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(995,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(996,plain,
$true = $true,
inference(copy,[status(thm)],[777]) ).
thf(997,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(998,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(999,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1000,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1001,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1002,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1003,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1004,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1005,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1006,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1007,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1008,plain,
( ( ~ ! [SY205: $i] :
( ( net_str @ SY205 @ sK1_A )
=> ! [SY206: $i] :
( ( subnetstr @ SY206 @ sK1_A @ SY205 )
=> ( subset @ ( the_carrier @ SY206 ) @ ( the_carrier @ SY205 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1009,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)],[891]) ).
thf(1010,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 ) )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(1011,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(1012,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( empty @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(1013,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ( subset @ ( fiber @ ( relation_restriction @ SX2 @ SX0 ) @ SX1 ) @ ( fiber @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[915]) ).
thf(1014,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( finite @ SX1 ) )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(1015,plain,
( ( ~ ! [SX0: $i] :
( ~ ( net_str @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( subnetstr @ SX1 @ sK1_A @ SX0 )
| ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1008]) ).
thf(1016,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[952]) ).
thf(1017,plain,
( ( ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[991]) ).
thf(1018,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(1019,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)],[925]) ).
thf(1020,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1006]) ).
thf(1021,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(1022,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[912]) ).
thf(1023,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[935]) ).
thf(1024,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ! [SX1: $i] :
( ~ ( net_str @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( net_str @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( subnetstr @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ( subrelstr @ SX2 @ SX1 )
| ( ( the_mapping @ SX0 @ SX2 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) @ ( the_mapping @ SX0 @ SX1 ) @ ( the_carrier @ SX2 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SX2 @ SX1 )
| ( ( the_mapping @ SX0 @ SX2 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) @ ( the_mapping @ SX0 @ SX1 ) @ ( the_carrier @ SX2 ) ) ) )
| ( subnetstr @ SX2 @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[955]) ).
thf(1025,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1002]) ).
thf(1026,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)],[947]) ).
thf(1027,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[929]) ).
thf(1028,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( ( unordered_pair_as_carrier_subset @ SX0 @ SX1 @ SX2 )
= ( unordered_pair_as_carrier_subset @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[942]) ).
thf(1029,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SX0 @ SX1 ) ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(1030,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_image @ SX1 @ SX0 ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1031,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[949]) ).
thf(1032,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_rng @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[931]) ).
thf(1033,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ( net_str @ SX1 @ SX0 ) )
| ! [SX2: $i] :
( ~ ( subnetstr @ SX2 @ SX0 @ SX1 )
| ( net_str @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[994]) ).
thf(1034,plain,
( ( ~ ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[997]) ).
thf(1035,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( cast_as_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[971]) ).
thf(1036,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1001]) ).
thf(1037,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SX1 @ SX0 ) ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(1038,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_str @ SX0 )
| ( element @ ( meet_on_relstr @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[975]) ).
thf(1039,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[917]) ).
thf(1040,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) )
| ~ ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(1041,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom_restriction @ SX1 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[937]) ).
thf(1042,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(1043,plain,
( ( ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[986]) ).
thf(1044,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( relation_of2_as_subset @ SX3 @ SX2 @ SX0 )
| ~ ( subset @ ( relation_rng @ SX3 ) @ SX1 )
| ( relation_of2_as_subset @ SX3 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(1045,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1003]) ).
thf(1046,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( empty_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[962]) ).
thf(1047,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( identity_on_carrier @ SX0 )
= ( identity_as_relation_of @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[944]) ).
thf(1048,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ( net_str @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
~ ( subnetstr @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(1049,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[954]) ).
thf(1050,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[953]) ).
thf(1051,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)],[995]) ).
thf(1052,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[918]) ).
thf(1053,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_inverse_image @ SX2 @ SX0 ) @ ( relation_inverse_image @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(1054,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ~ ( empty_carrier @ SX1 ) )
| ~ ( net_str @ SX1 @ SX0 ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX1 ) ) )
| ( element @ ( apply_netmap @ SX0 @ SX1 @ SX2 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[979]) ).
thf(1055,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[934]) ).
thf(1056,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ! [SX1: $i] :
( ~ ( net_str @ SX1 @ SX0 )
| ( rel_str @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[990]) ).
thf(1057,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( subset @ SX2 @ SX3 )
| ~ ( ~ ( ~ ( is_eventually_in @ SX0 @ SX1 @ SX2 )
| ( is_eventually_in @ SX0 @ SX1 @ SX3 ) )
| ~ ( ~ ( is_often_in @ SX0 @ SX1 @ SX2 )
| ( is_often_in @ SX0 @ SX1 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[938]) ).
thf(1058,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)],[919]) ).
thf(1059,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[914]) ).
thf(1060,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( relation_of2_as_subset @ SX3 @ SX2 @ SX0 )
| ~ ( subset @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX3 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(1061,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( powerset @ SX2 ) @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[903]) ).
thf(1062,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ~ ! [SX1: $i] :
~ ( net_str @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[998]) ).
thf(1063,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( element @ ( bottom_of_relstr @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[981]) ).
thf(1064,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[900]) ).
thf(1065,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)],[928]) ).
thf(1066,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng_restriction @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[896]) ).
thf(1067,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)],[1005]) ).
thf(1068,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ ( boole_POSet @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ ( boole_POSet @ SX0 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SX0 ) @ SX1 @ SX2 )
| ( subset @ SX1 @ SX2 ) )
| ~ ( ~ ( subset @ SX1 @ SX2 )
| ( related_reflexive @ ( boole_POSet @ SX0 ) @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[921]) ).
thf(1069,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_inverse_image @ SX1 @ SX0 ) @ ( relation_dom @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(1070,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(1071,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( rel_str @ SX1 )
| ~ ( ~ ( ~ ( subrelstr @ SX1 @ SX0 )
| ~ ( ~ ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) )
| ~ ( subset @ ( the_InternalRel @ SX1 ) @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) )
| ~ ( subset @ ( the_InternalRel @ SX1 ) @ ( the_InternalRel @ SX0 ) ) )
| ( subrelstr @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[945]) ).
thf(1072,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( SX1
= ( set_union2 @ SX0 @ ( set_difference @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(1073,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX3 ) )
| ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(1074,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[902]) ).
thf(1075,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( ordinal @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(1076,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)],[893]) ).
thf(1077,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( empty_carrier_subset @ SX0 )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(1078,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[894]) ).
thf(1079,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( powerset @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(1080,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_str @ SX0 )
| ( element @ ( join_on_relstr @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[968]) ).
thf(1081,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[916]) ).
thf(1082,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[933]) ).
thf(1083,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[943]) ).
thf(1084,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX2 @ SX0 )
| ( subset @ SX0 @ ( set_difference @ SX1 @ ( singleton @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[892]) ).
thf(1085,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[987]) ).
thf(1086,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ( ~ ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[946]) ).
thf(1087,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[926]) ).
thf(1088,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[911]) ).
thf(1089,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[930]) ).
thf(1090,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SX0 @ SX1 ) ) @ ( relation_dom @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[889]) ).
thf(1091,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[923]) ).
thf(1092,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX2 ) @ SX0 )
| ~ ( subset @ ( relation_rng @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[901]) ).
thf(1093,plain,
( ( ! [SX0: $i] :
~ ( ( ( the_carrier @ ( incl_POSet @ SX0 ) )
!= SX0 )
| ( ( the_InternalRel @ ( incl_POSet @ SX0 ) )
!= ( inclusion_order @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[913]) ).
thf(1094,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[988]) ).
thf(1095,plain,
! [SV1: $i] :
( ( ! [SY207: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY207 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1096,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1097,plain,
! [SV3: $i] :
( ( ! [SY208: $i] : ( subset @ ( set_difference @ SV3 @ SY208 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1098,plain,
! [SV4: $i] :
( ( ! [SY209: $i] : ( subset @ SV4 @ ( set_union2 @ SV4 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1099,plain,
! [SV5: $i] :
( ( ! [SY210: $i] : ( subset @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1100,plain,
! [SV6: $i] :
( ( ! [SY211: $i] :
~ ( ~ ( ( ( set_difference @ SV6 @ SY211 )
!= empty_set )
| ( subset @ SV6 @ SY211 ) )
| ~ ( ~ ( subset @ SV6 @ SY211 )
| ( ( set_difference @ SV6 @ SY211 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1101,plain,
! [SV7: $i] :
( ( ! [SY212: $i,SY213: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV7 @ SY212 ) @ SY213 )
| ~ ( ~ ( in @ SV7 @ SY213 )
| ~ ( in @ SY212 @ SY213 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SY213 )
| ~ ( in @ SY212 @ SY213 ) )
| ( subset @ ( unordered_pair @ SV7 @ SY212 ) @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1102,plain,
! [SV8: $i] :
( ( ! [SY214: $i] :
( ~ ( relation @ SY214 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV8 @ SY214 ) ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1103,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) )
| ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1104,plain,
! [SV10: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ~ ( relation @ SY216 )
| ( subset @ ( fiber @ ( relation_restriction @ SY216 @ SV10 ) @ SY215 ) @ ( fiber @ SY216 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1105,plain,
! [SV11: $i] :
( ( ! [SY217: $i] :
( ~ ~ ( ~ ( subset @ SV11 @ SY217 )
| ~ ( finite @ SY217 ) )
| ( finite @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1106,plain,
( ( ! [SX0: $i] :
( ~ ( net_str @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( subnetstr @ SX1 @ sK1_A @ SX0 )
| ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1107,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ! [SY218: $i] :
( ~ ( relation @ SY218 )
| ~ ( ~ ( ~ ( subset @ SV12 @ SY218 )
| ! [SY219: $i,SY220: $i] :
( ~ ( in @ ( ordered_pair @ SY219 @ SY220 ) @ SV12 )
| ( in @ ( ordered_pair @ SY219 @ SY220 ) @ SY218 ) ) )
| ~ ( ~ ! [SY221: $i,SY222: $i] :
( ~ ( in @ ( ordered_pair @ SY221 @ SY222 ) @ SV12 )
| ( in @ ( ordered_pair @ SY221 @ SY222 ) @ SY218 ) )
| ( subset @ SV12 @ SY218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1108,plain,
! [SV13: $i] :
( ( ~ ( join_semilatt_str @ SV13 )
| ( one_sorted_str @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1109,plain,
! [SV14: $i] :
( ( ~ ( one_sorted_str @ SV14 )
| ( ( cast_as_carrier_subset @ SV14 )
= ( the_carrier @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1110,plain,
! [SV15: $i] :
( ( ! [SY223: $i] :
~ ( ~ ( ( ( set_difference @ SV15 @ SY223 )
!= empty_set )
| ( subset @ SV15 @ SY223 ) )
| ~ ( ~ ( subset @ SV15 @ SY223 )
| ( ( set_difference @ SV15 @ SY223 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1111,plain,
! [SV16: $i] :
( ( ~ ! [SY224: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV16 @ SY224 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY224 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY224 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY224 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY224 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY224 )
| ~ ~ ( are_equipotent @ SX2 @ SY224 ) )
| ~ ~ ( in @ SX2 @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1112,plain,
! [SV17: $i] :
( ( ! [SY231: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV17 ) @ SY231 )
| ( in @ SV17 @ SY231 ) )
| ~ ( ~ ( in @ SV17 @ SY231 )
| ( subset @ ( singleton @ SV17 ) @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1113,plain,
! [SV18: $i] :
( ( ! [SY232: $i,SY233: $i] :
( ~ ~ ( ~ ( subset @ SV18 @ SY232 )
| ~ ( subset @ SY232 @ SY233 ) )
| ( subset @ SV18 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1114,plain,
! [SV19: $i] :
( ( ! [SY234: $i] :
( ~ ( subset @ ( singleton @ SV19 ) @ ( singleton @ SY234 ) )
| ( SV19 = SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1115,plain,
! [SV20: $i] :
( ( ~ ( one_sorted_str @ SV20 )
| ! [SY235: $i] :
( ~ ( net_str @ SY235 @ SV20 )
| ! [SY236: $i] :
( ~ ( net_str @ SY236 @ SV20 )
| ~ ( ~ ( ~ ( subnetstr @ SY236 @ SV20 @ SY235 )
| ~ ( ~ ( subrelstr @ SY236 @ SY235 )
| ( ( the_mapping @ SV20 @ SY236 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY235 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SY235 ) @ ( the_carrier @ SY236 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY236 @ SY235 )
| ( ( the_mapping @ SV20 @ SY236 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY235 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SY235 ) @ ( the_carrier @ SY236 ) ) ) )
| ( subnetstr @ SY236 @ SV20 @ SY235 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1116,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1117,plain,
! [SV21: $i] :
( ( ~ ( one_sorted_str @ SV21 )
| ~ ( ~ ( ~ ( empty_carrier @ SV21 )
| ( empty @ ( the_carrier @ SV21 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV21 ) )
| ( empty_carrier @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1118,plain,
! [SV22: $i] :
( ( ~ ( subset @ SV22 @ empty_set )
| ( SV22 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1119,plain,
! [SV23: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SY237 @ ( the_carrier @ SV23 ) ) )
| ~ ( element @ SY238 @ ( the_carrier @ SV23 ) ) )
| ( ( unordered_pair_as_carrier_subset @ SV23 @ SY237 @ SY238 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SY238 @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1120,plain,
! [SV24: $i] :
( ( ! [SY239: $i] :
( ~ ( relation @ SY239 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV24 @ SY239 ) ) @ ( relation_rng @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1121,plain,
! [SV25: $i] :
( ( ! [SY240: $i] :
( ~ ( relation @ SY240 )
| ( subset @ ( relation_image @ SY240 @ SV25 ) @ ( relation_rng @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1122,plain,
! [SV26: $i] :
( ( ~ ( ~ ( ~ ( epsilon_transitive @ SV26 )
| ! [SY241: $i] :
( ~ ( in @ SY241 @ SV26 )
| ( subset @ SY241 @ SV26 ) ) )
| ~ ( ~ ! [SY242: $i] :
( ~ ( in @ SY242 @ SV26 )
| ( subset @ SY242 @ SV26 ) )
| ( epsilon_transitive @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1123,plain,
! [SV27: $i] :
( ( ~ ( relation @ SV27 )
| ! [SY243: $i] :
( ~ ( relation @ SY243 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV27 @ SY243 ) ) @ ( relation_rng @ SY243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1124,plain,
! [SV28: $i] :
( ( ! [SY244: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SV28 )
| ~ ( net_str @ SY244 @ SV28 ) )
| ! [SY245: $i] :
( ~ ( subnetstr @ SY245 @ SV28 @ SY244 )
| ( net_str @ SY245 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1125,plain,
( ( ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1126,plain,
! [SV29: $i] :
( ( ~ ( one_sorted_str @ SV29 )
| ( element @ ( cast_as_carrier_subset @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1127,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV30 )
| ~ ( one_sorted_str @ SV30 ) )
| ~ ( empty @ ( cast_as_carrier_subset @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1128,plain,
! [SV31: $i] :
( ( ! [SY246: $i] :
( ~ ( relation @ SY246 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY246 @ SV31 ) ) @ ( relation_rng @ SY246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1129,plain,
! [SV32: $i] :
( ( ! [SY247: $i] :
( ~ ( rel_str @ SV32 )
| ( element @ ( meet_on_relstr @ SV32 @ SY247 ) @ ( the_carrier @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1130,plain,
! [SV33: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ~ ( subset @ SV33 @ SY248 )
| ( subset @ ( set_intersection2 @ SV33 @ SY249 ) @ ( set_intersection2 @ SY248 @ SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1131,plain,
! [SV34: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ~ ( subset @ SV34 @ SY250 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SY251 ) @ ( cartesian_product2 @ SY250 @ SY251 ) )
| ~ ( subset @ ( cartesian_product2 @ SY251 @ SV34 ) @ ( cartesian_product2 @ SY251 @ SY250 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1132,plain,
! [SV35: $i] :
( ( ! [SY252: $i] :
( ~ ( relation @ SY252 )
| ( subset @ ( relation_dom_restriction @ SY252 @ SV35 ) @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1133,plain,
! [SV36: $i] :
( ( ! [SY253: $i,SY254: $i] :
( ~ ~ ( ~ ( subset @ SV36 @ SY253 )
| ~ ( subset @ SY254 @ SY253 ) )
| ( subset @ ( set_union2 @ SV36 @ SY254 ) @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1134,plain,
! [SV37: $i] :
( ( ~ ( meet_semilatt_str @ SV37 )
| ( one_sorted_str @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1135,plain,
! [SV38: $i] :
( ( ! [SY255: $i,SY256: $i,SY257: $i] :
( ~ ( relation_of2_as_subset @ SY257 @ SY256 @ SV38 )
| ~ ( subset @ ( relation_rng @ SY257 ) @ SY255 )
| ( relation_of2_as_subset @ SY257 @ SY256 @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1136,plain,
! [SV39: $i] :
( ( ! [SY258: $i] :
( ~ ~ ( ~ ( ordinal @ SV39 )
| ~ ( ordinal @ SY258 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SV39 @ SY258 )
| ( subset @ SV39 @ SY258 ) )
| ~ ( ~ ( subset @ SV39 @ SY258 )
| ( ordinal_subset @ SV39 @ SY258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1137,plain,
! [SV40: $i] :
( ( ~ ( one_sorted_str @ SV40 )
| ( element @ ( empty_carrier_subset @ SV40 ) @ ( powerset @ ( the_carrier @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1138,plain,
! [SV41: $i] :
( ( ~ ( one_sorted_str @ SV41 )
| ( ( identity_on_carrier @ SV41 )
= ( identity_as_relation_of @ ( the_carrier @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1139,plain,
! [SV42: $i] :
( ( ! [SY259: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SV42 )
| ~ ( net_str @ SY259 @ SV42 ) )
| ~ ! [SY260: $i] :
~ ( subnetstr @ SY260 @ SV42 @ SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1140,plain,
! [SV43: $i] :
( ( ! [SY261: $i] :
~ ( ~ ( ~ ( proper_subset @ SV43 @ SY261 )
| ~ ( ~ ( subset @ SV43 @ SY261 )
| ~ ( ( SV43 != SY261 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV43 @ SY261 )
| ~ ( ( SV43 != SY261 ) ) )
| ( proper_subset @ SV43 @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1141,plain,
! [SV44: $i] :
( ( ! [SY262: $i] :
~ ( ~ ( ~ ( subset @ SV44 @ SY262 )
| ! [SY263: $i] :
( ~ ( in @ SY263 @ SV44 )
| ( in @ SY263 @ SY262 ) ) )
| ~ ( ~ ! [SY264: $i] :
( ~ ( in @ SY264 @ SV44 )
| ( in @ SY264 @ SY262 ) )
| ( subset @ SV44 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1142,plain,
! [SV45: $i] :
( ( ~ ( rel_str @ SV45 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV45 ) @ ( the_carrier @ SV45 ) @ ( the_carrier @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1143,plain,
! [SV46: $i] :
( ( ! [SY265: $i] :
( ~ ( subset @ SV46 @ SY265 )
| ( ( set_intersection2 @ SV46 @ SY265 )
= SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1144,plain,
! [SV47: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ~ ( relation @ SY267 )
| ~ ( subset @ SV47 @ SY266 )
| ( subset @ ( relation_inverse_image @ SY267 @ SV47 ) @ ( relation_inverse_image @ SY267 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1145,plain,
! [SV48: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SY268 ) )
| ~ ( net_str @ SY268 @ SV48 ) )
| ~ ( element @ SY269 @ ( the_carrier @ SY268 ) ) )
| ( element @ ( apply_netmap @ SV48 @ SY268 @ SY269 ) @ ( the_carrier @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1146,plain,
! [SV49: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ~ ( ~ ( subset @ SV49 @ SY270 )
| ~ ( disjoint @ SY270 @ SY271 ) )
| ( disjoint @ SV49 @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1147,plain,
! [SV50: $i] :
( ( ~ ( one_sorted_str @ SV50 )
| ! [SY272: $i] :
( ~ ( net_str @ SY272 @ SV50 )
| ( rel_str @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1148,plain,
! [SV51: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV51 )
| ~ ( one_sorted_str @ SV51 ) )
| ! [SY273: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SY273 )
| ~ ( net_str @ SY273 @ SV51 ) )
| ! [SY274: $i,SY275: $i] :
( ~ ( subset @ SY274 @ SY275 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SY273 @ SY274 )
| ( is_eventually_in @ SV51 @ SY273 @ SY275 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SY273 @ SY274 )
| ( is_often_in @ SV51 @ SY273 @ SY275 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1149,plain,
! [SV52: $i] :
( ( ! [SY276: $i] :
( ~ ( element @ SY276 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
| ! [SY277: $i] :
( ~ ( element @ SY277 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SY276 @ SY277 )
| ( subset @ SY276 @ SY277 ) )
| ~ ( ~ ( subset @ SY276 @ SY277 )
| ( below @ ( boole_lattice @ SV52 ) @ SY276 @ SY277 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1150,plain,
! [SV53: $i] :
( ( ! [SY278: $i] :
( ~ ( relation @ SY278 )
| ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SY278 @ SV53 ) ) @ ( relation_field @ SY278 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SY278 @ SV53 ) ) @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1151,plain,
! [SV54: $i] :
( ( ! [SY279: $i,SY280: $i,SY281: $i] :
( ~ ( relation_of2_as_subset @ SY281 @ SY280 @ SV54 )
| ~ ( subset @ SV54 @ SY279 )
| ( relation_of2_as_subset @ SY281 @ SY280 @ SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1152,plain,
! [SV55: $i] :
( ( ~ ! [SY282: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV55 @ SY282 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY282 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY282 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY282 )
| ( in @ ( powerset @ SX2 ) @ SY282 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY282 )
| ~ ~ ( are_equipotent @ SX2 @ SY282 ) )
| ~ ~ ( in @ SX2 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1153,plain,
! [SV56: $i] :
( ( ~ ( one_sorted_str @ SV56 )
| ~ ! [SY287: $i] :
~ ( net_str @ SY287 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1154,plain,
! [SV57: $i] :
( ( ~ ( rel_str @ SV57 )
| ( element @ ( bottom_of_relstr @ SV57 ) @ ( the_carrier @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1155,plain,
! [SV58: $i] :
( ( ~ ( one_sorted_str @ SV58 )
| ( ( cast_as_carrier_subset @ SV58 )
= ( the_carrier @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1156,plain,
! [SV59: $i] :
( ( ! [SY288: $i] :
~ ( ~ ( ~ ( subset @ SV59 @ ( singleton @ SY288 ) )
| ( SV59 = empty_set )
| ( SV59
= ( singleton @ SY288 ) ) )
| ~ ( ~ ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SY288 ) ) )
| ( subset @ SV59 @ ( singleton @ SY288 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1157,plain,
! [SV60: $i] :
( ( ! [SY289: $i] :
( ~ ( relation @ SY289 )
| ( subset @ ( relation_rng_restriction @ SV60 @ SY289 ) @ SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1158,plain,
! [SV61: $i] :
( ( ! [SY290: $i] :
~ ( ~ ( ~ ( element @ SV61 @ ( powerset @ SY290 ) )
| ( subset @ SV61 @ SY290 ) )
| ~ ( ~ ( subset @ SV61 @ SY290 )
| ( element @ SV61 @ ( powerset @ SY290 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1159,plain,
! [SV62: $i] :
( ( ! [SY291: $i] :
( ~ ( element @ SY291 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
| ! [SY292: $i] :
( ~ ( element @ SY292 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SY291 @ SY292 )
| ( subset @ SY291 @ SY292 ) )
| ~ ( ~ ( subset @ SY291 @ SY292 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SY291 @ SY292 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1160,plain,
! [SV63: $i] :
( ( ! [SY293: $i] :
( ~ ( relation @ SY293 )
| ( subset @ ( relation_inverse_image @ SY293 @ SV63 ) @ ( relation_dom @ SY293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1161,plain,
! [SV64: $i] :
( ( ! [SY294: $i] :
( ~ ( in @ SV64 @ SY294 )
| ( subset @ SV64 @ ( union @ SY294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1162,plain,
! [SV65: $i] :
( ( ~ ( rel_str @ SV65 )
| ! [SY295: $i] :
( ~ ( rel_str @ SY295 )
| ~ ( ~ ( ~ ( subrelstr @ SY295 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SY295 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SY295 ) @ ( the_InternalRel @ SV65 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY295 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SY295 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SY295 @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1163,plain,
! [SV66: $i] :
( ( ! [SY296: $i] :
( ~ ( subset @ SV66 @ SY296 )
| ( SY296
= ( set_union2 @ SV66 @ ( set_difference @ SY296 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1164,plain,
! [SV67: $i] :
( ( ! [SY297: $i,SY298: $i,SY299: $i] :
( ~ ~ ( ~ ( subset @ SV67 @ SY297 )
| ~ ( subset @ SY298 @ SY299 ) )
| ( subset @ ( cartesian_product2 @ SV67 @ SY298 ) @ ( cartesian_product2 @ SY297 @ SY299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1165,plain,
! [SV68: $i] :
( ( ! [SY300: $i] :
( ~ ( subset @ SV68 @ SY300 )
| ( ( set_union2 @ SV68 @ SY300 )
= SY300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1166,plain,
! [SV69: $i] :
( ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV69 )
| ~ ( ~ ( ordinal @ SY301 )
| ~ ( subset @ SY301 @ SV69 ) ) )
| ( ordinal @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1167,plain,
! [SV70: $i] :
( ( ! [SY302: $i] :
~ ( ~ ( ~ ( subset @ SV70 @ ( singleton @ SY302 ) )
| ( SV70 = empty_set )
| ( SV70
= ( singleton @ SY302 ) ) )
| ~ ( ~ ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SY302 ) ) )
| ( subset @ SV70 @ ( singleton @ SY302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1168,plain,
! [SV71: $i] :
( ( ~ ( one_sorted_str @ SV71 )
| ( ( empty_carrier_subset @ SV71 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1169,plain,
! [SV72: $i] :
( ( ! [SY303: $i] :
( ~ ( in @ SV72 @ SY303 )
| ( subset @ SV72 @ ( union @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1170,plain,
! [SV73: $i] :
( ( ! [SY304: $i] :
~ ( ~ ( ( SY304
!= ( powerset @ SV73 ) )
| ! [SY305: $i] :
~ ( ~ ( ~ ( in @ SY305 @ SY304 )
| ( subset @ SY305 @ SV73 ) )
| ~ ( ~ ( subset @ SY305 @ SV73 )
| ( in @ SY305 @ SY304 ) ) ) )
| ~ ( ~ ! [SY306: $i] :
~ ( ~ ( ~ ( in @ SY306 @ SY304 )
| ( subset @ SY306 @ SV73 ) )
| ~ ( ~ ( subset @ SY306 @ SV73 )
| ( in @ SY306 @ SY304 ) ) )
| ( SY304
= ( powerset @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1171,plain,
! [SV74: $i] :
( ( ! [SY307: $i] :
( ~ ( rel_str @ SV74 )
| ( element @ ( join_on_relstr @ SV74 @ SY307 ) @ ( the_carrier @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1172,plain,
! [SV75: $i] :
( ( ~ ( relation @ SV75 )
| ! [SY308: $i] :
( ~ ( relation @ SY308 )
| ~ ( subset @ SV75 @ SY308 )
| ~ ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SY308 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SY308 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1173,plain,
! [SV76: $i] :
( ( ! [SY309: $i] :
~ ~ ( ~ ( subset @ SV76 @ SY309 )
| ~ ( proper_subset @ SY309 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1174,plain,
! [SV77: $i] :
( ( ! [SY310: $i] :
~ ( ~ ( ( SV77 != SY310 )
| ~ ( ~ ( subset @ SV77 @ SY310 )
| ~ ( subset @ SY310 @ SV77 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV77 @ SY310 )
| ~ ( subset @ SY310 @ SV77 ) )
| ( SV77 = SY310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1175,plain,
! [SV78: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ~ ( subset @ SV78 @ SY311 )
| ( in @ SY312 @ SV78 )
| ( subset @ SV78 @ ( set_difference @ SY311 @ ( singleton @ SY312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1176,plain,
! [SV79: $i] :
( ( ~ ( rel_str @ SV79 )
| ( one_sorted_str @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1177,plain,
! [SV80: $i] :
( ( ! [SY313: $i,SY314: $i] :
~ ( ~ ( ~ ( relation_of2 @ SY314 @ SV80 @ SY313 )
| ( subset @ SY314 @ ( cartesian_product2 @ SV80 @ SY313 ) ) )
| ~ ( ~ ( subset @ SY314 @ ( cartesian_product2 @ SV80 @ SY313 ) )
| ( relation_of2 @ SY314 @ SV80 @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1178,plain,
! [SV81: $i] :
( ( ! [SY315: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV81 ) @ SY315 )
| ( in @ SV81 @ SY315 ) )
| ~ ( ~ ( in @ SV81 @ SY315 )
| ( subset @ ( singleton @ SV81 ) @ SY315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1179,plain,
! [SV82: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ~ ( ~ ( subset @ SV82 @ SY316 )
| ~ ( subset @ SV82 @ SY317 ) )
| ( subset @ SV82 @ ( set_intersection2 @ SY316 @ SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1180,plain,
! [SV83: $i] :
( ( ~ ( relation @ SV83 )
| ! [SY318: $i] :
( ~ ( relation @ SY318 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV83 @ SY318 ) ) @ ( relation_dom @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1181,plain,
! [SV84: $i] :
( ( ! [SY319: $i] :
( ~ ( relation @ SY319 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV84 @ SY319 ) ) @ ( relation_dom @ SY319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1182,plain,
! [SV85: $i] :
( ( ! [SY320: $i,SY321: $i] :
( ~ ( subset @ SV85 @ SY320 )
| ( subset @ ( set_difference @ SV85 @ SY321 ) @ ( set_difference @ SY320 @ SY321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1183,plain,
! [SV86: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ~ ( relation_of2_as_subset @ SY323 @ SV86 @ SY322 )
| ~ ( ~ ( subset @ ( relation_dom @ SY323 ) @ SV86 )
| ~ ( subset @ ( relation_rng @ SY323 ) @ SY322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1184,plain,
! [SV87: $i] :
( ( ~ ( ( ( the_carrier @ ( incl_POSet @ SV87 ) )
!= SV87 )
| ( ( the_InternalRel @ ( incl_POSet @ SV87 ) )
!= ( inclusion_order @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1185,plain,
! [SV88: $i] :
( ( ~ ( top_str @ SV88 )
| ( one_sorted_str @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1186,plain,
! [SV89: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV89 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1187,plain,
! [SV90: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV90 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1188,plain,
! [SV91: $i,SV4: $i] :
( ( subset @ SV4 @ ( set_union2 @ SV4 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1189,plain,
! [SV5: $i] :
( ( subset @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1190,plain,
! [SV93: $i,SV6: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV6 @ SV93 )
!= empty_set )
| ( subset @ SV6 @ SV93 ) )
| ~ ( ~ ( subset @ SV6 @ SV93 )
| ( ( set_difference @ SV6 @ SV93 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1191,plain,
! [SV94: $i,SV7: $i] :
( ( ! [SY324: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SY324 )
| ~ ( ~ ( in @ SV7 @ SY324 )
| ~ ( in @ SV94 @ SY324 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SY324 )
| ~ ( in @ SV94 @ SY324 ) )
| ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SY324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1192,plain,
! [SV8: $i,SV95: $i] :
( ( ~ ( relation @ SV95 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV8 @ SV95 ) ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1193,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1194,plain,
! [SV96: $i,SV10: $i] :
( ( ! [SY325: $i] :
( ~ ( relation @ SY325 )
| ( subset @ ( fiber @ ( relation_restriction @ SY325 @ SV10 ) @ SV96 ) @ ( fiber @ SY325 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1195,plain,
! [SV97: $i,SV11: $i] :
( ( ~ ~ ( ~ ( subset @ SV11 @ SV97 )
| ~ ( finite @ SV97 ) )
| ( finite @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1196,plain,
( ( ~ ( net_str @ sK2_SX0 @ sK1_A )
| ! [SY326: $i] :
( ~ ( subnetstr @ SY326 @ sK1_A @ sK2_SX0 )
| ( subset @ ( the_carrier @ SY326 ) @ ( the_carrier @ sK2_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1106]) ).
thf(1197,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( ! [SY218: $i] :
( ~ ( relation @ SY218 )
| ~ ( ~ ( ~ ( subset @ SV12 @ SY218 )
| ! [SY219: $i,SY220: $i] :
( ~ ( in @ ( ordered_pair @ SY219 @ SY220 ) @ SV12 )
| ( in @ ( ordered_pair @ SY219 @ SY220 ) @ SY218 ) ) )
| ~ ( ~ ! [SY221: $i,SY222: $i] :
( ~ ( in @ ( ordered_pair @ SY221 @ SY222 ) @ SV12 )
| ( in @ ( ordered_pair @ SY221 @ SY222 ) @ SY218 ) )
| ( subset @ SV12 @ SY218 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1198,plain,
! [SV13: $i] :
( ( ( ~ ( join_semilatt_str @ SV13 ) )
= $true )
| ( ( one_sorted_str @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1199,plain,
! [SV14: $i] :
( ( ( ~ ( one_sorted_str @ SV14 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV14 )
= ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1200,plain,
! [SV98: $i,SV15: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV15 @ SV98 )
!= empty_set )
| ( subset @ SV15 @ SV98 ) )
| ~ ( ~ ( subset @ SV15 @ SV98 )
| ( ( set_difference @ SV15 @ SV98 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1201,plain,
! [SV16: $i] :
( ( ! [SY224: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV16 @ SY224 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY224 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY224 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY224 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY224 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY224 )
| ~ ~ ( are_equipotent @ SX2 @ SY224 ) )
| ~ ~ ( in @ SX2 @ SY224 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1202,plain,
! [SV99: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV17 ) @ SV99 )
| ( in @ SV17 @ SV99 ) )
| ~ ( ~ ( in @ SV17 @ SV99 )
| ( subset @ ( singleton @ SV17 ) @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1203,plain,
! [SV100: $i,SV18: $i] :
( ( ! [SY327: $i] :
( ~ ~ ( ~ ( subset @ SV18 @ SV100 )
| ~ ( subset @ SV100 @ SY327 ) )
| ( subset @ SV18 @ SY327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1204,plain,
! [SV101: $i,SV19: $i] :
( ( ~ ( subset @ ( singleton @ SV19 ) @ ( singleton @ SV101 ) )
| ( SV19 = SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1205,plain,
! [SV20: $i] :
( ( ( ~ ( one_sorted_str @ SV20 ) )
= $true )
| ( ( ! [SY235: $i] :
( ~ ( net_str @ SY235 @ SV20 )
| ! [SY236: $i] :
( ~ ( net_str @ SY236 @ SV20 )
| ~ ( ~ ( ~ ( subnetstr @ SY236 @ SV20 @ SY235 )
| ~ ( ~ ( subrelstr @ SY236 @ SY235 )
| ( ( the_mapping @ SV20 @ SY236 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY235 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SY235 ) @ ( the_carrier @ SY236 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY236 @ SY235 )
| ( ( the_mapping @ SV20 @ SY236 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY235 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SY235 ) @ ( the_carrier @ SY236 ) ) ) )
| ( subnetstr @ SY236 @ SV20 @ SY235 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1206,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1116]) ).
thf(1207,plain,
! [SV21: $i] :
( ( ( ~ ( one_sorted_str @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( empty_carrier @ SV21 )
| ( empty @ ( the_carrier @ SV21 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV21 ) )
| ( empty_carrier @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1208,plain,
! [SV22: $i] :
( ( ( ~ ( subset @ SV22 @ empty_set ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1209,plain,
! [SV102: $i,SV23: $i] :
( ( ! [SY328: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
| ~ ( element @ SY328 @ ( the_carrier @ SV23 ) ) )
| ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SY328 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SY328 @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1210,plain,
! [SV24: $i,SV103: $i] :
( ( ~ ( relation @ SV103 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV24 @ SV103 ) ) @ ( relation_rng @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1211,plain,
! [SV25: $i,SV104: $i] :
( ( ~ ( relation @ SV104 )
| ( subset @ ( relation_image @ SV104 @ SV25 ) @ ( relation_rng @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1212,plain,
! [SV26: $i] :
( ( ~ ( ~ ( epsilon_transitive @ SV26 )
| ! [SY241: $i] :
( ~ ( in @ SY241 @ SV26 )
| ( subset @ SY241 @ SV26 ) ) )
| ~ ( ~ ! [SY242: $i] :
( ~ ( in @ SY242 @ SV26 )
| ( subset @ SY242 @ SV26 ) )
| ( epsilon_transitive @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1213,plain,
! [SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ! [SY243: $i] :
( ~ ( relation @ SY243 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV27 @ SY243 ) ) @ ( relation_rng @ SY243 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1214,plain,
! [SV105: $i,SV28: $i] :
( ( ~ ~ ( ~ ( one_sorted_str @ SV28 )
| ~ ( net_str @ SV105 @ SV28 ) )
| ! [SY329: $i] :
( ~ ( subnetstr @ SY329 @ SV28 @ SV105 )
| ( net_str @ SY329 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1215,plain,
( ( ~ ( one_sorted_str @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1125]) ).
thf(1216,plain,
! [SV29: $i] :
( ( ( ~ ( one_sorted_str @ SV29 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1217,plain,
! [SV30: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV30 )
| ~ ( one_sorted_str @ SV30 ) ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1218,plain,
! [SV31: $i,SV106: $i] :
( ( ~ ( relation @ SV106 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV106 @ SV31 ) ) @ ( relation_rng @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1219,plain,
! [SV107: $i,SV32: $i] :
( ( ~ ( rel_str @ SV32 )
| ( element @ ( meet_on_relstr @ SV32 @ SV107 ) @ ( the_carrier @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1220,plain,
! [SV108: $i,SV33: $i] :
( ( ! [SY330: $i] :
( ~ ( subset @ SV33 @ SV108 )
| ( subset @ ( set_intersection2 @ SV33 @ SY330 ) @ ( set_intersection2 @ SV108 @ SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1221,plain,
! [SV109: $i,SV34: $i] :
( ( ! [SY331: $i] :
( ~ ( subset @ SV34 @ SV109 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SY331 ) @ ( cartesian_product2 @ SV109 @ SY331 ) )
| ~ ( subset @ ( cartesian_product2 @ SY331 @ SV34 ) @ ( cartesian_product2 @ SY331 @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1222,plain,
! [SV35: $i,SV110: $i] :
( ( ~ ( relation @ SV110 )
| ( subset @ ( relation_dom_restriction @ SV110 @ SV35 ) @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1223,plain,
! [SV111: $i,SV36: $i] :
( ( ! [SY332: $i] :
( ~ ~ ( ~ ( subset @ SV36 @ SV111 )
| ~ ( subset @ SY332 @ SV111 ) )
| ( subset @ ( set_union2 @ SV36 @ SY332 ) @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1224,plain,
! [SV37: $i] :
( ( ( ~ ( meet_semilatt_str @ SV37 ) )
= $true )
| ( ( one_sorted_str @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1225,plain,
! [SV112: $i,SV38: $i] :
( ( ! [SY333: $i,SY334: $i] :
( ~ ( relation_of2_as_subset @ SY334 @ SY333 @ SV38 )
| ~ ( subset @ ( relation_rng @ SY334 ) @ SV112 )
| ( relation_of2_as_subset @ SY334 @ SY333 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1226,plain,
! [SV113: $i,SV39: $i] :
( ( ~ ~ ( ~ ( ordinal @ SV39 )
| ~ ( ordinal @ SV113 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
| ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1227,plain,
! [SV40: $i] :
( ( ( ~ ( one_sorted_str @ SV40 ) )
= $true )
| ( ( element @ ( empty_carrier_subset @ SV40 ) @ ( powerset @ ( the_carrier @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1228,plain,
! [SV41: $i] :
( ( ( ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( ( identity_on_carrier @ SV41 )
= ( identity_as_relation_of @ ( the_carrier @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1229,plain,
! [SV114: $i,SV42: $i] :
( ( ~ ~ ( ~ ( one_sorted_str @ SV42 )
| ~ ( net_str @ SV114 @ SV42 ) )
| ~ ! [SY335: $i] :
~ ( subnetstr @ SY335 @ SV42 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1230,plain,
! [SV115: $i,SV43: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV43 @ SV115 )
| ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) )
| ( proper_subset @ SV43 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1231,plain,
! [SV116: $i,SV44: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV44 @ SV116 )
| ! [SY336: $i] :
( ~ ( in @ SY336 @ SV44 )
| ( in @ SY336 @ SV116 ) ) )
| ~ ( ~ ! [SY337: $i] :
( ~ ( in @ SY337 @ SV44 )
| ( in @ SY337 @ SV116 ) )
| ( subset @ SV44 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1232,plain,
! [SV45: $i] :
( ( ( ~ ( rel_str @ SV45 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV45 ) @ ( the_carrier @ SV45 ) @ ( the_carrier @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1233,plain,
! [SV117: $i,SV46: $i] :
( ( ~ ( subset @ SV46 @ SV117 )
| ( ( set_intersection2 @ SV46 @ SV117 )
= SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1234,plain,
! [SV118: $i,SV47: $i] :
( ( ! [SY338: $i] :
( ~ ( relation @ SY338 )
| ~ ( subset @ SV47 @ SV118 )
| ( subset @ ( relation_inverse_image @ SY338 @ SV47 ) @ ( relation_inverse_image @ SY338 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1235,plain,
! [SV119: $i,SV48: $i] :
( ( ! [SY339: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
| ~ ( net_str @ SV119 @ SV48 ) )
| ~ ( element @ SY339 @ ( the_carrier @ SV119 ) ) )
| ( element @ ( apply_netmap @ SV48 @ SV119 @ SY339 ) @ ( the_carrier @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1236,plain,
! [SV120: $i,SV49: $i] :
( ( ! [SY340: $i] :
( ~ ~ ( ~ ( subset @ SV49 @ SV120 )
| ~ ( disjoint @ SV120 @ SY340 ) )
| ( disjoint @ SV49 @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1237,plain,
! [SV50: $i] :
( ( ( ~ ( one_sorted_str @ SV50 ) )
= $true )
| ( ( ! [SY272: $i] :
( ~ ( net_str @ SY272 @ SV50 )
| ( rel_str @ SY272 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1238,plain,
! [SV51: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV51 )
| ~ ( one_sorted_str @ SV51 ) ) )
= $true )
| ( ( ! [SY273: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SY273 )
| ~ ( net_str @ SY273 @ SV51 ) )
| ! [SY274: $i,SY275: $i] :
( ~ ( subset @ SY274 @ SY275 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SY273 @ SY274 )
| ( is_eventually_in @ SV51 @ SY273 @ SY275 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SY273 @ SY274 )
| ( is_often_in @ SV51 @ SY273 @ SY275 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1239,plain,
! [SV52: $i,SV121: $i] :
( ( ~ ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
| ! [SY341: $i] :
( ~ ( element @ SY341 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SY341 )
| ( subset @ SV121 @ SY341 ) )
| ~ ( ~ ( subset @ SV121 @ SY341 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SY341 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1240,plain,
! [SV53: $i,SV122: $i] :
( ( ~ ( relation @ SV122 )
| ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ ( relation_field @ SV122 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1241,plain,
! [SV123: $i,SV54: $i] :
( ( ! [SY342: $i,SY343: $i] :
( ~ ( relation_of2_as_subset @ SY343 @ SY342 @ SV54 )
| ~ ( subset @ SV54 @ SV123 )
| ( relation_of2_as_subset @ SY343 @ SY342 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1242,plain,
! [SV55: $i] :
( ( ! [SY282: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV55 @ SY282 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY282 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY282 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY282 )
| ( in @ ( powerset @ SX2 ) @ SY282 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY282 )
| ~ ~ ( are_equipotent @ SX2 @ SY282 ) )
| ~ ~ ( in @ SX2 @ SY282 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1243,plain,
! [SV56: $i] :
( ( ( ~ ( one_sorted_str @ SV56 ) )
= $true )
| ( ( ~ ! [SY287: $i] :
~ ( net_str @ SY287 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1244,plain,
! [SV57: $i] :
( ( ( ~ ( rel_str @ SV57 ) )
= $true )
| ( ( element @ ( bottom_of_relstr @ SV57 ) @ ( the_carrier @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1245,plain,
! [SV58: $i] :
( ( ( ~ ( one_sorted_str @ SV58 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV58 )
= ( the_carrier @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1246,plain,
! [SV124: $i,SV59: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV59 @ ( singleton @ SV124 ) )
| ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
| ~ ( ~ ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
| ( subset @ SV59 @ ( singleton @ SV124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1247,plain,
! [SV60: $i,SV125: $i] :
( ( ~ ( relation @ SV125 )
| ( subset @ ( relation_rng_restriction @ SV60 @ SV125 ) @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1248,plain,
! [SV126: $i,SV61: $i] :
( ( ~ ( ~ ( ~ ( element @ SV61 @ ( powerset @ SV126 ) )
| ( subset @ SV61 @ SV126 ) )
| ~ ( ~ ( subset @ SV61 @ SV126 )
| ( element @ SV61 @ ( powerset @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1249,plain,
! [SV62: $i,SV127: $i] :
( ( ~ ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
| ! [SY344: $i] :
( ~ ( element @ SY344 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SY344 )
| ( subset @ SV127 @ SY344 ) )
| ~ ( ~ ( subset @ SV127 @ SY344 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SY344 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1250,plain,
! [SV63: $i,SV128: $i] :
( ( ~ ( relation @ SV128 )
| ( subset @ ( relation_inverse_image @ SV128 @ SV63 ) @ ( relation_dom @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1251,plain,
! [SV129: $i,SV64: $i] :
( ( ~ ( in @ SV64 @ SV129 )
| ( subset @ SV64 @ ( union @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1252,plain,
! [SV65: $i] :
( ( ( ~ ( rel_str @ SV65 ) )
= $true )
| ( ( ! [SY295: $i] :
( ~ ( rel_str @ SY295 )
| ~ ( ~ ( ~ ( subrelstr @ SY295 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SY295 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SY295 ) @ ( the_InternalRel @ SV65 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY295 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SY295 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SY295 @ SV65 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1253,plain,
! [SV130: $i,SV66: $i] :
( ( ~ ( subset @ SV66 @ SV130 )
| ( SV130
= ( set_union2 @ SV66 @ ( set_difference @ SV130 @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1254,plain,
! [SV131: $i,SV67: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ~ ~ ( ~ ( subset @ SV67 @ SV131 )
| ~ ( subset @ SY345 @ SY346 ) )
| ( subset @ ( cartesian_product2 @ SV67 @ SY345 ) @ ( cartesian_product2 @ SV131 @ SY346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1255,plain,
! [SV132: $i,SV68: $i] :
( ( ~ ( subset @ SV68 @ SV132 )
| ( ( set_union2 @ SV68 @ SV132 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1256,plain,
! [SV69: $i] :
( ( ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV69 )
| ~ ( ~ ( ordinal @ SY301 )
| ~ ( subset @ SY301 @ SV69 ) ) ) )
= $true )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1257,plain,
! [SV133: $i,SV70: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV70 @ ( singleton @ SV133 ) )
| ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
| ~ ( ~ ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
| ( subset @ SV70 @ ( singleton @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1258,plain,
! [SV71: $i] :
( ( ( ~ ( one_sorted_str @ SV71 ) )
= $true )
| ( ( ( empty_carrier_subset @ SV71 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1259,plain,
! [SV134: $i,SV72: $i] :
( ( ~ ( in @ SV72 @ SV134 )
| ( subset @ SV72 @ ( union @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1260,plain,
! [SV73: $i,SV135: $i] :
( ( ~ ( ~ ( ( SV135
!= ( powerset @ SV73 ) )
| ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV135 )
| ( subset @ SY347 @ SV73 ) )
| ~ ( ~ ( subset @ SY347 @ SV73 )
| ( in @ SY347 @ SV135 ) ) ) )
| ~ ( ~ ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV135 )
| ( subset @ SY348 @ SV73 ) )
| ~ ( ~ ( subset @ SY348 @ SV73 )
| ( in @ SY348 @ SV135 ) ) )
| ( SV135
= ( powerset @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1261,plain,
! [SV136: $i,SV74: $i] :
( ( ~ ( rel_str @ SV74 )
| ( element @ ( join_on_relstr @ SV74 @ SV136 ) @ ( the_carrier @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1262,plain,
! [SV75: $i] :
( ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( ! [SY308: $i] :
( ~ ( relation @ SY308 )
| ~ ( subset @ SV75 @ SY308 )
| ~ ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SY308 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SY308 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1263,plain,
! [SV137: $i,SV76: $i] :
( ( ~ ~ ( ~ ( subset @ SV76 @ SV137 )
| ~ ( proper_subset @ SV137 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1264,plain,
! [SV138: $i,SV77: $i] :
( ( ~ ( ~ ( ( SV77 != SV138 )
| ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) )
| ( SV77 = SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1265,plain,
! [SV139: $i,SV78: $i] :
( ( ! [SY349: $i] :
( ~ ( subset @ SV78 @ SV139 )
| ( in @ SY349 @ SV78 )
| ( subset @ SV78 @ ( set_difference @ SV139 @ ( singleton @ SY349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1266,plain,
! [SV79: $i] :
( ( ( ~ ( rel_str @ SV79 ) )
= $true )
| ( ( one_sorted_str @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1267,plain,
! [SV140: $i,SV80: $i] :
( ( ! [SY350: $i] :
~ ( ~ ( ~ ( relation_of2 @ SY350 @ SV80 @ SV140 )
| ( subset @ SY350 @ ( cartesian_product2 @ SV80 @ SV140 ) ) )
| ~ ( ~ ( subset @ SY350 @ ( cartesian_product2 @ SV80 @ SV140 ) )
| ( relation_of2 @ SY350 @ SV80 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1268,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV81 ) @ SV141 )
| ( in @ SV81 @ SV141 ) )
| ~ ( ~ ( in @ SV81 @ SV141 )
| ( subset @ ( singleton @ SV81 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1269,plain,
! [SV142: $i,SV82: $i] :
( ( ! [SY351: $i] :
( ~ ~ ( ~ ( subset @ SV82 @ SV142 )
| ~ ( subset @ SV82 @ SY351 ) )
| ( subset @ SV82 @ ( set_intersection2 @ SV142 @ SY351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1270,plain,
! [SV83: $i] :
( ( ( ~ ( relation @ SV83 ) )
= $true )
| ( ( ! [SY318: $i] :
( ~ ( relation @ SY318 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV83 @ SY318 ) ) @ ( relation_dom @ SV83 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1271,plain,
! [SV84: $i,SV143: $i] :
( ( ~ ( relation @ SV143 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV84 @ SV143 ) ) @ ( relation_dom @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1272,plain,
! [SV144: $i,SV85: $i] :
( ( ! [SY352: $i] :
( ~ ( subset @ SV85 @ SV144 )
| ( subset @ ( set_difference @ SV85 @ SY352 ) @ ( set_difference @ SV144 @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1273,plain,
! [SV145: $i,SV86: $i] :
( ( ! [SY353: $i] :
( ~ ( relation_of2_as_subset @ SY353 @ SV86 @ SV145 )
| ~ ( ~ ( subset @ ( relation_dom @ SY353 ) @ SV86 )
| ~ ( subset @ ( relation_rng @ SY353 ) @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1274,plain,
! [SV87: $i] :
( ( ( ( the_carrier @ ( incl_POSet @ SV87 ) )
!= SV87 )
| ( ( the_InternalRel @ ( incl_POSet @ SV87 ) )
!= ( inclusion_order @ SV87 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1275,plain,
! [SV88: $i] :
( ( ( ~ ( top_str @ SV88 ) )
= $true )
| ( ( one_sorted_str @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1276,plain,
! [SV93: $i,SV6: $i] :
( ( ~ ( ( ( set_difference @ SV6 @ SV93 )
!= empty_set )
| ( subset @ SV6 @ SV93 ) )
| ~ ( ~ ( subset @ SV6 @ SV93 )
| ( ( set_difference @ SV6 @ SV93 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1277,plain,
! [SV146: $i,SV94: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
| ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) )
| ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1278,plain,
! [SV8: $i,SV95: $i] :
( ( ( ~ ( relation @ SV95 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV8 @ SV95 ) ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1279,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) ) )
= $false )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1280,plain,
! [SV96: $i,SV10: $i,SV147: $i] :
( ( ~ ( relation @ SV147 )
| ( subset @ ( fiber @ ( relation_restriction @ SV147 @ SV10 ) @ SV96 ) @ ( fiber @ SV147 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1281,plain,
! [SV97: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV11 @ SV97 )
| ~ ( finite @ SV97 ) ) )
= $true )
| ( ( finite @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1282,plain,
( ( ~ ( net_str @ sK2_SX0 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1283,plain,
( ( ! [SY326: $i] :
( ~ ( subnetstr @ SY326 @ sK1_A @ sK2_SX0 )
| ( subset @ ( the_carrier @ SY326 ) @ ( the_carrier @ sK2_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1284,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( ! [SY218: $i] :
( ~ ( relation @ SY218 )
| ~ ( ~ ( ~ ( subset @ SV12 @ SY218 )
| ! [SY219: $i,SY220: $i] :
( ~ ( in @ ( ordered_pair @ SY219 @ SY220 ) @ SV12 )
| ( in @ ( ordered_pair @ SY219 @ SY220 ) @ SY218 ) ) )
| ~ ( ~ ! [SY221: $i,SY222: $i] :
( ~ ( in @ ( ordered_pair @ SY221 @ SY222 ) @ SV12 )
| ( in @ ( ordered_pair @ SY221 @ SY222 ) @ SY218 ) )
| ( subset @ SV12 @ SY218 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1285,plain,
! [SV13: $i] :
( ( ( join_semilatt_str @ SV13 )
= $false )
| ( ( one_sorted_str @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1286,plain,
! [SV14: $i] :
( ( ( one_sorted_str @ SV14 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV14 )
= ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1287,plain,
! [SV98: $i,SV15: $i] :
( ( ~ ( ( ( set_difference @ SV15 @ SV98 )
!= empty_set )
| ( subset @ SV15 @ SV98 ) )
| ~ ( ~ ( subset @ SV15 @ SV98 )
| ( ( set_difference @ SV15 @ SV98 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1288,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
| ~ ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ( in @ SY357 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY356 )
| ( in @ SX4 @ SY357 ) ) ) ) )
| ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY359 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SY359 @ ( sK5_SY224 @ SV16 ) ) )
| ~ ~ ( in @ SY359 @ ( sK5_SY224 @ SV16 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1201]) ).
thf(1289,plain,
! [SV99: $i,SV17: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV17 ) @ SV99 )
| ( in @ SV17 @ SV99 ) )
| ~ ( ~ ( in @ SV17 @ SV99 )
| ( subset @ ( singleton @ SV17 ) @ SV99 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1290,plain,
! [SV148: $i,SV100: $i,SV18: $i] :
( ( ~ ~ ( ~ ( subset @ SV18 @ SV100 )
| ~ ( subset @ SV100 @ SV148 ) )
| ( subset @ SV18 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1291,plain,
! [SV101: $i,SV19: $i] :
( ( ( ~ ( subset @ ( singleton @ SV19 ) @ ( singleton @ SV101 ) ) )
= $true )
| ( ( SV19 = SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1292,plain,
! [SV20: $i] :
( ( ( one_sorted_str @ SV20 )
= $false )
| ( ( ! [SY235: $i] :
( ~ ( net_str @ SY235 @ SV20 )
| ! [SY236: $i] :
( ~ ( net_str @ SY236 @ SV20 )
| ~ ( ~ ( ~ ( subnetstr @ SY236 @ SV20 @ SY235 )
| ~ ( ~ ( subrelstr @ SY236 @ SY235 )
| ( ( the_mapping @ SV20 @ SY236 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY235 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SY235 ) @ ( the_carrier @ SY236 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY236 @ SY235 )
| ( ( the_mapping @ SV20 @ SY236 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY235 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SY235 ) @ ( the_carrier @ SY236 ) ) ) )
| ( subnetstr @ SY236 @ SV20 @ SY235 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1293,plain,
( ( ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1294,plain,
! [SV21: $i] :
( ( ( one_sorted_str @ SV21 )
= $false )
| ( ( ~ ( ~ ( ~ ( empty_carrier @ SV21 )
| ( empty @ ( the_carrier @ SV21 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV21 ) )
| ( empty_carrier @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1295,plain,
! [SV22: $i] :
( ( ( subset @ SV22 @ empty_set )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1296,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
| ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
| ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1297,plain,
! [SV24: $i,SV103: $i] :
( ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV24 @ SV103 ) ) @ ( relation_rng @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1298,plain,
! [SV25: $i,SV104: $i] :
( ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( subset @ ( relation_image @ SV104 @ SV25 ) @ ( relation_rng @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1299,plain,
! [SV26: $i] :
( ( ~ ( ~ ( epsilon_transitive @ SV26 )
| ! [SY241: $i] :
( ~ ( in @ SY241 @ SV26 )
| ( subset @ SY241 @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1300,plain,
! [SV26: $i] :
( ( ~ ( ~ ! [SY242: $i] :
( ~ ( in @ SY242 @ SV26 )
| ( subset @ SY242 @ SV26 ) )
| ( epsilon_transitive @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1301,plain,
! [SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( ! [SY243: $i] :
( ~ ( relation @ SY243 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV27 @ SY243 ) ) @ ( relation_rng @ SY243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1302,plain,
! [SV105: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( one_sorted_str @ SV28 )
| ~ ( net_str @ SV105 @ SV28 ) ) )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( subnetstr @ SY329 @ SV28 @ SV105 )
| ( net_str @ SY329 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1303,plain,
( ( one_sorted_str @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1215]) ).
thf(1304,plain,
! [SV29: $i] :
( ( ( one_sorted_str @ SV29 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1305,plain,
! [SV30: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV30 )
| ~ ( one_sorted_str @ SV30 ) ) )
= $false )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1306,plain,
! [SV31: $i,SV106: $i] :
( ( ( ~ ( relation @ SV106 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV106 @ SV31 ) ) @ ( relation_rng @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1307,plain,
! [SV107: $i,SV32: $i] :
( ( ( ~ ( rel_str @ SV32 ) )
= $true )
| ( ( element @ ( meet_on_relstr @ SV32 @ SV107 ) @ ( the_carrier @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1308,plain,
! [SV150: $i,SV108: $i,SV33: $i] :
( ( ~ ( subset @ SV33 @ SV108 )
| ( subset @ ( set_intersection2 @ SV33 @ SV150 ) @ ( set_intersection2 @ SV108 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1309,plain,
! [SV151: $i,SV109: $i,SV34: $i] :
( ( ~ ( subset @ SV34 @ SV109 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV151 ) @ ( cartesian_product2 @ SV109 @ SV151 ) )
| ~ ( subset @ ( cartesian_product2 @ SV151 @ SV34 ) @ ( cartesian_product2 @ SV151 @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1310,plain,
! [SV35: $i,SV110: $i] :
( ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV110 @ SV35 ) @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1311,plain,
! [SV152: $i,SV111: $i,SV36: $i] :
( ( ~ ~ ( ~ ( subset @ SV36 @ SV111 )
| ~ ( subset @ SV152 @ SV111 ) )
| ( subset @ ( set_union2 @ SV36 @ SV152 ) @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1312,plain,
! [SV37: $i] :
( ( ( meet_semilatt_str @ SV37 )
= $false )
| ( ( one_sorted_str @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1313,plain,
! [SV112: $i,SV38: $i,SV153: $i] :
( ( ! [SY360: $i] :
( ~ ( relation_of2_as_subset @ SY360 @ SV153 @ SV38 )
| ~ ( subset @ ( relation_rng @ SY360 ) @ SV112 )
| ( relation_of2_as_subset @ SY360 @ SV153 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1314,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ( ordinal @ SV39 )
| ~ ( ordinal @ SV113 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
| ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1315,plain,
! [SV40: $i] :
( ( ( one_sorted_str @ SV40 )
= $false )
| ( ( element @ ( empty_carrier_subset @ SV40 ) @ ( powerset @ ( the_carrier @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1316,plain,
! [SV41: $i] :
( ( ( one_sorted_str @ SV41 )
= $false )
| ( ( ( identity_on_carrier @ SV41 )
= ( identity_as_relation_of @ ( the_carrier @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1317,plain,
! [SV114: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( one_sorted_str @ SV42 )
| ~ ( net_str @ SV114 @ SV42 ) ) )
= $true )
| ( ( ~ ! [SY335: $i] :
~ ( subnetstr @ SY335 @ SV42 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1318,plain,
! [SV115: $i,SV43: $i] :
( ( ~ ( ~ ( proper_subset @ SV43 @ SV115 )
| ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) )
| ( proper_subset @ SV43 @ SV115 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1319,plain,
! [SV116: $i,SV44: $i] :
( ( ~ ( ~ ( subset @ SV44 @ SV116 )
| ! [SY336: $i] :
( ~ ( in @ SY336 @ SV44 )
| ( in @ SY336 @ SV116 ) ) )
| ~ ( ~ ! [SY337: $i] :
( ~ ( in @ SY337 @ SV44 )
| ( in @ SY337 @ SV116 ) )
| ( subset @ SV44 @ SV116 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1320,plain,
! [SV45: $i] :
( ( ( rel_str @ SV45 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV45 ) @ ( the_carrier @ SV45 ) @ ( the_carrier @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1321,plain,
! [SV117: $i,SV46: $i] :
( ( ( ~ ( subset @ SV46 @ SV117 ) )
= $true )
| ( ( ( set_intersection2 @ SV46 @ SV117 )
= SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1322,plain,
! [SV118: $i,SV47: $i,SV154: $i] :
( ( ~ ( relation @ SV154 )
| ~ ( subset @ SV47 @ SV118 )
| ( subset @ ( relation_inverse_image @ SV154 @ SV47 ) @ ( relation_inverse_image @ SV154 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1323,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
| ~ ( net_str @ SV119 @ SV48 ) )
| ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
| ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1324,plain,
! [SV156: $i,SV120: $i,SV49: $i] :
( ( ~ ~ ( ~ ( subset @ SV49 @ SV120 )
| ~ ( disjoint @ SV120 @ SV156 ) )
| ( disjoint @ SV49 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1325,plain,
! [SV50: $i] :
( ( ( one_sorted_str @ SV50 )
= $false )
| ( ( ! [SY272: $i] :
( ~ ( net_str @ SY272 @ SV50 )
| ( rel_str @ SY272 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1326,plain,
! [SV51: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV51 )
| ~ ( one_sorted_str @ SV51 ) ) )
= $false )
| ( ( ! [SY273: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SY273 )
| ~ ( net_str @ SY273 @ SV51 ) )
| ! [SY274: $i,SY275: $i] :
( ~ ( subset @ SY274 @ SY275 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SY273 @ SY274 )
| ( is_eventually_in @ SV51 @ SY273 @ SY275 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SY273 @ SY274 )
| ( is_often_in @ SV51 @ SY273 @ SY275 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1327,plain,
! [SV52: $i,SV121: $i] :
( ( ( ~ ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) ) )
= $true )
| ( ( ! [SY341: $i] :
( ~ ( element @ SY341 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SY341 )
| ( subset @ SV121 @ SY341 ) )
| ~ ( ~ ( subset @ SV121 @ SY341 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SY341 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1328,plain,
! [SV53: $i,SV122: $i] :
( ( ( ~ ( relation @ SV122 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ ( relation_field @ SV122 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1329,plain,
! [SV123: $i,SV54: $i,SV157: $i] :
( ( ! [SY361: $i] :
( ~ ( relation_of2_as_subset @ SY361 @ SV157 @ SV54 )
| ~ ( subset @ SV54 @ SV123 )
| ( relation_of2_as_subset @ SY361 @ SV157 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1330,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY364: $i] :
( ~ ( in @ SY364 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SY364 ) @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY365 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SY365 @ ( sK6_SY282 @ SV55 ) ) )
| ~ ~ ( in @ SY365 @ ( sK6_SY282 @ SV55 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1242]) ).
thf(1331,plain,
! [SV56: $i] :
( ( ( one_sorted_str @ SV56 )
= $false )
| ( ( ~ ! [SY287: $i] :
~ ( net_str @ SY287 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1332,plain,
! [SV57: $i] :
( ( ( rel_str @ SV57 )
= $false )
| ( ( element @ ( bottom_of_relstr @ SV57 ) @ ( the_carrier @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1333,plain,
! [SV58: $i] :
( ( ( one_sorted_str @ SV58 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV58 )
= ( the_carrier @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1334,plain,
! [SV124: $i,SV59: $i] :
( ( ~ ( ~ ( subset @ SV59 @ ( singleton @ SV124 ) )
| ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
| ~ ( ~ ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
| ( subset @ SV59 @ ( singleton @ SV124 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1335,plain,
! [SV60: $i,SV125: $i] :
( ( ( ~ ( relation @ SV125 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV60 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1336,plain,
! [SV126: $i,SV61: $i] :
( ( ~ ( ~ ( element @ SV61 @ ( powerset @ SV126 ) )
| ( subset @ SV61 @ SV126 ) )
| ~ ( ~ ( subset @ SV61 @ SV126 )
| ( element @ SV61 @ ( powerset @ SV126 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1337,plain,
! [SV62: $i,SV127: $i] :
( ( ( ~ ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) ) )
= $true )
| ( ( ! [SY344: $i] :
( ~ ( element @ SY344 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SY344 )
| ( subset @ SV127 @ SY344 ) )
| ~ ( ~ ( subset @ SV127 @ SY344 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SY344 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1338,plain,
! [SV63: $i,SV128: $i] :
( ( ( ~ ( relation @ SV128 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV128 @ SV63 ) @ ( relation_dom @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1339,plain,
! [SV129: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV129 ) )
= $true )
| ( ( subset @ SV64 @ ( union @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1340,plain,
! [SV65: $i] :
( ( ( rel_str @ SV65 )
= $false )
| ( ( ! [SY295: $i] :
( ~ ( rel_str @ SY295 )
| ~ ( ~ ( ~ ( subrelstr @ SY295 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SY295 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SY295 ) @ ( the_InternalRel @ SV65 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY295 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SY295 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SY295 @ SV65 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1341,plain,
! [SV130: $i,SV66: $i] :
( ( ( ~ ( subset @ SV66 @ SV130 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV66 @ ( set_difference @ SV130 @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1342,plain,
! [SV158: $i,SV131: $i,SV67: $i] :
( ( ! [SY366: $i] :
( ~ ~ ( ~ ( subset @ SV67 @ SV131 )
| ~ ( subset @ SV158 @ SY366 ) )
| ( subset @ ( cartesian_product2 @ SV67 @ SV158 ) @ ( cartesian_product2 @ SV131 @ SY366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1343,plain,
! [SV132: $i,SV68: $i] :
( ( ( ~ ( subset @ SV68 @ SV132 ) )
= $true )
| ( ( ( set_union2 @ SV68 @ SV132 )
= SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1344,plain,
! [SV69: $i] :
( ( ( ! [SY301: $i] :
( ~ ( in @ SY301 @ SV69 )
| ~ ( ~ ( ordinal @ SY301 )
| ~ ( subset @ SY301 @ SV69 ) ) ) )
= $false )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1345,plain,
! [SV133: $i,SV70: $i] :
( ( ~ ( ~ ( subset @ SV70 @ ( singleton @ SV133 ) )
| ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
| ~ ( ~ ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
| ( subset @ SV70 @ ( singleton @ SV133 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1346,plain,
! [SV71: $i] :
( ( ( one_sorted_str @ SV71 )
= $false )
| ( ( ( empty_carrier_subset @ SV71 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1347,plain,
! [SV134: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ SV134 ) )
= $true )
| ( ( subset @ SV72 @ ( union @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1348,plain,
! [SV73: $i,SV135: $i] :
( ( ~ ( ( SV135
!= ( powerset @ SV73 ) )
| ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV135 )
| ( subset @ SY347 @ SV73 ) )
| ~ ( ~ ( subset @ SY347 @ SV73 )
| ( in @ SY347 @ SV135 ) ) ) )
| ~ ( ~ ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV135 )
| ( subset @ SY348 @ SV73 ) )
| ~ ( ~ ( subset @ SY348 @ SV73 )
| ( in @ SY348 @ SV135 ) ) )
| ( SV135
= ( powerset @ SV73 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1349,plain,
! [SV136: $i,SV74: $i] :
( ( ( ~ ( rel_str @ SV74 ) )
= $true )
| ( ( element @ ( join_on_relstr @ SV74 @ SV136 ) @ ( the_carrier @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1350,plain,
! [SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( ! [SY308: $i] :
( ~ ( relation @ SY308 )
| ~ ( subset @ SV75 @ SY308 )
| ~ ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SY308 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SY308 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1351,plain,
! [SV137: $i,SV76: $i] :
( ( ~ ( ~ ( subset @ SV76 @ SV137 )
| ~ ( proper_subset @ SV137 @ SV76 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1352,plain,
! [SV138: $i,SV77: $i] :
( ( ~ ( ( SV77 != SV138 )
| ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) )
| ( SV77 = SV138 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1353,plain,
! [SV159: $i,SV139: $i,SV78: $i] :
( ( ~ ( subset @ SV78 @ SV139 )
| ( in @ SV159 @ SV78 )
| ( subset @ SV78 @ ( set_difference @ SV139 @ ( singleton @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1354,plain,
! [SV79: $i] :
( ( ( rel_str @ SV79 )
= $false )
| ( ( one_sorted_str @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1355,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ~ ( ~ ( ~ ( relation_of2 @ SV160 @ SV80 @ SV140 )
| ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) ) )
| ~ ( ~ ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) )
| ( relation_of2 @ SV160 @ SV80 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1356,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV81 ) @ SV141 )
| ( in @ SV81 @ SV141 ) )
| ~ ( ~ ( in @ SV81 @ SV141 )
| ( subset @ ( singleton @ SV81 ) @ SV141 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1357,plain,
! [SV161: $i,SV142: $i,SV82: $i] :
( ( ~ ~ ( ~ ( subset @ SV82 @ SV142 )
| ~ ( subset @ SV82 @ SV161 ) )
| ( subset @ SV82 @ ( set_intersection2 @ SV142 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1358,plain,
! [SV83: $i] :
( ( ( relation @ SV83 )
= $false )
| ( ( ! [SY318: $i] :
( ~ ( relation @ SY318 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV83 @ SY318 ) ) @ ( relation_dom @ SV83 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1359,plain,
! [SV84: $i,SV143: $i] :
( ( ( ~ ( relation @ SV143 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV84 @ SV143 ) ) @ ( relation_dom @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1360,plain,
! [SV162: $i,SV144: $i,SV85: $i] :
( ( ~ ( subset @ SV85 @ SV144 )
| ( subset @ ( set_difference @ SV85 @ SV162 ) @ ( set_difference @ SV144 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1361,plain,
! [SV145: $i,SV86: $i,SV163: $i] :
( ( ~ ( relation_of2_as_subset @ SV163 @ SV86 @ SV145 )
| ~ ( ~ ( subset @ ( relation_dom @ SV163 ) @ SV86 )
| ~ ( subset @ ( relation_rng @ SV163 ) @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1362,plain,
! [SV87: $i] :
( ( ( the_carrier @ ( incl_POSet @ SV87 ) )
!= SV87 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1274]) ).
thf(1363,plain,
! [SV87: $i] :
( ( ( the_InternalRel @ ( incl_POSet @ SV87 ) )
!= ( inclusion_order @ SV87 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1274]) ).
thf(1364,plain,
! [SV88: $i] :
( ( ( top_str @ SV88 )
= $false )
| ( ( one_sorted_str @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1365,plain,
! [SV93: $i,SV6: $i] :
( ( ~ ( ( ( set_difference @ SV6 @ SV93 )
!= empty_set )
| ( subset @ SV6 @ SV93 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1366,plain,
! [SV93: $i,SV6: $i] :
( ( ~ ( ~ ( subset @ SV6 @ SV93 )
| ( ( set_difference @ SV6 @ SV93 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1367,plain,
! [SV146: $i,SV94: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
| ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) )
| ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1368,plain,
! [SV8: $i,SV95: $i] :
( ( ( relation @ SV95 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV8 @ SV95 ) ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1369,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1370,plain,
! [SV96: $i,SV10: $i,SV147: $i] :
( ( ( ~ ( relation @ SV147 ) )
= $true )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV147 @ SV10 ) @ SV96 ) @ ( fiber @ SV147 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1371,plain,
! [SV97: $i,SV11: $i] :
( ( ( ~ ( ~ ( subset @ SV11 @ SV97 )
| ~ ( finite @ SV97 ) ) )
= $false )
| ( ( finite @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1372,plain,
( ( net_str @ sK2_SX0 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1282]) ).
thf(1373,plain,
( ( ~ ( subnetstr @ sK7_SY326 @ sK1_A @ sK2_SX0 )
| ( subset @ ( the_carrier @ sK7_SY326 ) @ ( the_carrier @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1283]) ).
thf(1374,plain,
! [SV12: $i,SV164: $i] :
( ( ( ~ ( relation @ SV164 )
| ~ ( ~ ( ~ ( subset @ SV12 @ SV164 )
| ! [SY367: $i,SY368: $i] :
( ~ ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV12 )
| ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV164 ) ) )
| ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV12 )
| ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV164 ) )
| ( subset @ SV12 @ SV164 ) ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1375,plain,
! [SV98: $i,SV15: $i] :
( ( ~ ( ( ( set_difference @ SV15 @ SV98 )
!= empty_set )
| ( subset @ SV15 @ SV98 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1376,plain,
! [SV98: $i,SV15: $i] :
( ( ~ ( ~ ( subset @ SV15 @ SV98 )
| ( ( set_difference @ SV15 @ SV98 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1377,plain,
! [SV16: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
| ~ ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ( in @ SY357 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY356 )
| ( in @ SX4 @ SY357 ) ) ) ) )
| ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY359 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SY359 @ ( sK5_SY224 @ SV16 ) ) )
| ~ ~ ( in @ SY359 @ ( sK5_SY224 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1288]) ).
thf(1378,plain,
! [SV99: $i,SV17: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV17 ) @ SV99 )
| ( in @ SV17 @ SV99 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1379,plain,
! [SV99: $i,SV17: $i] :
( ( ~ ( ~ ( in @ SV17 @ SV99 )
| ( subset @ ( singleton @ SV17 ) @ SV99 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1380,plain,
! [SV148: $i,SV100: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV18 @ SV100 )
| ~ ( subset @ SV100 @ SV148 ) ) )
= $true )
| ( ( subset @ SV18 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1381,plain,
! [SV101: $i,SV19: $i] :
( ( ( subset @ ( singleton @ SV19 ) @ ( singleton @ SV101 ) )
= $false )
| ( ( SV19 = SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1382,plain,
! [SV20: $i,SV165: $i] :
( ( ( ~ ( net_str @ SV165 @ SV20 )
| ! [SY371: $i] :
( ~ ( net_str @ SY371 @ SV20 )
| ~ ( ~ ( ~ ( subnetstr @ SY371 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SY371 @ SV165 )
| ( ( the_mapping @ SV20 @ SY371 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SY371 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY371 @ SV165 )
| ( ( the_mapping @ SV20 @ SY371 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SY371 ) ) ) )
| ( subnetstr @ SY371 @ SV20 @ SV165 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1383,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1384,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( empty_carrier @ SV21 )
| ( empty @ ( the_carrier @ SV21 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV21 ) )
| ( empty_carrier @ SV21 ) ) )
= $false )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1385,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
| ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1386,plain,
! [SV24: $i,SV103: $i] :
( ( ( relation @ SV103 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV24 @ SV103 ) ) @ ( relation_rng @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1387,plain,
! [SV25: $i,SV104: $i] :
( ( ( relation @ SV104 )
= $false )
| ( ( subset @ ( relation_image @ SV104 @ SV25 ) @ ( relation_rng @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1388,plain,
! [SV26: $i] :
( ( ~ ( epsilon_transitive @ SV26 )
| ! [SY241: $i] :
( ~ ( in @ SY241 @ SV26 )
| ( subset @ SY241 @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1389,plain,
! [SV26: $i] :
( ( ~ ! [SY242: $i] :
( ~ ( in @ SY242 @ SV26 )
| ( subset @ SY242 @ SV26 ) )
| ( epsilon_transitive @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1390,plain,
! [SV27: $i,SV166: $i] :
( ( ( ~ ( relation @ SV166 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV27 @ SV166 ) ) @ ( relation_rng @ SV166 ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1391,plain,
! [SV105: $i,SV28: $i] :
( ( ( ~ ( ~ ( one_sorted_str @ SV28 )
| ~ ( net_str @ SV105 @ SV28 ) ) )
= $false )
| ( ( ! [SY329: $i] :
( ~ ( subnetstr @ SY329 @ SV28 @ SV105 )
| ( net_str @ SY329 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1392,plain,
! [SV30: $i] :
( ( ( ~ ~ ( empty_carrier @ SV30 )
| ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1305]) ).
thf(1393,plain,
! [SV31: $i,SV106: $i] :
( ( ( relation @ SV106 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV106 @ SV31 ) ) @ ( relation_rng @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1394,plain,
! [SV107: $i,SV32: $i] :
( ( ( rel_str @ SV32 )
= $false )
| ( ( element @ ( meet_on_relstr @ SV32 @ SV107 ) @ ( the_carrier @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1395,plain,
! [SV150: $i,SV108: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV108 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV33 @ SV150 ) @ ( set_intersection2 @ SV108 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1396,plain,
! [SV151: $i,SV109: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV109 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV151 ) @ ( cartesian_product2 @ SV109 @ SV151 ) )
| ~ ( subset @ ( cartesian_product2 @ SV151 @ SV34 ) @ ( cartesian_product2 @ SV151 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1397,plain,
! [SV35: $i,SV110: $i] :
( ( ( relation @ SV110 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV110 @ SV35 ) @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1398,plain,
! [SV152: $i,SV111: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV36 @ SV111 )
| ~ ( subset @ SV152 @ SV111 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV36 @ SV152 ) @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1399,plain,
! [SV112: $i,SV38: $i,SV153: $i,SV167: $i] :
( ( ~ ( relation_of2_as_subset @ SV167 @ SV153 @ SV38 )
| ~ ( subset @ ( relation_rng @ SV167 ) @ SV112 )
| ( relation_of2_as_subset @ SV167 @ SV153 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1400,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( ~ ( ordinal @ SV39 )
| ~ ( ordinal @ SV113 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
| ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1401,plain,
! [SV114: $i,SV42: $i] :
( ( ( ~ ( ~ ( one_sorted_str @ SV42 )
| ~ ( net_str @ SV114 @ SV42 ) ) )
= $false )
| ( ( ~ ! [SY335: $i] :
~ ( subnetstr @ SY335 @ SV42 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1402,plain,
! [SV115: $i,SV43: $i] :
( ( ~ ( ~ ( proper_subset @ SV43 @ SV115 )
| ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1403,plain,
! [SV115: $i,SV43: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) )
| ( proper_subset @ SV43 @ SV115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1404,plain,
! [SV116: $i,SV44: $i] :
( ( ~ ( ~ ( subset @ SV44 @ SV116 )
| ! [SY336: $i] :
( ~ ( in @ SY336 @ SV44 )
| ( in @ SY336 @ SV116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1405,plain,
! [SV116: $i,SV44: $i] :
( ( ~ ( ~ ! [SY337: $i] :
( ~ ( in @ SY337 @ SV44 )
| ( in @ SY337 @ SV116 ) )
| ( subset @ SV44 @ SV116 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1406,plain,
! [SV117: $i,SV46: $i] :
( ( ( subset @ SV46 @ SV117 )
= $false )
| ( ( ( set_intersection2 @ SV46 @ SV117 )
= SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1407,plain,
! [SV118: $i,SV47: $i,SV154: $i] :
( ( ( ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( subset @ SV47 @ SV118 )
| ( subset @ ( relation_inverse_image @ SV154 @ SV47 ) @ ( relation_inverse_image @ SV154 @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1408,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
| ~ ( net_str @ SV119 @ SV48 ) )
| ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1409,plain,
! [SV156: $i,SV120: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV49 @ SV120 )
| ~ ( disjoint @ SV120 @ SV156 ) ) )
= $true )
| ( ( disjoint @ SV49 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1410,plain,
! [SV50: $i,SV168: $i] :
( ( ( ~ ( net_str @ SV168 @ SV50 )
| ( rel_str @ SV168 ) )
= $true )
| ( ( one_sorted_str @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1411,plain,
! [SV51: $i] :
( ( ( ~ ~ ( empty_carrier @ SV51 )
| ~ ( one_sorted_str @ SV51 ) )
= $true )
| ( ( ! [SY273: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SY273 )
| ~ ( net_str @ SY273 @ SV51 ) )
| ! [SY274: $i,SY275: $i] :
( ~ ( subset @ SY274 @ SY275 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SY273 @ SY274 )
| ( is_eventually_in @ SV51 @ SY273 @ SY275 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SY273 @ SY274 )
| ( is_often_in @ SV51 @ SY273 @ SY275 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1412,plain,
! [SV52: $i,SV121: $i] :
( ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( ! [SY341: $i] :
( ~ ( element @ SY341 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SY341 )
| ( subset @ SV121 @ SY341 ) )
| ~ ( ~ ( subset @ SV121 @ SY341 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SY341 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1413,plain,
! [SV53: $i,SV122: $i] :
( ( ( relation @ SV122 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ ( relation_field @ SV122 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1414,plain,
! [SV123: $i,SV54: $i,SV157: $i,SV169: $i] :
( ( ~ ( relation_of2_as_subset @ SV169 @ SV157 @ SV54 )
| ~ ( subset @ SV54 @ SV123 )
| ( relation_of2_as_subset @ SV169 @ SV157 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1415,plain,
! [SV55: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY364: $i] :
( ~ ( in @ SY364 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SY364 ) @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY365 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SY365 @ ( sK6_SY282 @ SV55 ) ) )
| ~ ~ ( in @ SY365 @ ( sK6_SY282 @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1416,plain,
! [SV56: $i] :
( ( ( ! [SY287: $i] :
~ ( net_str @ SY287 @ SV56 ) )
= $false )
| ( ( one_sorted_str @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1417,plain,
! [SV124: $i,SV59: $i] :
( ( ~ ( ~ ( subset @ SV59 @ ( singleton @ SV124 ) )
| ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1418,plain,
! [SV124: $i,SV59: $i] :
( ( ~ ( ~ ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
| ( subset @ SV59 @ ( singleton @ SV124 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1419,plain,
! [SV60: $i,SV125: $i] :
( ( ( relation @ SV125 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV60 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1420,plain,
! [SV126: $i,SV61: $i] :
( ( ~ ( ~ ( element @ SV61 @ ( powerset @ SV126 ) )
| ( subset @ SV61 @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1421,plain,
! [SV126: $i,SV61: $i] :
( ( ~ ( ~ ( subset @ SV61 @ SV126 )
| ( element @ SV61 @ ( powerset @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1422,plain,
! [SV62: $i,SV127: $i] :
( ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( ! [SY344: $i] :
( ~ ( element @ SY344 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SY344 )
| ( subset @ SV127 @ SY344 ) )
| ~ ( ~ ( subset @ SV127 @ SY344 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SY344 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1423,plain,
! [SV63: $i,SV128: $i] :
( ( ( relation @ SV128 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV128 @ SV63 ) @ ( relation_dom @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1424,plain,
! [SV129: $i,SV64: $i] :
( ( ( in @ SV64 @ SV129 )
= $false )
| ( ( subset @ SV64 @ ( union @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1425,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( rel_str @ SV170 )
| ~ ( ~ ( ~ ( subrelstr @ SV170 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SV170 @ SV65 ) ) ) )
= $true )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1426,plain,
! [SV130: $i,SV66: $i] :
( ( ( subset @ SV66 @ SV130 )
= $false )
| ( ( SV130
= ( set_union2 @ SV66 @ ( set_difference @ SV130 @ SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1427,plain,
! [SV171: $i,SV158: $i,SV131: $i,SV67: $i] :
( ( ~ ~ ( ~ ( subset @ SV67 @ SV131 )
| ~ ( subset @ SV158 @ SV171 ) )
| ( subset @ ( cartesian_product2 @ SV67 @ SV158 ) @ ( cartesian_product2 @ SV131 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1428,plain,
! [SV132: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV132 )
= $false )
| ( ( ( set_union2 @ SV68 @ SV132 )
= SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1429,plain,
! [SV69: $i] :
( ( ( ~ ( in @ ( sK8_SY301 @ SV69 ) @ SV69 )
| ~ ( ~ ( ordinal @ ( sK8_SY301 @ SV69 ) )
| ~ ( subset @ ( sK8_SY301 @ SV69 ) @ SV69 ) ) )
= $false )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1344]) ).
thf(1430,plain,
! [SV133: $i,SV70: $i] :
( ( ~ ( ~ ( subset @ SV70 @ ( singleton @ SV133 ) )
| ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1431,plain,
! [SV133: $i,SV70: $i] :
( ( ~ ( ~ ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
| ( subset @ SV70 @ ( singleton @ SV133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1432,plain,
! [SV134: $i,SV72: $i] :
( ( ( in @ SV72 @ SV134 )
= $false )
| ( ( subset @ SV72 @ ( union @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1433,plain,
! [SV73: $i,SV135: $i] :
( ( ~ ( ( SV135
!= ( powerset @ SV73 ) )
| ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV135 )
| ( subset @ SY347 @ SV73 ) )
| ~ ( ~ ( subset @ SY347 @ SV73 )
| ( in @ SY347 @ SV135 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1434,plain,
! [SV73: $i,SV135: $i] :
( ( ~ ( ~ ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV135 )
| ( subset @ SY348 @ SV73 ) )
| ~ ( ~ ( subset @ SY348 @ SV73 )
| ( in @ SY348 @ SV135 ) ) )
| ( SV135
= ( powerset @ SV73 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1435,plain,
! [SV136: $i,SV74: $i] :
( ( ( rel_str @ SV74 )
= $false )
| ( ( element @ ( join_on_relstr @ SV74 @ SV136 ) @ ( the_carrier @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1436,plain,
! [SV75: $i,SV172: $i] :
( ( ( ~ ( relation @ SV172 )
| ~ ( subset @ SV75 @ SV172 )
| ~ ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SV172 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SV172 ) ) ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1437,plain,
! [SV137: $i,SV76: $i] :
( ( ~ ( subset @ SV76 @ SV137 )
| ~ ( proper_subset @ SV137 @ SV76 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1438,plain,
! [SV138: $i,SV77: $i] :
( ( ~ ( ( SV77 != SV138 )
| ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1439,plain,
! [SV138: $i,SV77: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) )
| ( SV77 = SV138 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1440,plain,
! [SV159: $i,SV139: $i,SV78: $i] :
( ( ( ~ ( subset @ SV78 @ SV139 ) )
= $true )
| ( ( ( in @ SV159 @ SV78 )
| ( subset @ SV78 @ ( set_difference @ SV139 @ ( singleton @ SV159 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1441,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ~ ( ~ ( relation_of2 @ SV160 @ SV80 @ SV140 )
| ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) ) )
| ~ ( ~ ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) )
| ( relation_of2 @ SV160 @ SV80 @ SV140 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1442,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV81 ) @ SV141 )
| ( in @ SV81 @ SV141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1443,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ~ ( in @ SV81 @ SV141 )
| ( subset @ ( singleton @ SV81 ) @ SV141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1444,plain,
! [SV161: $i,SV142: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV82 @ SV142 )
| ~ ( subset @ SV82 @ SV161 ) ) )
= $true )
| ( ( subset @ SV82 @ ( set_intersection2 @ SV142 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1445,plain,
! [SV83: $i,SV173: $i] :
( ( ( ~ ( relation @ SV173 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV83 @ SV173 ) ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1446,plain,
! [SV84: $i,SV143: $i] :
( ( ( relation @ SV143 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV84 @ SV143 ) ) @ ( relation_dom @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1447,plain,
! [SV162: $i,SV144: $i,SV85: $i] :
( ( ( ~ ( subset @ SV85 @ SV144 ) )
= $true )
| ( ( subset @ ( set_difference @ SV85 @ SV162 ) @ ( set_difference @ SV144 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1448,plain,
! [SV145: $i,SV86: $i,SV163: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV163 @ SV86 @ SV145 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV163 ) @ SV86 )
| ~ ( subset @ ( relation_rng @ SV163 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1449,plain,
! [SV87: $i] :
( ( ( the_carrier @ ( incl_POSet @ SV87 ) )
= SV87 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1450,plain,
! [SV87: $i] :
( ( ( the_InternalRel @ ( incl_POSet @ SV87 ) )
= ( inclusion_order @ SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1451,plain,
! [SV93: $i,SV6: $i] :
( ( ( ( set_difference @ SV6 @ SV93 )
!= empty_set )
| ( subset @ SV6 @ SV93 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1452,plain,
! [SV93: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV93 )
| ( ( set_difference @ SV6 @ SV93 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1453,plain,
! [SV146: $i,SV94: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
| ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1454,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) )
| ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1455,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty_carrier @ SV9 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1456,plain,
! [SV96: $i,SV10: $i,SV147: $i] :
( ( ( relation @ SV147 )
= $false )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV147 @ SV10 ) @ SV96 ) @ ( fiber @ SV147 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1457,plain,
! [SV97: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV97 )
| ~ ( finite @ SV97 ) )
= $true )
| ( ( finite @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1458,plain,
( ( ~ ( subnetstr @ sK7_SY326 @ sK1_A @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1373]) ).
thf(1459,plain,
( ( subset @ ( the_carrier @ sK7_SY326 ) @ ( the_carrier @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1373]) ).
thf(1460,plain,
! [SV12: $i,SV164: $i] :
( ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV12 @ SV164 )
| ! [SY367: $i,SY368: $i] :
( ~ ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV12 )
| ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV164 ) ) )
| ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV12 )
| ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV164 ) )
| ( subset @ SV12 @ SV164 ) ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1461,plain,
! [SV98: $i,SV15: $i] :
( ( ( ( set_difference @ SV15 @ SV98 )
!= empty_set )
| ( subset @ SV15 @ SV98 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1462,plain,
! [SV98: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV98 )
| ( ( set_difference @ SV15 @ SV98 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1463,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
| ~ ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ( in @ SY357 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY356 )
| ( in @ SX4 @ SY357 ) ) ) ) )
| ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY359 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SY359 @ ( sK5_SY224 @ SV16 ) ) )
| ~ ~ ( in @ SY359 @ ( sK5_SY224 @ SV16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1464,plain,
! [SV99: $i,SV17: $i] :
( ( ~ ( subset @ ( singleton @ SV17 ) @ SV99 )
| ( in @ SV17 @ SV99 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1465,plain,
! [SV99: $i,SV17: $i] :
( ( ~ ( in @ SV17 @ SV99 )
| ( subset @ ( singleton @ SV17 ) @ SV99 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1466,plain,
! [SV148: $i,SV100: $i,SV18: $i] :
( ( ( ~ ( ~ ( subset @ SV18 @ SV100 )
| ~ ( subset @ SV100 @ SV148 ) ) )
= $false )
| ( ( subset @ SV18 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1467,plain,
! [SV20: $i,SV165: $i] :
( ( ( ~ ( net_str @ SV165 @ SV20 ) )
= $true )
| ( ( ! [SY371: $i] :
( ~ ( net_str @ SY371 @ SV20 )
| ~ ( ~ ( ~ ( subnetstr @ SY371 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SY371 @ SV165 )
| ( ( the_mapping @ SV20 @ SY371 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SY371 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY371 @ SV165 )
| ( ( the_mapping @ SV20 @ SY371 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SY371 ) ) ) )
| ( subnetstr @ SY371 @ SV20 @ SV165 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1468,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1469,plain,
( ( ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1470,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( empty_carrier @ SV21 )
| ( empty @ ( the_carrier @ SV21 ) ) ) )
= $false )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1471,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( empty @ ( the_carrier @ SV21 ) )
| ( empty_carrier @ SV21 ) ) )
= $false )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1472,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
| ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) ) )
= $false )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1473,plain,
! [SV26: $i] :
( ( ( ~ ( epsilon_transitive @ SV26 ) )
= $true )
| ( ( ! [SY241: $i] :
( ~ ( in @ SY241 @ SV26 )
| ( subset @ SY241 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1474,plain,
! [SV26: $i] :
( ( ( ~ ! [SY242: $i] :
( ~ ( in @ SY242 @ SV26 )
| ( subset @ SY242 @ SV26 ) ) )
= $true )
| ( ( epsilon_transitive @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1475,plain,
! [SV27: $i,SV166: $i] :
( ( ( ~ ( relation @ SV166 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV27 @ SV166 ) ) @ ( relation_rng @ SV166 ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1476,plain,
! [SV105: $i,SV28: $i] :
( ( ( ~ ( one_sorted_str @ SV28 )
| ~ ( net_str @ SV105 @ SV28 ) )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( subnetstr @ SY329 @ SV28 @ SV105 )
| ( net_str @ SY329 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1391]) ).
thf(1477,plain,
! [SV30: $i] :
( ( ( ~ ~ ( empty_carrier @ SV30 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1478,plain,
! [SV150: $i,SV108: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV108 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV33 @ SV150 ) @ ( set_intersection2 @ SV108 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1479,plain,
! [SV151: $i,SV109: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV109 )
= $false )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV151 ) @ ( cartesian_product2 @ SV109 @ SV151 ) )
| ~ ( subset @ ( cartesian_product2 @ SV151 @ SV34 ) @ ( cartesian_product2 @ SV151 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1480,plain,
! [SV152: $i,SV111: $i,SV36: $i] :
( ( ( ~ ( ~ ( subset @ SV36 @ SV111 )
| ~ ( subset @ SV152 @ SV111 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV36 @ SV152 ) @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1481,plain,
! [SV112: $i,SV38: $i,SV153: $i,SV167: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV167 @ SV153 @ SV38 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV167 ) @ SV112 )
| ( relation_of2_as_subset @ SV167 @ SV153 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1482,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( ordinal @ SV39 )
| ~ ( ordinal @ SV113 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
| ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1483,plain,
! [SV114: $i,SV42: $i] :
( ( ( ~ ( one_sorted_str @ SV42 )
| ~ ( net_str @ SV114 @ SV42 ) )
= $true )
| ( ( ~ ! [SY335: $i] :
~ ( subnetstr @ SY335 @ SV42 @ SV114 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1484,plain,
! [SV115: $i,SV43: $i] :
( ( ~ ( proper_subset @ SV43 @ SV115 )
| ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1485,plain,
! [SV115: $i,SV43: $i] :
( ( ~ ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) )
| ( proper_subset @ SV43 @ SV115 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1486,plain,
! [SV116: $i,SV44: $i] :
( ( ~ ( subset @ SV44 @ SV116 )
| ! [SY336: $i] :
( ~ ( in @ SY336 @ SV44 )
| ( in @ SY336 @ SV116 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1487,plain,
! [SV116: $i,SV44: $i] :
( ( ~ ! [SY337: $i] :
( ~ ( in @ SY337 @ SV44 )
| ( in @ SY337 @ SV116 ) )
| ( subset @ SV44 @ SV116 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1488,plain,
! [SV118: $i,SV47: $i,SV154: $i] :
( ( ( relation @ SV154 )
= $false )
| ( ( ~ ( subset @ SV47 @ SV118 )
| ( subset @ ( relation_inverse_image @ SV154 @ SV47 ) @ ( relation_inverse_image @ SV154 @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1489,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
| ~ ( net_str @ SV119 @ SV48 ) )
| ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) ) )
= $false )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1490,plain,
! [SV156: $i,SV120: $i,SV49: $i] :
( ( ( ~ ( ~ ( subset @ SV49 @ SV120 )
| ~ ( disjoint @ SV120 @ SV156 ) ) )
= $false )
| ( ( disjoint @ SV49 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1491,plain,
! [SV50: $i,SV168: $i] :
( ( ( ~ ( net_str @ SV168 @ SV50 ) )
= $true )
| ( ( rel_str @ SV168 )
= $true )
| ( ( one_sorted_str @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1492,plain,
! [SV51: $i] :
( ( ( ~ ~ ( empty_carrier @ SV51 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV51 ) )
= $true )
| ( ( ! [SY273: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SY273 )
| ~ ( net_str @ SY273 @ SV51 ) )
| ! [SY274: $i,SY275: $i] :
( ~ ( subset @ SY274 @ SY275 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SY273 @ SY274 )
| ( is_eventually_in @ SV51 @ SY273 @ SY275 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SY273 @ SY274 )
| ( is_often_in @ SV51 @ SY273 @ SY275 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1493,plain,
! [SV121: $i,SV52: $i,SV174: $i] :
( ( ( ~ ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
| ( subset @ SV121 @ SV174 ) )
| ~ ( ~ ( subset @ SV121 @ SV174 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 ) ) ) )
= $true )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1494,plain,
! [SV53: $i,SV122: $i] :
( ( ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ ( relation_field @ SV122 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ SV53 ) )
= $false )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1495,plain,
! [SV123: $i,SV54: $i,SV157: $i,SV169: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV169 @ SV157 @ SV54 ) )
= $true )
| ( ( ~ ( subset @ SV54 @ SV123 )
| ( relation_of2_as_subset @ SV169 @ SV157 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1496,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY364: $i] :
( ~ ( in @ SY364 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SY364 ) @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY365 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SY365 @ ( sK6_SY282 @ SV55 ) ) )
| ~ ~ ( in @ SY365 @ ( sK6_SY282 @ SV55 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1497,plain,
! [SV56: $i] :
( ( ( ~ ( net_str @ ( sK9_SY287 @ SV56 ) @ SV56 ) )
= $false )
| ( ( one_sorted_str @ SV56 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1416]) ).
thf(1498,plain,
! [SV124: $i,SV59: $i] :
( ( ~ ( subset @ SV59 @ ( singleton @ SV124 ) )
| ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1499,plain,
! [SV124: $i,SV59: $i] :
( ( ~ ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
| ( subset @ SV59 @ ( singleton @ SV124 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1500,plain,
! [SV126: $i,SV61: $i] :
( ( ~ ( element @ SV61 @ ( powerset @ SV126 ) )
| ( subset @ SV61 @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1501,plain,
! [SV126: $i,SV61: $i] :
( ( ~ ( subset @ SV61 @ SV126 )
| ( element @ SV61 @ ( powerset @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1502,plain,
! [SV127: $i,SV62: $i,SV175: $i] :
( ( ( ~ ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
| ( subset @ SV127 @ SV175 ) )
| ~ ( ~ ( subset @ SV127 @ SV175 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 ) ) ) )
= $true )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1503,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( rel_str @ SV170 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subrelstr @ SV170 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SV170 @ SV65 ) ) ) )
= $true )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1504,plain,
! [SV171: $i,SV158: $i,SV131: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV67 @ SV131 )
| ~ ( subset @ SV158 @ SV171 ) ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV67 @ SV158 ) @ ( cartesian_product2 @ SV131 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1505,plain,
! [SV69: $i] :
( ( ( ~ ( in @ ( sK8_SY301 @ SV69 ) @ SV69 ) )
= $false )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1506,plain,
! [SV69: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK8_SY301 @ SV69 ) )
| ~ ( subset @ ( sK8_SY301 @ SV69 ) @ SV69 ) ) )
= $false )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1507,plain,
! [SV133: $i,SV70: $i] :
( ( ~ ( subset @ SV70 @ ( singleton @ SV133 ) )
| ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1508,plain,
! [SV133: $i,SV70: $i] :
( ( ~ ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
| ( subset @ SV70 @ ( singleton @ SV133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1509,plain,
! [SV73: $i,SV135: $i] :
( ( ( SV135
!= ( powerset @ SV73 ) )
| ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV135 )
| ( subset @ SY347 @ SV73 ) )
| ~ ( ~ ( subset @ SY347 @ SV73 )
| ( in @ SY347 @ SV135 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1510,plain,
! [SV73: $i,SV135: $i] :
( ( ~ ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV135 )
| ( subset @ SY348 @ SV73 ) )
| ~ ( ~ ( subset @ SY348 @ SV73 )
| ( in @ SY348 @ SV135 ) ) )
| ( SV135
= ( powerset @ SV73 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1511,plain,
! [SV75: $i,SV172: $i] :
( ( ( ~ ( relation @ SV172 ) )
= $true )
| ( ( ~ ( subset @ SV75 @ SV172 )
| ~ ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SV172 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SV172 ) ) ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1512,plain,
! [SV137: $i,SV76: $i] :
( ( ( ~ ( subset @ SV76 @ SV137 ) )
= $true )
| ( ( ~ ( proper_subset @ SV137 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1513,plain,
! [SV138: $i,SV77: $i] :
( ( ( SV77 != SV138 )
| ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1514,plain,
! [SV138: $i,SV77: $i] :
( ( ~ ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) )
| ( SV77 = SV138 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1515,plain,
! [SV159: $i,SV139: $i,SV78: $i] :
( ( ( subset @ SV78 @ SV139 )
= $false )
| ( ( ( in @ SV159 @ SV78 )
| ( subset @ SV78 @ ( set_difference @ SV139 @ ( singleton @ SV159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1516,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ~ ( ~ ( relation_of2 @ SV160 @ SV80 @ SV140 )
| ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1517,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ~ ( ~ ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) )
| ( relation_of2 @ SV160 @ SV80 @ SV140 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1518,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( subset @ ( singleton @ SV81 ) @ SV141 )
| ( in @ SV81 @ SV141 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1442]) ).
thf(1519,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( in @ SV81 @ SV141 )
| ( subset @ ( singleton @ SV81 ) @ SV141 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1520,plain,
! [SV161: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( ~ ( subset @ SV82 @ SV142 )
| ~ ( subset @ SV82 @ SV161 ) ) )
= $false )
| ( ( subset @ SV82 @ ( set_intersection2 @ SV142 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1521,plain,
! [SV83: $i,SV173: $i] :
( ( ( ~ ( relation @ SV173 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV83 @ SV173 ) ) @ ( relation_dom @ SV83 ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1522,plain,
! [SV162: $i,SV144: $i,SV85: $i] :
( ( ( subset @ SV85 @ SV144 )
= $false )
| ( ( subset @ ( set_difference @ SV85 @ SV162 ) @ ( set_difference @ SV144 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1523,plain,
! [SV145: $i,SV86: $i,SV163: $i] :
( ( ( relation_of2_as_subset @ SV163 @ SV86 @ SV145 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV163 ) @ SV86 )
| ~ ( subset @ ( relation_rng @ SV163 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1524,plain,
! [SV93: $i,SV6: $i] :
( ( ( ( set_difference @ SV6 @ SV93 )
!= empty_set )
= $true )
| ( ( subset @ SV6 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1525,plain,
! [SV93: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV93 ) )
= $true )
| ( ( ( set_difference @ SV6 @ SV93 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1452]) ).
thf(1526,plain,
! [SV146: $i,SV94: $i,SV7: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
| ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1527,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ~ ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) )
| ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1528,plain,
! [SV9: $i] :
( ( ( ~ ( empty_carrier @ SV9 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1529,plain,
! [SV97: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV97 ) )
= $true )
| ( ( ~ ( finite @ SV97 ) )
= $true )
| ( ( finite @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1530,plain,
( ( subnetstr @ sK7_SY326 @ sK1_A @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1458]) ).
thf(1531,plain,
! [SV12: $i,SV164: $i] :
( ( ( relation @ SV164 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV12 @ SV164 )
| ! [SY367: $i,SY368: $i] :
( ~ ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV12 )
| ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV164 ) ) )
| ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV12 )
| ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV164 ) )
| ( subset @ SV12 @ SV164 ) ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1532,plain,
! [SV98: $i,SV15: $i] :
( ( ( ( set_difference @ SV15 @ SV98 )
!= empty_set )
= $true )
| ( ( subset @ SV15 @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1533,plain,
! [SV98: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV98 ) )
= $true )
| ( ( ( set_difference @ SV15 @ SV98 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1534,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
| ~ ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ( in @ SY357 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY356 )
| ( in @ SX4 @ SY357 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1535,plain,
! [SV16: $i] :
( ( ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY359 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SY359 @ ( sK5_SY224 @ SV16 ) ) )
| ~ ~ ( in @ SY359 @ ( sK5_SY224 @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1536,plain,
! [SV99: $i,SV17: $i] :
( ( ( ~ ( subset @ ( singleton @ SV17 ) @ SV99 ) )
= $true )
| ( ( in @ SV17 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1537,plain,
! [SV99: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV99 ) )
= $true )
| ( ( subset @ ( singleton @ SV17 ) @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1538,plain,
! [SV148: $i,SV100: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV100 )
| ~ ( subset @ SV100 @ SV148 ) )
= $true )
| ( ( subset @ SV18 @ SV148 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1539,plain,
! [SV20: $i,SV165: $i] :
( ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( ! [SY371: $i] :
( ~ ( net_str @ SY371 @ SV20 )
| ~ ( ~ ( ~ ( subnetstr @ SY371 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SY371 @ SV165 )
| ( ( the_mapping @ SV20 @ SY371 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SY371 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY371 @ SV165 )
| ( ( the_mapping @ SV20 @ SY371 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SY371 ) ) ) )
| ( subnetstr @ SY371 @ SV20 @ SV165 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1540,plain,
( ( one_sorted_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1541,plain,
( ( ~ ( empty_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1542,plain,
! [SV21: $i] :
( ( ( ~ ( empty_carrier @ SV21 )
| ( empty @ ( the_carrier @ SV21 ) ) )
= $true )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1543,plain,
! [SV21: $i] :
( ( ( ~ ( empty @ ( the_carrier @ SV21 ) )
| ( empty_carrier @ SV21 ) )
= $true )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1544,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
| ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1472]) ).
thf(1545,plain,
! [SV26: $i] :
( ( ( epsilon_transitive @ SV26 )
= $false )
| ( ( ! [SY241: $i] :
( ~ ( in @ SY241 @ SV26 )
| ( subset @ SY241 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1546,plain,
! [SV26: $i] :
( ( ( ! [SY242: $i] :
( ~ ( in @ SY242 @ SV26 )
| ( subset @ SY242 @ SV26 ) ) )
= $false )
| ( ( epsilon_transitive @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1547,plain,
! [SV27: $i,SV166: $i] :
( ( ( relation @ SV166 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV27 @ SV166 ) ) @ ( relation_rng @ SV166 ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1548,plain,
! [SV105: $i,SV28: $i] :
( ( ( ~ ( one_sorted_str @ SV28 ) )
= $true )
| ( ( ~ ( net_str @ SV105 @ SV28 ) )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( subnetstr @ SY329 @ SV28 @ SV105 )
| ( net_str @ SY329 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1549,plain,
! [SV30: $i] :
( ( ( ~ ( empty_carrier @ SV30 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1550,plain,
! [SV109: $i,SV151: $i,SV34: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV151 ) @ ( cartesian_product2 @ SV109 @ SV151 ) )
| ~ ( subset @ ( cartesian_product2 @ SV151 @ SV34 ) @ ( cartesian_product2 @ SV151 @ SV109 ) ) )
= $false )
| ( ( subset @ SV34 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1551,plain,
! [SV152: $i,SV111: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV111 )
| ~ ( subset @ SV152 @ SV111 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV36 @ SV152 ) @ SV111 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1552,plain,
! [SV112: $i,SV38: $i,SV153: $i,SV167: $i] :
( ( ( relation_of2_as_subset @ SV167 @ SV153 @ SV38 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV167 ) @ SV112 )
| ( relation_of2_as_subset @ SV167 @ SV153 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1553,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( ordinal @ SV39 ) )
= $true )
| ( ( ~ ( ordinal @ SV113 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
| ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1554,plain,
! [SV114: $i,SV42: $i] :
( ( ( ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( net_str @ SV114 @ SV42 ) )
= $true )
| ( ( ~ ! [SY335: $i] :
~ ( subnetstr @ SY335 @ SV42 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1483]) ).
thf(1555,plain,
! [SV115: $i,SV43: $i] :
( ( ( ~ ( proper_subset @ SV43 @ SV115 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1556,plain,
! [SV115: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) ) )
= $true )
| ( ( proper_subset @ SV43 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1557,plain,
! [SV116: $i,SV44: $i] :
( ( ( ~ ( subset @ SV44 @ SV116 ) )
= $true )
| ( ( ! [SY336: $i] :
( ~ ( in @ SY336 @ SV44 )
| ( in @ SY336 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1558,plain,
! [SV116: $i,SV44: $i] :
( ( ( ~ ! [SY337: $i] :
( ~ ( in @ SY337 @ SV44 )
| ( in @ SY337 @ SV116 ) ) )
= $true )
| ( ( subset @ SV44 @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1559,plain,
! [SV154: $i,SV118: $i,SV47: $i] :
( ( ( ~ ( subset @ SV47 @ SV118 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV154 @ SV47 ) @ ( relation_inverse_image @ SV154 @ SV118 ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1560,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
| ~ ( net_str @ SV119 @ SV48 ) )
| ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1489]) ).
thf(1561,plain,
! [SV156: $i,SV120: $i,SV49: $i] :
( ( ( ~ ( subset @ SV49 @ SV120 )
| ~ ( disjoint @ SV120 @ SV156 ) )
= $true )
| ( ( disjoint @ SV49 @ SV156 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1490]) ).
thf(1562,plain,
! [SV50: $i,SV168: $i] :
( ( ( net_str @ SV168 @ SV50 )
= $false )
| ( ( rel_str @ SV168 )
= $true )
| ( ( one_sorted_str @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1563,plain,
! [SV51: $i] :
( ( ( ~ ( empty_carrier @ SV51 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV51 ) )
= $true )
| ( ( ! [SY273: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SY273 )
| ~ ( net_str @ SY273 @ SV51 ) )
| ! [SY274: $i,SY275: $i] :
( ~ ( subset @ SY274 @ SY275 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SY273 @ SY274 )
| ( is_eventually_in @ SV51 @ SY273 @ SY275 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SY273 @ SY274 )
| ( is_often_in @ SV51 @ SY273 @ SY275 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1564,plain,
! [SV121: $i,SV52: $i,SV174: $i] :
( ( ( ~ ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
| ( subset @ SV121 @ SV174 ) )
| ~ ( ~ ( subset @ SV121 @ SV174 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 ) ) ) )
= $true )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1565,plain,
! [SV53: $i,SV122: $i] :
( ( ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ ( relation_field @ SV122 ) ) )
= $false )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1566,plain,
! [SV53: $i,SV122: $i] :
( ( ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ SV53 ) )
= $false )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1567,plain,
! [SV123: $i,SV54: $i,SV157: $i,SV169: $i] :
( ( ( relation_of2_as_subset @ SV169 @ SV157 @ SV54 )
= $false )
| ( ( ~ ( subset @ SV54 @ SV123 )
| ( relation_of2_as_subset @ SV169 @ SV157 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1568,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY364: $i] :
( ~ ( in @ SY364 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SY364 ) @ ( sK6_SY282 @ SV55 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1569,plain,
! [SV55: $i] :
( ( ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY365 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SY365 @ ( sK6_SY282 @ SV55 ) ) )
| ~ ~ ( in @ SY365 @ ( sK6_SY282 @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1570,plain,
! [SV56: $i] :
( ( ( net_str @ ( sK9_SY287 @ SV56 ) @ SV56 )
= $true )
| ( ( one_sorted_str @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1571,plain,
! [SV124: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ ( singleton @ SV124 ) ) )
= $true )
| ( ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1572,plain,
! [SV124: $i,SV59: $i] :
( ( ( ~ ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) ) )
= $true )
| ( ( subset @ SV59 @ ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1573,plain,
! [SV126: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ ( powerset @ SV126 ) ) )
= $true )
| ( ( subset @ SV61 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1574,plain,
! [SV126: $i,SV61: $i] :
( ( ( ~ ( subset @ SV61 @ SV126 ) )
= $true )
| ( ( element @ SV61 @ ( powerset @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1575,plain,
! [SV127: $i,SV62: $i,SV175: $i] :
( ( ( ~ ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
| ( subset @ SV127 @ SV175 ) )
| ~ ( ~ ( subset @ SV127 @ SV175 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 ) ) ) )
= $true )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1576,plain,
! [SV65: $i,SV170: $i] :
( ( ( rel_str @ SV170 )
= $false )
| ( ( ~ ( ~ ( ~ ( subrelstr @ SV170 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SV170 @ SV65 ) ) ) )
= $true )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1577,plain,
! [SV171: $i,SV158: $i,SV131: $i,SV67: $i] :
( ( ( ~ ( ~ ( subset @ SV67 @ SV131 )
| ~ ( subset @ SV158 @ SV171 ) ) )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV67 @ SV158 ) @ ( cartesian_product2 @ SV131 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1578,plain,
! [SV69: $i] :
( ( ( in @ ( sK8_SY301 @ SV69 ) @ SV69 )
= $true )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1579,plain,
! [SV69: $i] :
( ( ( ~ ( ordinal @ ( sK8_SY301 @ SV69 ) )
| ~ ( subset @ ( sK8_SY301 @ SV69 ) @ SV69 ) )
= $true )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1506]) ).
thf(1580,plain,
! [SV133: $i,SV70: $i] :
( ( ( ~ ( subset @ SV70 @ ( singleton @ SV133 ) ) )
= $true )
| ( ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1581,plain,
! [SV133: $i,SV70: $i] :
( ( ( ~ ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) ) )
= $true )
| ( ( subset @ SV70 @ ( singleton @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1582,plain,
! [SV73: $i,SV135: $i] :
( ( ( SV135
!= ( powerset @ SV73 ) )
= $true )
| ( ( ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV135 )
| ( subset @ SY347 @ SV73 ) )
| ~ ( ~ ( subset @ SY347 @ SV73 )
| ( in @ SY347 @ SV135 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1583,plain,
! [SV73: $i,SV135: $i] :
( ( ( ~ ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV135 )
| ( subset @ SY348 @ SV73 ) )
| ~ ( ~ ( subset @ SY348 @ SV73 )
| ( in @ SY348 @ SV135 ) ) ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1584,plain,
! [SV75: $i,SV172: $i] :
( ( ( relation @ SV172 )
= $false )
| ( ( ~ ( subset @ SV75 @ SV172 )
| ~ ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SV172 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SV172 ) ) ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1585,plain,
! [SV137: $i,SV76: $i] :
( ( ( subset @ SV76 @ SV137 )
= $false )
| ( ( ~ ( proper_subset @ SV137 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1586,plain,
! [SV138: $i,SV77: $i] :
( ( ( SV77 != SV138 )
= $true )
| ( ( ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1587,plain,
! [SV138: $i,SV77: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) ) )
= $true )
| ( ( SV77 = SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1514]) ).
thf(1588,plain,
! [SV139: $i,SV78: $i,SV159: $i] :
( ( ( in @ SV159 @ SV78 )
= $true )
| ( ( subset @ SV78 @ ( set_difference @ SV139 @ ( singleton @ SV159 ) ) )
= $true )
| ( ( subset @ SV78 @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1589,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ~ ( relation_of2 @ SV160 @ SV80 @ SV140 )
| ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1516]) ).
thf(1590,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ~ ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) )
| ( relation_of2 @ SV160 @ SV80 @ SV140 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1517]) ).
thf(1591,plain,
! [SV141: $i,SV81: $i] :
( ( ( ~ ( subset @ ( singleton @ SV81 ) @ SV141 ) )
= $true )
| ( ( in @ SV81 @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1592,plain,
! [SV141: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV141 ) )
= $true )
| ( ( subset @ ( singleton @ SV81 ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1593,plain,
! [SV161: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( subset @ SV82 @ SV142 )
| ~ ( subset @ SV82 @ SV161 ) )
= $true )
| ( ( subset @ SV82 @ ( set_intersection2 @ SV142 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1594,plain,
! [SV83: $i,SV173: $i] :
( ( ( relation @ SV173 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV83 @ SV173 ) ) @ ( relation_dom @ SV83 ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1595,plain,
! [SV145: $i,SV86: $i,SV163: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV163 ) @ SV86 )
| ~ ( subset @ ( relation_rng @ SV163 ) @ SV145 ) )
= $false )
| ( ( relation_of2_as_subset @ SV163 @ SV86 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1596,plain,
! [SV93: $i,SV6: $i] :
( ( ( ( set_difference @ SV6 @ SV93 )
= empty_set )
= $false )
| ( ( subset @ SV6 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1597,plain,
! [SV93: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV93 )
= $false )
| ( ( ( set_difference @ SV6 @ SV93 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1598,plain,
! [SV146: $i,SV94: $i,SV7: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1599,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1600,plain,
! [SV9: $i] :
( ( ( empty_carrier @ SV9 )
= $true )
| ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1601,plain,
! [SV97: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV97 )
= $false )
| ( ( ~ ( finite @ SV97 ) )
= $true )
| ( ( finite @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1602,plain,
! [SV164: $i,SV12: $i] :
( ( ( ~ ( ~ ( subset @ SV12 @ SV164 )
| ! [SY367: $i,SY368: $i] :
( ~ ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV12 )
| ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV164 ) ) )
| ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV12 )
| ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV164 ) )
| ( subset @ SV12 @ SV164 ) ) )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1603,plain,
! [SV98: $i,SV15: $i] :
( ( ( ( set_difference @ SV15 @ SV98 )
= empty_set )
= $false )
| ( ( subset @ SV15 @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1604,plain,
! [SV98: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV98 )
= $false )
| ( ( ( set_difference @ SV15 @ SV98 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1605,plain,
! [SV16: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
| ~ ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ( in @ SY357 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY356 )
| ( in @ SX4 @ SY357 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1606,plain,
! [SV16: $i] :
( ( ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY359 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SY359 @ ( sK5_SY224 @ SV16 ) ) )
| ~ ~ ( in @ SY359 @ ( sK5_SY224 @ SV16 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1607,plain,
! [SV99: $i,SV17: $i] :
( ( ( subset @ ( singleton @ SV17 ) @ SV99 )
= $false )
| ( ( in @ SV17 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1608,plain,
! [SV99: $i,SV17: $i] :
( ( ( in @ SV17 @ SV99 )
= $false )
| ( ( subset @ ( singleton @ SV17 ) @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1609,plain,
! [SV148: $i,SV100: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV100 ) )
= $true )
| ( ( ~ ( subset @ SV100 @ SV148 ) )
= $true )
| ( ( subset @ SV18 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1610,plain,
! [SV165: $i,SV20: $i,SV176: $i] :
( ( ( ~ ( net_str @ SV176 @ SV20 )
| ~ ( ~ ( ~ ( subnetstr @ SV176 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) )
| ( subnetstr @ SV176 @ SV20 @ SV165 ) ) ) )
= $true )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1611,plain,
( ( empty_carrier @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1612,plain,
! [SV21: $i] :
( ( ( ~ ( empty_carrier @ SV21 ) )
= $true )
| ( ( empty @ ( the_carrier @ SV21 ) )
= $true )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1613,plain,
! [SV21: $i] :
( ( ( ~ ( empty @ ( the_carrier @ SV21 ) ) )
= $true )
| ( ( empty_carrier @ SV21 )
= $true )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1614,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1615,plain,
! [SV26: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ SV26 )
| ( subset @ SV177 @ SV26 ) )
= $true )
| ( ( epsilon_transitive @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1616,plain,
! [SV26: $i] :
( ( ( ~ ( in @ ( sK10_SY242 @ SV26 ) @ SV26 )
| ( subset @ ( sK10_SY242 @ SV26 ) @ SV26 ) )
= $false )
| ( ( epsilon_transitive @ SV26 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1546]) ).
thf(1617,plain,
! [SV105: $i,SV28: $i] :
( ( ( one_sorted_str @ SV28 )
= $false )
| ( ( ~ ( net_str @ SV105 @ SV28 ) )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( subnetstr @ SY329 @ SV28 @ SV105 )
| ( net_str @ SY329 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1618,plain,
! [SV30: $i] :
( ( ( empty_carrier @ SV30 )
= $true )
| ( ( ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1619,plain,
! [SV109: $i,SV151: $i,SV34: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV151 ) @ ( cartesian_product2 @ SV109 @ SV151 ) ) )
= $false )
| ( ( subset @ SV34 @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1620,plain,
! [SV109: $i,SV34: $i,SV151: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV151 @ SV34 ) @ ( cartesian_product2 @ SV151 @ SV109 ) ) )
= $false )
| ( ( subset @ SV34 @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1621,plain,
! [SV152: $i,SV111: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV111 ) )
= $true )
| ( ( ~ ( subset @ SV152 @ SV111 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV36 @ SV152 ) @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1622,plain,
! [SV38: $i,SV153: $i,SV112: $i,SV167: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV167 ) @ SV112 ) )
= $true )
| ( ( relation_of2_as_subset @ SV167 @ SV153 @ SV112 )
= $true )
| ( ( relation_of2_as_subset @ SV167 @ SV153 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1552]) ).
thf(1623,plain,
! [SV113: $i,SV39: $i] :
( ( ( ordinal @ SV39 )
= $false )
| ( ( ~ ( ordinal @ SV113 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
| ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1624,plain,
! [SV114: $i,SV42: $i] :
( ( ( one_sorted_str @ SV42 )
= $false )
| ( ( ~ ( net_str @ SV114 @ SV42 ) )
= $true )
| ( ( ~ ! [SY335: $i] :
~ ( subnetstr @ SY335 @ SV42 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1625,plain,
! [SV115: $i,SV43: $i] :
( ( ( proper_subset @ SV43 @ SV115 )
= $false )
| ( ( ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1626,plain,
! [SV115: $i,SV43: $i] :
( ( ( ~ ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) ) )
= $false )
| ( ( proper_subset @ SV43 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1627,plain,
! [SV116: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV116 )
= $false )
| ( ( ! [SY336: $i] :
( ~ ( in @ SY336 @ SV44 )
| ( in @ SY336 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1628,plain,
! [SV116: $i,SV44: $i] :
( ( ( ! [SY337: $i] :
( ~ ( in @ SY337 @ SV44 )
| ( in @ SY337 @ SV116 ) ) )
= $false )
| ( ( subset @ SV44 @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1629,plain,
! [SV154: $i,SV118: $i,SV47: $i] :
( ( ( subset @ SV47 @ SV118 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV154 @ SV47 ) @ ( relation_inverse_image @ SV154 @ SV118 ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1630,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
| ~ ( net_str @ SV119 @ SV48 ) ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1631,plain,
! [SV156: $i,SV120: $i,SV49: $i] :
( ( ( ~ ( subset @ SV49 @ SV120 ) )
= $true )
| ( ( ~ ( disjoint @ SV120 @ SV156 ) )
= $true )
| ( ( disjoint @ SV49 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1632,plain,
! [SV51: $i] :
( ( ( empty_carrier @ SV51 )
= $true )
| ( ( ~ ( one_sorted_str @ SV51 ) )
= $true )
| ( ( ! [SY273: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SY273 )
| ~ ( net_str @ SY273 @ SV51 ) )
| ! [SY274: $i,SY275: $i] :
( ~ ( subset @ SY274 @ SY275 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SY273 @ SY274 )
| ( is_eventually_in @ SV51 @ SY273 @ SY275 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SY273 @ SY274 )
| ( is_often_in @ SV51 @ SY273 @ SY275 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1633,plain,
! [SV121: $i,SV52: $i,SV174: $i] :
( ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
| ( subset @ SV121 @ SV174 ) )
| ~ ( ~ ( subset @ SV121 @ SV174 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 ) ) ) )
= $true )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1634,plain,
! [SV53: $i,SV122: $i] :
( ( ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ ( relation_field @ SV122 ) )
= $true )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1635,plain,
! [SV53: $i,SV122: $i] :
( ( ( subset @ ( relation_field @ ( relation_restriction @ SV122 @ SV53 ) ) @ SV53 )
= $true )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1636,plain,
! [SV157: $i,SV169: $i,SV123: $i,SV54: $i] :
( ( ( ~ ( subset @ SV54 @ SV123 ) )
= $true )
| ( ( relation_of2_as_subset @ SV169 @ SV157 @ SV123 )
= $true )
| ( ( relation_of2_as_subset @ SV169 @ SV157 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1637,plain,
! [SV55: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY364: $i] :
( ~ ( in @ SY364 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SY364 ) @ ( sK6_SY282 @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1568]) ).
thf(1638,plain,
! [SV55: $i] :
( ( ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY365 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SY365 @ ( sK6_SY282 @ SV55 ) ) )
| ~ ~ ( in @ SY365 @ ( sK6_SY282 @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1639,plain,
! [SV124: $i,SV59: $i] :
( ( ( subset @ SV59 @ ( singleton @ SV124 ) )
= $false )
| ( ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1640,plain,
! [SV124: $i,SV59: $i] :
( ( ( ( SV59 = empty_set )
| ( SV59
= ( singleton @ SV124 ) ) )
= $false )
| ( ( subset @ SV59 @ ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1641,plain,
! [SV126: $i,SV61: $i] :
( ( ( element @ SV61 @ ( powerset @ SV126 ) )
= $false )
| ( ( subset @ SV61 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1642,plain,
! [SV126: $i,SV61: $i] :
( ( ( subset @ SV61 @ SV126 )
= $false )
| ( ( element @ SV61 @ ( powerset @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1643,plain,
! [SV127: $i,SV62: $i,SV175: $i] :
( ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
| ( subset @ SV127 @ SV175 ) )
| ~ ( ~ ( subset @ SV127 @ SV175 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 ) ) ) )
= $true )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1644,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV170 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SV170 @ SV65 ) ) )
= $false )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1645,plain,
! [SV171: $i,SV158: $i,SV131: $i,SV67: $i] :
( ( ( ~ ( subset @ SV67 @ SV131 )
| ~ ( subset @ SV158 @ SV171 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV67 @ SV158 ) @ ( cartesian_product2 @ SV131 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1646,plain,
! [SV69: $i] :
( ( ( ~ ( ordinal @ ( sK8_SY301 @ SV69 ) ) )
= $true )
| ( ( ~ ( subset @ ( sK8_SY301 @ SV69 ) @ SV69 ) )
= $true )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1647,plain,
! [SV133: $i,SV70: $i] :
( ( ( subset @ SV70 @ ( singleton @ SV133 ) )
= $false )
| ( ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1648,plain,
! [SV133: $i,SV70: $i] :
( ( ( ( SV70 = empty_set )
| ( SV70
= ( singleton @ SV133 ) ) )
= $false )
| ( ( subset @ SV70 @ ( singleton @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1649,plain,
! [SV73: $i,SV135: $i] :
( ( ( SV135
= ( powerset @ SV73 ) )
= $false )
| ( ( ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV135 )
| ( subset @ SY347 @ SV73 ) )
| ~ ( ~ ( subset @ SY347 @ SV73 )
| ( in @ SY347 @ SV135 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1650,plain,
! [SV73: $i,SV135: $i] :
( ( ( ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV135 )
| ( subset @ SY348 @ SV73 ) )
| ~ ( ~ ( subset @ SY348 @ SV73 )
| ( in @ SY348 @ SV135 ) ) ) )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1651,plain,
! [SV172: $i,SV75: $i] :
( ( ( ~ ( subset @ SV75 @ SV172 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SV172 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SV172 ) ) ) )
= $true )
| ( ( relation @ SV172 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1652,plain,
! [SV76: $i,SV137: $i] :
( ( ( proper_subset @ SV137 @ SV76 )
= $false )
| ( ( subset @ SV76 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1653,plain,
! [SV138: $i,SV77: $i] :
( ( ( SV77 = SV138 )
= $false )
| ( ( ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1654,plain,
! [SV138: $i,SV77: $i] :
( ( ( ~ ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) ) )
= $false )
| ( ( SV77 = SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1655,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ( ~ ( relation_of2 @ SV160 @ SV80 @ SV140 ) )
= $true )
| ( ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1656,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ( ~ ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) ) )
= $true )
| ( ( relation_of2 @ SV160 @ SV80 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1657,plain,
! [SV141: $i,SV81: $i] :
( ( ( subset @ ( singleton @ SV81 ) @ SV141 )
= $false )
| ( ( in @ SV81 @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1658,plain,
! [SV141: $i,SV81: $i] :
( ( ( in @ SV81 @ SV141 )
= $false )
| ( ( subset @ ( singleton @ SV81 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1659,plain,
! [SV161: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( subset @ SV82 @ SV142 ) )
= $true )
| ( ( ~ ( subset @ SV82 @ SV161 ) )
= $true )
| ( ( subset @ SV82 @ ( set_intersection2 @ SV142 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1660,plain,
! [SV145: $i,SV86: $i,SV163: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV163 ) @ SV86 ) )
= $false )
| ( ( relation_of2_as_subset @ SV163 @ SV86 @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1661,plain,
! [SV86: $i,SV145: $i,SV163: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV163 ) @ SV145 ) )
= $false )
| ( ( relation_of2_as_subset @ SV163 @ SV86 @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1662,plain,
! [SV146: $i,SV94: $i,SV7: $i] :
( ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1663,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1664,plain,
! [SV9: $i] :
( ( ( one_sorted_str @ SV9 )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1665,plain,
! [SV11: $i,SV97: $i] :
( ( ( finite @ SV97 )
= $false )
| ( ( subset @ SV11 @ SV97 )
= $false )
| ( ( finite @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1666,plain,
! [SV164: $i,SV12: $i] :
( ( ( ~ ( ~ ( subset @ SV12 @ SV164 )
| ! [SY367: $i,SY368: $i] :
( ~ ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV12 )
| ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV164 ) ) ) )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1667,plain,
! [SV164: $i,SV12: $i] :
( ( ( ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV12 )
| ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV164 ) )
| ( subset @ SV12 @ SV164 ) ) )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1668,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
| ~ ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ( in @ SY357 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY356 )
| ( in @ SX4 @ SY357 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1669,plain,
! [SV16: $i,SV178: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
| ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1670,plain,
! [SV148: $i,SV100: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV100 )
= $false )
| ( ( ~ ( subset @ SV100 @ SV148 ) )
= $true )
| ( ( subset @ SV18 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1671,plain,
! [SV165: $i,SV20: $i,SV176: $i] :
( ( ( ~ ( net_str @ SV176 @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subnetstr @ SV176 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) )
| ( subnetstr @ SV176 @ SV20 @ SV165 ) ) ) )
= $true )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1610]) ).
thf(1672,plain,
! [SV21: $i] :
( ( ( empty_carrier @ SV21 )
= $false )
| ( ( empty @ ( the_carrier @ SV21 ) )
= $true )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1673,plain,
! [SV21: $i] :
( ( ( empty @ ( the_carrier @ SV21 ) )
= $false )
| ( ( empty_carrier @ SV21 )
= $true )
| ( ( one_sorted_str @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1674,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) ) )
= $false )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1675,plain,
! [SV26: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ SV26 ) )
= $true )
| ( ( subset @ SV177 @ SV26 )
= $true )
| ( ( epsilon_transitive @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1676,plain,
! [SV26: $i] :
( ( ( ~ ( in @ ( sK10_SY242 @ SV26 ) @ SV26 ) )
= $false )
| ( ( epsilon_transitive @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1616]) ).
thf(1677,plain,
! [SV26: $i] :
( ( ( subset @ ( sK10_SY242 @ SV26 ) @ SV26 )
= $false )
| ( ( epsilon_transitive @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1616]) ).
thf(1678,plain,
! [SV28: $i,SV105: $i] :
( ( ( net_str @ SV105 @ SV28 )
= $false )
| ( ( one_sorted_str @ SV28 )
= $false )
| ( ( ! [SY329: $i] :
( ~ ( subnetstr @ SY329 @ SV28 @ SV105 )
| ( net_str @ SY329 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1679,plain,
! [SV30: $i] :
( ( ( one_sorted_str @ SV30 )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1680,plain,
! [SV109: $i,SV151: $i,SV34: $i] :
( ( ( subset @ ( cartesian_product2 @ SV34 @ SV151 ) @ ( cartesian_product2 @ SV109 @ SV151 ) )
= $true )
| ( ( subset @ SV34 @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1681,plain,
! [SV109: $i,SV34: $i,SV151: $i] :
( ( ( subset @ ( cartesian_product2 @ SV151 @ SV34 ) @ ( cartesian_product2 @ SV151 @ SV109 ) )
= $true )
| ( ( subset @ SV34 @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1682,plain,
! [SV152: $i,SV111: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV111 )
= $false )
| ( ( ~ ( subset @ SV152 @ SV111 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV36 @ SV152 ) @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1683,plain,
! [SV38: $i,SV153: $i,SV112: $i,SV167: $i] :
( ( ( subset @ ( relation_rng @ SV167 ) @ SV112 )
= $false )
| ( ( relation_of2_as_subset @ SV167 @ SV153 @ SV112 )
= $true )
| ( ( relation_of2_as_subset @ SV167 @ SV153 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1684,plain,
! [SV39: $i,SV113: $i] :
( ( ( ordinal @ SV113 )
= $false )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
| ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1685,plain,
! [SV42: $i,SV114: $i] :
( ( ( net_str @ SV114 @ SV42 )
= $false )
| ( ( one_sorted_str @ SV42 )
= $false )
| ( ( ~ ! [SY335: $i] :
~ ( subnetstr @ SY335 @ SV42 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1686,plain,
! [SV115: $i,SV43: $i] :
( ( ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) )
= $false )
| ( ( proper_subset @ SV43 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1687,plain,
! [SV115: $i,SV43: $i] :
( ( ( ~ ( subset @ SV43 @ SV115 )
| ~ ( ( SV43 != SV115 ) ) )
= $true )
| ( ( proper_subset @ SV43 @ SV115 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1688,plain,
! [SV116: $i,SV44: $i,SV179: $i] :
( ( ( ~ ( in @ SV179 @ SV44 )
| ( in @ SV179 @ SV116 ) )
= $true )
| ( ( subset @ SV44 @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1689,plain,
! [SV44: $i,SV116: $i] :
( ( ( ~ ( in @ ( sK11_SY337 @ SV116 @ SV44 ) @ SV44 )
| ( in @ ( sK11_SY337 @ SV116 @ SV44 ) @ SV116 ) )
= $false )
| ( ( subset @ SV44 @ SV116 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1628]) ).
thf(1690,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
| ~ ( net_str @ SV119 @ SV48 ) ) )
= $false )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1691,plain,
! [SV156: $i,SV120: $i,SV49: $i] :
( ( ( subset @ SV49 @ SV120 )
= $false )
| ( ( ~ ( disjoint @ SV120 @ SV156 ) )
= $true )
| ( ( disjoint @ SV49 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1692,plain,
! [SV51: $i] :
( ( ( one_sorted_str @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( ! [SY273: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SY273 )
| ~ ( net_str @ SY273 @ SV51 ) )
| ! [SY274: $i,SY275: $i] :
( ~ ( subset @ SY274 @ SY275 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SY273 @ SY274 )
| ( is_eventually_in @ SV51 @ SY273 @ SY275 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SY273 @ SY274 )
| ( is_often_in @ SV51 @ SY273 @ SY275 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1693,plain,
! [SV174: $i,SV121: $i,SV52: $i] :
( ( ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
| ( subset @ SV121 @ SV174 ) )
| ~ ( ~ ( subset @ SV121 @ SV174 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 ) ) )
= $false )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1694,plain,
! [SV157: $i,SV169: $i,SV123: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV123 )
= $false )
| ( ( relation_of2_as_subset @ SV169 @ SV157 @ SV123 )
= $true )
| ( ( relation_of2_as_subset @ SV169 @ SV157 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1695,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
| ~ ! [SY364: $i] :
( ~ ( in @ SY364 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SY364 ) @ ( sK6_SY282 @ SV55 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1696,plain,
! [SV55: $i,SV180: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
| ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1697,plain,
! [SV124: $i,SV59: $i] :
( ( ( SV59 = empty_set )
= $true )
| ( ( SV59
= ( singleton @ SV124 ) )
= $true )
| ( ( subset @ SV59 @ ( singleton @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1698,plain,
! [SV124: $i,SV59: $i] :
( ( ( SV59 = empty_set )
= $false )
| ( ( subset @ SV59 @ ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1699,plain,
! [SV124: $i,SV59: $i] :
( ( ( SV59
= ( singleton @ SV124 ) )
= $false )
| ( ( subset @ SV59 @ ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1700,plain,
! [SV175: $i,SV127: $i,SV62: $i] :
( ( ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
| ( subset @ SV127 @ SV175 ) )
| ~ ( ~ ( subset @ SV127 @ SV175 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 ) ) )
= $false )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1701,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV170 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) ) )
= $false )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1702,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SV170 @ SV65 ) ) )
= $false )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1703,plain,
! [SV171: $i,SV158: $i,SV131: $i,SV67: $i] :
( ( ( ~ ( subset @ SV67 @ SV131 ) )
= $true )
| ( ( ~ ( subset @ SV158 @ SV171 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV67 @ SV158 ) @ ( cartesian_product2 @ SV131 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1704,plain,
! [SV69: $i] :
( ( ( ordinal @ ( sK8_SY301 @ SV69 ) )
= $false )
| ( ( ~ ( subset @ ( sK8_SY301 @ SV69 ) @ SV69 ) )
= $true )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1705,plain,
! [SV133: $i,SV70: $i] :
( ( ( SV70 = empty_set )
= $true )
| ( ( SV70
= ( singleton @ SV133 ) )
= $true )
| ( ( subset @ SV70 @ ( singleton @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1706,plain,
! [SV133: $i,SV70: $i] :
( ( ( SV70 = empty_set )
= $false )
| ( ( subset @ SV70 @ ( singleton @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1648]) ).
thf(1707,plain,
! [SV133: $i,SV70: $i] :
( ( ( SV70
= ( singleton @ SV133 ) )
= $false )
| ( ( subset @ SV70 @ ( singleton @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1648]) ).
thf(1708,plain,
! [SV73: $i,SV135: $i,SV181: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV181 @ SV135 )
| ( subset @ SV181 @ SV73 ) )
| ~ ( ~ ( subset @ SV181 @ SV73 )
| ( in @ SV181 @ SV135 ) ) ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1709,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
| ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 ) )
| ~ ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) ) ) )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1650]) ).
thf(1710,plain,
! [SV172: $i,SV75: $i] :
( ( ( subset @ SV75 @ SV172 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SV172 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SV172 ) ) ) )
= $true )
| ( ( relation @ SV172 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1711,plain,
! [SV138: $i,SV77: $i] :
( ( ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) )
= $false )
| ( ( SV77 = SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1712,plain,
! [SV138: $i,SV77: $i] :
( ( ( ~ ( subset @ SV77 @ SV138 )
| ~ ( subset @ SV138 @ SV77 ) )
= $true )
| ( ( SV77 = SV138 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1713,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ( relation_of2 @ SV160 @ SV80 @ SV140 )
= $false )
| ( ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1714,plain,
! [SV140: $i,SV80: $i,SV160: $i] :
( ( ( subset @ SV160 @ ( cartesian_product2 @ SV80 @ SV140 ) )
= $false )
| ( ( relation_of2 @ SV160 @ SV80 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1715,plain,
! [SV161: $i,SV142: $i,SV82: $i] :
( ( ( subset @ SV82 @ SV142 )
= $false )
| ( ( ~ ( subset @ SV82 @ SV161 ) )
= $true )
| ( ( subset @ SV82 @ ( set_intersection2 @ SV142 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1716,plain,
! [SV145: $i,SV86: $i,SV163: $i] :
( ( ( subset @ ( relation_dom @ SV163 ) @ SV86 )
= $true )
| ( ( relation_of2_as_subset @ SV163 @ SV86 @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1717,plain,
! [SV86: $i,SV145: $i,SV163: $i] :
( ( ( subset @ ( relation_rng @ SV163 ) @ SV145 )
= $true )
| ( ( relation_of2_as_subset @ SV163 @ SV86 @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1718,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1719,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV146 )
| ~ ( in @ SV94 @ SV146 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1720,plain,
! [SV9: $i] :
( ( ( empty @ ( the_carrier @ SV9 ) )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( one_sorted_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1721,plain,
! [SV164: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV164 )
| ! [SY367: $i,SY368: $i] :
( ~ ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV12 )
| ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV164 ) ) )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1722,plain,
! [SV164: $i,SV12: $i] :
( ( ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV12 )
| ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV164 ) )
| ( subset @ SV12 @ SV164 ) )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1723,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1724,plain,
! [SV16: $i] :
( ( ~ ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ( in @ SY357 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY356 )
| ( in @ SX4 @ SY357 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1725,plain,
! [SV16: $i,SV178: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
| ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1726,plain,
! [SV18: $i,SV148: $i,SV100: $i] :
( ( ( subset @ SV100 @ SV148 )
= $false )
| ( ( subset @ SV18 @ SV100 )
= $false )
| ( ( subset @ SV18 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1727,plain,
! [SV165: $i,SV20: $i,SV176: $i] :
( ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( ~ ( ~ ( ~ ( subnetstr @ SV176 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) )
| ( subnetstr @ SV176 @ SV20 @ SV165 ) ) ) )
= $true )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1728,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
| ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1729,plain,
! [SV26: $i,SV177: $i] :
( ( ( in @ SV177 @ SV26 )
= $false )
| ( ( subset @ SV177 @ SV26 )
= $true )
| ( ( epsilon_transitive @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1730,plain,
! [SV26: $i] :
( ( ( in @ ( sK10_SY242 @ SV26 ) @ SV26 )
= $true )
| ( ( epsilon_transitive @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1731,plain,
! [SV105: $i,SV28: $i,SV182: $i] :
( ( ( ~ ( subnetstr @ SV182 @ SV28 @ SV105 )
| ( net_str @ SV182 @ SV28 ) )
= $true )
| ( ( one_sorted_str @ SV28 )
= $false )
| ( ( net_str @ SV105 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1732,plain,
! [SV30: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV30 ) )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1733,plain,
! [SV36: $i,SV111: $i,SV152: $i] :
( ( ( subset @ SV152 @ SV111 )
= $false )
| ( ( subset @ SV36 @ SV111 )
= $false )
| ( ( subset @ ( set_union2 @ SV36 @ SV152 ) @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1734,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
| ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) )
= $false )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1735,plain,
! [SV114: $i,SV42: $i] :
( ( ( ! [SY335: $i] :
~ ( subnetstr @ SY335 @ SV42 @ SV114 ) )
= $false )
| ( ( one_sorted_str @ SV42 )
= $false )
| ( ( net_str @ SV114 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1736,plain,
! [SV115: $i,SV43: $i] :
( ( ( ~ ( subset @ SV43 @ SV115 ) )
= $false )
| ( ( proper_subset @ SV43 @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1737,plain,
! [SV115: $i,SV43: $i] :
( ( ( ~ ( ( SV43 != SV115 ) ) )
= $false )
| ( ( proper_subset @ SV43 @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1738,plain,
! [SV115: $i,SV43: $i] :
( ( ( ~ ( subset @ SV43 @ SV115 ) )
= $true )
| ( ( ~ ( ( SV43 != SV115 ) ) )
= $true )
| ( ( proper_subset @ SV43 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1739,plain,
! [SV116: $i,SV44: $i,SV179: $i] :
( ( ( ~ ( in @ SV179 @ SV44 ) )
= $true )
| ( ( in @ SV179 @ SV116 )
= $true )
| ( ( subset @ SV44 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1740,plain,
! [SV44: $i,SV116: $i] :
( ( ( ~ ( in @ ( sK11_SY337 @ SV116 @ SV44 ) @ SV44 ) )
= $false )
| ( ( subset @ SV44 @ SV116 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1741,plain,
! [SV44: $i,SV116: $i] :
( ( ( in @ ( sK11_SY337 @ SV116 @ SV44 ) @ SV116 )
= $false )
| ( ( subset @ SV44 @ SV116 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1742,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
| ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1743,plain,
! [SV49: $i,SV156: $i,SV120: $i] :
( ( ( disjoint @ SV120 @ SV156 )
= $false )
| ( ( subset @ SV49 @ SV120 )
= $false )
| ( ( disjoint @ SV49 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1744,plain,
! [SV51: $i,SV183: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV183 )
| ~ ( net_str @ SV183 @ SV51 ) )
| ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SY372 @ SY373 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SY372 )
| ( is_eventually_in @ SV51 @ SV183 @ SY373 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SY372 )
| ( is_often_in @ SV51 @ SV183 @ SY373 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1745,plain,
! [SV174: $i,SV121: $i,SV52: $i] :
( ( ( ~ ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
| ( subset @ SV121 @ SV174 ) ) )
= $false )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1746,plain,
! [SV52: $i,SV174: $i,SV121: $i] :
( ( ( ~ ( ~ ( subset @ SV121 @ SV174 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 ) ) )
= $false )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1747,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1748,plain,
! [SV55: $i] :
( ( ~ ! [SY364: $i] :
( ~ ( in @ SY364 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SY364 ) @ ( sK6_SY282 @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1749,plain,
! [SV55: $i,SV180: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
| ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1750,plain,
! [SV175: $i,SV127: $i,SV62: $i] :
( ( ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
| ( subset @ SV127 @ SV175 ) ) )
= $false )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1751,plain,
! [SV62: $i,SV175: $i,SV127: $i] :
( ( ( ~ ( ~ ( subset @ SV127 @ SV175 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 ) ) )
= $false )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1752,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( subrelstr @ SV170 @ SV65 )
| ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1753,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
| ( subrelstr @ SV170 @ SV65 ) )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1754,plain,
! [SV171: $i,SV158: $i,SV131: $i,SV67: $i] :
( ( ( subset @ SV67 @ SV131 )
= $false )
| ( ( ~ ( subset @ SV158 @ SV171 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV67 @ SV158 ) @ ( cartesian_product2 @ SV131 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1755,plain,
! [SV69: $i] :
( ( ( subset @ ( sK8_SY301 @ SV69 ) @ SV69 )
= $false )
| ( ( ordinal @ ( sK8_SY301 @ SV69 ) )
= $false )
| ( ( ordinal @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1756,plain,
! [SV73: $i,SV135: $i,SV181: $i] :
( ( ( ~ ( ~ ( in @ SV181 @ SV135 )
| ( subset @ SV181 @ SV73 ) )
| ~ ( ~ ( subset @ SV181 @ SV73 )
| ( in @ SV181 @ SV135 ) ) )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1757,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
| ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 ) )
| ~ ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1758,plain,
! [SV172: $i,SV75: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SV172 ) )
| ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SV172 ) ) )
= $false )
| ( ( subset @ SV75 @ SV172 )
= $false )
| ( ( relation @ SV172 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1759,plain,
! [SV138: $i,SV77: $i] :
( ( ( ~ ( subset @ SV77 @ SV138 ) )
= $false )
| ( ( SV77 = SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1760,plain,
! [SV77: $i,SV138: $i] :
( ( ( ~ ( subset @ SV138 @ SV77 ) )
= $false )
| ( ( SV77 = SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1761,plain,
! [SV138: $i,SV77: $i] :
( ( ( ~ ( subset @ SV77 @ SV138 ) )
= $true )
| ( ( ~ ( subset @ SV138 @ SV77 ) )
= $true )
| ( ( SV77 = SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(1762,plain,
! [SV142: $i,SV161: $i,SV82: $i] :
( ( ( subset @ SV82 @ SV161 )
= $false )
| ( ( subset @ SV82 @ SV142 )
= $false )
| ( ( subset @ SV82 @ ( set_intersection2 @ SV142 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1763,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV146 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1764,plain,
! [SV7: $i,SV146: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ SV146 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1765,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV146 ) )
= $true )
| ( ( ~ ( in @ SV94 @ SV146 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1766,plain,
! [SV164: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV164 ) )
= $true )
| ( ( ! [SY367: $i,SY368: $i] :
( ~ ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV12 )
| ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV164 ) ) )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1767,plain,
! [SV164: $i,SV12: $i] :
( ( ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV12 )
| ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV164 ) ) )
= $true )
| ( ( subset @ SV12 @ SV164 )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1768,plain,
! [SV16: $i] :
( ( ~ ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1769,plain,
! [SV16: $i] :
( ( ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ( in @ SY357 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY356 )
| ( in @ SX4 @ SY357 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1724]) ).
thf(1770,plain,
! [SV16: $i,SV178: $i] :
( ( ~ ~ ( ~ ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
| ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1771,plain,
! [SV165: $i,SV20: $i,SV176: $i] :
( ( ( ~ ( ~ ( subnetstr @ SV176 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) )
| ( subnetstr @ SV176 @ SV20 @ SV165 ) ) )
= $false )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1772,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(1773,plain,
! [SV105: $i,SV28: $i,SV182: $i] :
( ( ( ~ ( subnetstr @ SV182 @ SV28 @ SV105 ) )
= $true )
| ( ( net_str @ SV182 @ SV28 )
= $true )
| ( ( one_sorted_str @ SV28 )
= $false )
| ( ( net_str @ SV105 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1774,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) ) )
= $false )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1775,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) ) )
= $false )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1776,plain,
! [SV42: $i,SV114: $i] :
( ( ( ~ ( subnetstr @ ( sK13_SY335 @ SV114 @ SV42 ) @ SV42 @ SV114 ) )
= $false )
| ( ( one_sorted_str @ SV42 )
= $false )
| ( ( net_str @ SV114 @ SV42 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1735]) ).
thf(1777,plain,
! [SV115: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV115 )
= $true )
| ( ( proper_subset @ SV43 @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1778,plain,
! [SV115: $i,SV43: $i] :
( ( ( SV43 != SV115 )
= $true )
| ( ( proper_subset @ SV43 @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1779,plain,
! [SV115: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV115 )
= $false )
| ( ( ~ ( ( SV43 != SV115 ) ) )
= $true )
| ( ( proper_subset @ SV43 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1780,plain,
! [SV116: $i,SV44: $i,SV179: $i] :
( ( ( in @ SV179 @ SV44 )
= $false )
| ( ( in @ SV179 @ SV116 )
= $true )
| ( ( subset @ SV44 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1781,plain,
! [SV44: $i,SV116: $i] :
( ( ( in @ ( sK11_SY337 @ SV116 @ SV44 ) @ SV44 )
= $true )
| ( ( subset @ SV44 @ SV116 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1782,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(1783,plain,
! [SV51: $i,SV183: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV183 )
| ~ ( net_str @ SV183 @ SV51 ) ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SY372 @ SY373 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SY372 )
| ( is_eventually_in @ SV51 @ SV183 @ SY373 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SY372 )
| ( is_often_in @ SV51 @ SV183 @ SY373 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(1784,plain,
! [SV174: $i,SV121: $i,SV52: $i] :
( ( ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
| ( subset @ SV121 @ SV174 ) )
= $true )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1785,plain,
! [SV52: $i,SV174: $i,SV121: $i] :
( ( ( ~ ( subset @ SV121 @ SV174 )
| ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 ) )
= $true )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1786,plain,
! [SV55: $i] :
( ( ~ ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1787,plain,
! [SV55: $i] :
( ( ! [SY364: $i] :
( ~ ( in @ SY364 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SY364 ) @ ( sK6_SY282 @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1788,plain,
! [SV55: $i,SV180: $i] :
( ( ~ ~ ( ~ ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
| ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1789,plain,
! [SV175: $i,SV127: $i,SV62: $i] :
( ( ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
| ( subset @ SV127 @ SV175 ) )
= $true )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1790,plain,
! [SV62: $i,SV175: $i,SV127: $i] :
( ( ( ~ ( subset @ SV127 @ SV175 )
| ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 ) )
= $true )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1791,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( subrelstr @ SV170 @ SV65 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1792,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
= $true )
| ( ( subrelstr @ SV170 @ SV65 )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1793,plain,
! [SV131: $i,SV67: $i,SV171: $i,SV158: $i] :
( ( ( subset @ SV158 @ SV171 )
= $false )
| ( ( subset @ SV67 @ SV131 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV67 @ SV158 ) @ ( cartesian_product2 @ SV131 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1794,plain,
! [SV73: $i,SV135: $i,SV181: $i] :
( ( ( ~ ( ~ ( in @ SV181 @ SV135 )
| ( subset @ SV181 @ SV73 ) ) )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1756]) ).
thf(1795,plain,
! [SV135: $i,SV73: $i,SV181: $i] :
( ( ( ~ ( ~ ( subset @ SV181 @ SV73 )
| ( in @ SV181 @ SV135 ) ) )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1756]) ).
thf(1796,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
| ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(1797,plain,
! [SV172: $i,SV75: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SV172 ) ) )
= $false )
| ( ( subset @ SV75 @ SV172 )
= $false )
| ( ( relation @ SV172 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1798,plain,
! [SV172: $i,SV75: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SV172 ) ) )
= $false )
| ( ( subset @ SV75 @ SV172 )
= $false )
| ( ( relation @ SV172 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1799,plain,
! [SV138: $i,SV77: $i] :
( ( ( subset @ SV77 @ SV138 )
= $true )
| ( ( SV77 = SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1800,plain,
! [SV77: $i,SV138: $i] :
( ( ( subset @ SV138 @ SV77 )
= $true )
| ( ( SV77 = SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(1801,plain,
! [SV138: $i,SV77: $i] :
( ( ( subset @ SV77 @ SV138 )
= $false )
| ( ( ~ ( subset @ SV138 @ SV77 ) )
= $true )
| ( ( SV77 = SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1802,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ( in @ SV7 @ SV146 )
= $true )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(1803,plain,
! [SV7: $i,SV146: $i,SV94: $i] :
( ( ( in @ SV94 @ SV146 )
= $true )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1804,plain,
! [SV94: $i,SV146: $i,SV7: $i] :
( ( ( in @ SV7 @ SV146 )
= $false )
| ( ( ~ ( in @ SV94 @ SV146 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1805,plain,
! [SV164: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV164 )
= $false )
| ( ( ! [SY367: $i,SY368: $i] :
( ~ ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV12 )
| ( in @ ( ordered_pair @ SY367 @ SY368 ) @ SV164 ) ) )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1806,plain,
! [SV164: $i,SV12: $i] :
( ( ( ! [SY369: $i,SY370: $i] :
( ~ ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV12 )
| ( in @ ( ordered_pair @ SY369 @ SY370 ) @ SV164 ) ) )
= $false )
| ( ( subset @ SV12 @ SV164 )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1807,plain,
! [SV16: $i] :
( ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1808,plain,
! [SV16: $i,SV184: $i] :
( ( ~ ~ ( ~ ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY375: $i] :
( ~ ( subset @ SY375 @ SV184 )
| ( in @ SY375 @ SY374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(1809,plain,
! [SV16: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1810,plain,
! [SV165: $i,SV20: $i,SV176: $i] :
( ( ( ~ ( ~ ( subnetstr @ SV176 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) ) )
= $false )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1811,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( ~ ( ~ ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) )
| ( subnetstr @ SV176 @ SV20 @ SV165 ) ) )
= $false )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1812,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1813,plain,
! [SV105: $i,SV28: $i,SV182: $i] :
( ( ( subnetstr @ SV182 @ SV28 @ SV105 )
= $false )
| ( ( net_str @ SV182 @ SV28 )
= $true )
| ( ( one_sorted_str @ SV28 )
= $false )
| ( ( net_str @ SV105 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1814,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( ordinal_subset @ SV39 @ SV113 )
| ( subset @ SV39 @ SV113 ) )
= $true )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1815,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV113 )
| ( ordinal_subset @ SV39 @ SV113 ) )
= $true )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1816,plain,
! [SV42: $i,SV114: $i] :
( ( ( subnetstr @ ( sK13_SY335 @ SV114 @ SV42 ) @ SV42 @ SV114 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false )
| ( ( net_str @ SV114 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1817,plain,
! [SV115: $i,SV43: $i] :
( ( ( SV43 = SV115 )
= $false )
| ( ( proper_subset @ SV43 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1818,plain,
! [SV115: $i,SV43: $i] :
( ( ( SV43 != SV115 )
= $false )
| ( ( subset @ SV43 @ SV115 )
= $false )
| ( ( proper_subset @ SV43 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1819,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) ) )
= $false )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1820,plain,
! [SV51: $i,SV183: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV183 )
| ~ ( net_str @ SV183 @ SV51 ) ) )
= $false )
| ( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SY372 @ SY373 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SY372 )
| ( is_eventually_in @ SV51 @ SV183 @ SY373 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SY372 )
| ( is_often_in @ SV51 @ SV183 @ SY373 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1821,plain,
! [SV174: $i,SV121: $i,SV52: $i] :
( ( ( ~ ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 ) )
= $true )
| ( ( subset @ SV121 @ SV174 )
= $true )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1822,plain,
! [SV52: $i,SV174: $i,SV121: $i] :
( ( ( ~ ( subset @ SV121 @ SV174 ) )
= $true )
| ( ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
= $true )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(1823,plain,
! [SV55: $i] :
( ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1824,plain,
! [SV55: $i,SV185: $i] :
( ( ~ ( in @ SV185 @ ( sK6_SY282 @ SV55 ) )
| ( in @ ( powerset @ SV185 ) @ ( sK6_SY282 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(1825,plain,
! [SV55: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(1826,plain,
! [SV175: $i,SV127: $i,SV62: $i] :
( ( ( ~ ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 ) )
= $true )
| ( ( subset @ SV127 @ SV175 )
= $true )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(1827,plain,
! [SV62: $i,SV175: $i,SV127: $i] :
( ( ( ~ ( subset @ SV127 @ SV175 ) )
= $true )
| ( ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
= $true )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1828,plain,
! [SV65: $i,SV170: $i] :
( ( ( subrelstr @ SV170 @ SV65 )
= $false )
| ( ( ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1829,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) ) )
= $false )
| ( ( subrelstr @ SV170 @ SV65 )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1830,plain,
! [SV73: $i,SV135: $i,SV181: $i] :
( ( ( ~ ( in @ SV181 @ SV135 )
| ( subset @ SV181 @ SV73 ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1831,plain,
! [SV135: $i,SV73: $i,SV181: $i] :
( ( ( ~ ( subset @ SV181 @ SV73 )
| ( in @ SV181 @ SV135 ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1832,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
| ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1833,plain,
! [SV172: $i,SV75: $i] :
( ( ( subset @ ( relation_dom @ SV75 ) @ ( relation_dom @ SV172 ) )
= $true )
| ( ( subset @ SV75 @ SV172 )
= $false )
| ( ( relation @ SV172 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1834,plain,
! [SV172: $i,SV75: $i] :
( ( ( subset @ ( relation_rng @ SV75 ) @ ( relation_rng @ SV172 ) )
= $true )
| ( ( subset @ SV75 @ SV172 )
= $false )
| ( ( relation @ SV172 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1835,plain,
! [SV77: $i,SV138: $i] :
( ( ( subset @ SV138 @ SV77 )
= $false )
| ( ( subset @ SV77 @ SV138 )
= $false )
| ( ( SV77 = SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1836,plain,
! [SV7: $i,SV146: $i,SV94: $i] :
( ( ( in @ SV94 @ SV146 )
= $false )
| ( ( in @ SV7 @ SV146 )
= $false )
| ( ( subset @ ( unordered_pair @ SV7 @ SV94 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1837,plain,
! [SV164: $i,SV12: $i,SV186: $i] :
( ( ( ! [SY376: $i] :
( ~ ( in @ ( ordered_pair @ SV186 @ SY376 ) @ SV12 )
| ( in @ ( ordered_pair @ SV186 @ SY376 ) @ SV164 ) ) )
= $true )
| ( ( subset @ SV12 @ SV164 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(1838,plain,
! [SV12: $i,SV164: $i] :
( ( ( ! [SY377: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_SY369 @ SV164 @ SV12 ) @ SY377 ) @ SV12 )
| ( in @ ( ordered_pair @ ( sK14_SY369 @ SV164 @ SV12 ) @ SY377 ) @ SV164 ) ) )
= $false )
| ( ( subset @ SV12 @ SV164 )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1806]) ).
thf(1839,plain,
! [SV16: $i] :
( ( ~ ( in @ SV16 @ ( sK5_SY224 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1840,plain,
! [SV16: $i] :
( ( ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1841,plain,
! [SV16: $i,SV184: $i] :
( ( ~ ( ~ ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY375: $i] :
( ~ ( subset @ SY375 @ SV184 )
| ( in @ SY375 @ SY374 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1842,plain,
! [SV16: $i,SV178: $i] :
( ( ( ~ ( ~ ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1843,plain,
! [SV165: $i,SV20: $i,SV176: $i] :
( ( ( ~ ( subnetstr @ SV176 @ SV20 @ SV165 )
| ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1844,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( ~ ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) )
| ( subnetstr @ SV176 @ SV20 @ SV165 ) )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1845,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ~ ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1846,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( ordinal_subset @ SV39 @ SV113 ) )
= $true )
| ( ( subset @ SV39 @ SV113 )
= $true )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(1847,plain,
! [SV113: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV113 ) )
= $true )
| ( ( ordinal_subset @ SV39 @ SV113 )
= $true )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(1848,plain,
! [SV115: $i,SV43: $i] :
( ( ( SV43 = SV115 )
= $true )
| ( ( subset @ SV43 @ SV115 )
= $false )
| ( ( proper_subset @ SV43 @ SV115 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1849,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
| ~ ~ ( empty_carrier @ SV119 ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1819]) ).
thf(1850,plain,
! [SV51: $i,SV183: $i] :
( ( ( ~ ~ ( empty_carrier @ SV183 )
| ~ ( net_str @ SV183 @ SV51 ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SY372 @ SY373 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SY372 )
| ( is_eventually_in @ SV51 @ SV183 @ SY373 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SY372 )
| ( is_often_in @ SV51 @ SV183 @ SY373 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1851,plain,
! [SV174: $i,SV121: $i,SV52: $i] :
( ( ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
= $false )
| ( ( subset @ SV121 @ SV174 )
= $true )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1852,plain,
! [SV52: $i,SV174: $i,SV121: $i] :
( ( ( subset @ SV121 @ SV174 )
= $false )
| ( ( below @ ( boole_lattice @ SV52 ) @ SV121 @ SV174 )
= $true )
| ( ( element @ SV174 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false )
| ( ( element @ SV121 @ ( the_carrier @ ( boole_lattice @ SV52 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1853,plain,
! [SV55: $i] :
( ( ~ ( in @ SV55 @ ( sK6_SY282 @ SV55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1854,plain,
! [SV55: $i] :
( ( ~ ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1855,plain,
! [SV55: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ ( sK6_SY282 @ SV55 ) ) )
= $true )
| ( ( in @ ( powerset @ SV185 ) @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(1856,plain,
! [SV55: $i,SV180: $i] :
( ( ( ~ ( ~ ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1857,plain,
! [SV175: $i,SV127: $i,SV62: $i] :
( ( ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
= $false )
| ( ( subset @ SV127 @ SV175 )
= $true )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1858,plain,
! [SV62: $i,SV175: $i,SV127: $i] :
( ( ( subset @ SV127 @ SV175 )
= $false )
| ( ( related_reflexive @ ( boole_POSet @ SV62 ) @ SV127 @ SV175 )
= $true )
| ( ( element @ SV175 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false )
| ( ( element @ SV127 @ ( the_carrier @ ( boole_POSet @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1859,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
= $false )
| ( ( subrelstr @ SV170 @ SV65 )
= $false )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(1860,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
| ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
= $true )
| ( ( subrelstr @ SV170 @ SV65 )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1829]) ).
thf(1861,plain,
! [SV73: $i,SV135: $i,SV181: $i] :
( ( ( ~ ( in @ SV181 @ SV135 ) )
= $true )
| ( ( subset @ SV181 @ SV73 )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1862,plain,
! [SV135: $i,SV73: $i,SV181: $i] :
( ( ( ~ ( subset @ SV181 @ SV73 ) )
= $true )
| ( ( in @ SV181 @ SV135 )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(1863,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1832]) ).
thf(1864,plain,
! [SV135: $i,SV73: $i] :
( ( ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1832]) ).
thf(1865,plain,
! [SV164: $i,SV12: $i,SV187: $i,SV186: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV186 @ SV187 ) @ SV12 )
| ( in @ ( ordered_pair @ SV186 @ SV187 ) @ SV164 ) )
= $true )
| ( ( subset @ SV12 @ SV164 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(1866,plain,
! [SV12: $i,SV164: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY369 @ SV164 @ SV12 ) @ ( sK15_SY377 @ SV12 @ SV164 ) ) @ SV12 )
| ( in @ ( ordered_pair @ ( sK14_SY369 @ SV164 @ SV12 ) @ ( sK15_SY377 @ SV12 @ SV164 ) ) @ SV164 ) )
= $false )
| ( ( subset @ SV12 @ SV164 )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1838]) ).
thf(1867,plain,
! [SV16: $i] :
( ( in @ SV16 @ ( sK5_SY224 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1868,plain,
! [SV16: $i] :
( ( ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY224 @ SV16 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(1869,plain,
! [SV16: $i,SV184: $i] :
( ( ~ ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY375: $i] :
( ~ ( subset @ SY375 @ SV184 )
| ( in @ SY375 @ SY374 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(1870,plain,
! [SV16: $i,SV178: $i] :
( ( ( ~ ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
| ~ ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(1871,plain,
! [SV165: $i,SV20: $i,SV176: $i] :
( ( ( ~ ( subnetstr @ SV176 @ SV20 @ SV165 ) )
= $true )
| ( ( ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(1872,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( ~ ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
= $true )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(1873,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ~ ( empty_carrier @ SV23 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1874,plain,
! [SV113: $i,SV39: $i] :
( ( ( ordinal_subset @ SV39 @ SV113 )
= $false )
| ( ( subset @ SV39 @ SV113 )
= $true )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1875,plain,
! [SV113: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV113 )
= $false )
| ( ( ordinal_subset @ SV39 @ SV113 )
= $true )
| ( ( ordinal @ SV39 )
= $false )
| ( ( ordinal @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1876,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) ) )
= $true )
| ( ( ~ ~ ( empty_carrier @ SV119 ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(1877,plain,
! [SV51: $i,SV183: $i] :
( ( ( ~ ~ ( empty_carrier @ SV183 ) )
= $true )
| ( ( ~ ( net_str @ SV183 @ SV51 ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SY372 @ SY373 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SY372 )
| ( is_eventually_in @ SV51 @ SV183 @ SY373 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SY372 )
| ( is_often_in @ SV51 @ SV183 @ SY373 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(1878,plain,
! [SV55: $i] :
( ( in @ SV55 @ ( sK6_SY282 @ SV55 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1879,plain,
! [SV55: $i] :
( ( ! [SY362: $i,SY363: $i] :
( ~ ~ ( ~ ( in @ SY362 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY363 @ SY362 ) )
| ( in @ SY363 @ ( sK6_SY282 @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1854]) ).
thf(1880,plain,
! [SV55: $i,SV185: $i] :
( ( ( in @ SV185 @ ( sK6_SY282 @ SV55 ) )
= $false )
| ( ( in @ ( powerset @ SV185 ) @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1881,plain,
! [SV55: $i,SV180: $i] :
( ( ( ~ ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
| ~ ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1882,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) ) )
= $false )
| ( ( subrelstr @ SV170 @ SV65 )
= $false )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1883,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
= $false )
| ( ( subrelstr @ SV170 @ SV65 )
= $false )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1884,plain,
! [SV65: $i,SV170: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) ) )
= $true )
| ( ( ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
= $true )
| ( ( subrelstr @ SV170 @ SV65 )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1885,plain,
! [SV73: $i,SV135: $i,SV181: $i] :
( ( ( in @ SV181 @ SV135 )
= $false )
| ( ( subset @ SV181 @ SV73 )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1886,plain,
! [SV135: $i,SV73: $i,SV181: $i] :
( ( ( subset @ SV181 @ SV73 )
= $false )
| ( ( in @ SV181 @ SV135 )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1887,plain,
! [SV135: $i,SV73: $i] :
( ( ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1863]) ).
thf(1888,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) )
= $false )
| ( ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1889,plain,
! [SV164: $i,SV12: $i,SV187: $i,SV186: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV186 @ SV187 ) @ SV12 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV186 @ SV187 ) @ SV164 )
= $true )
| ( ( subset @ SV12 @ SV164 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1890,plain,
! [SV12: $i,SV164: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY369 @ SV164 @ SV12 ) @ ( sK15_SY377 @ SV12 @ SV164 ) ) @ SV12 ) )
= $false )
| ( ( subset @ SV12 @ SV164 )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1866]) ).
thf(1891,plain,
! [SV12: $i,SV164: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY369 @ SV164 @ SV12 ) @ ( sK15_SY377 @ SV12 @ SV164 ) ) @ SV164 )
= $false )
| ( ( subset @ SV12 @ SV164 )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1866]) ).
thf(1892,plain,
! [SV16: $i,SV188: $i] :
( ( ! [SY378: $i] :
( ~ ~ ( ~ ( in @ SV188 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SY378 @ SV188 ) )
| ( in @ SY378 @ ( sK5_SY224 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(1893,plain,
! [SV16: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ ( sK5_SY224 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY375: $i] :
( ~ ( subset @ SY375 @ SV184 )
| ( in @ SY375 @ SY374 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1894,plain,
! [SV16: $i,SV178: $i] :
( ( ( ~ ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1895,plain,
! [SV165: $i,SV20: $i,SV176: $i] :
( ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $false )
| ( ( ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1896,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) ) )
= $false )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1897,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( ~ ( empty_carrier @ SV23 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1898,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) ) )
= $false )
| ( ( ~ ~ ( empty_carrier @ SV119 ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1899,plain,
! [SV51: $i,SV183: $i] :
( ( ( ~ ( empty_carrier @ SV183 ) )
= $false )
| ( ( ~ ( net_str @ SV183 @ SV51 ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SY372 @ SY373 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SY372 )
| ( is_eventually_in @ SV51 @ SV183 @ SY373 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SY372 )
| ( is_often_in @ SV51 @ SV183 @ SY373 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(1900,plain,
! [SV55: $i,SV189: $i] :
( ( ! [SY379: $i] :
( ~ ~ ( ~ ( in @ SV189 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SY379 @ SV189 ) )
| ( in @ SY379 @ ( sK6_SY282 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(1901,plain,
! [SV55: $i,SV180: $i] :
( ( ( ~ ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(1902,plain,
! [SV65: $i,SV170: $i] :
( ( ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
= $true )
| ( ( subrelstr @ SV170 @ SV65 )
= $false )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1882]) ).
thf(1903,plain,
! [SV65: $i,SV170: $i] :
( ( ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) )
= $true )
| ( ( subrelstr @ SV170 @ SV65 )
= $false )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1883]) ).
thf(1904,plain,
! [SV65: $i,SV170: $i] :
( ( ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
= $false )
| ( ( ~ ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) ) )
= $true )
| ( ( subrelstr @ SV170 @ SV65 )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1905,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
| ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 ) )
= $false )
| ( ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1906,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 ) )
= $false )
| ( ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(1907,plain,
! [SV135: $i,SV73: $i] :
( ( ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
= $false )
| ( ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(1908,plain,
! [SV164: $i,SV12: $i,SV187: $i,SV186: $i] :
( ( ( in @ ( ordered_pair @ SV186 @ SV187 ) @ SV12 )
= $false )
| ( ( in @ ( ordered_pair @ SV186 @ SV187 ) @ SV164 )
= $true )
| ( ( subset @ SV12 @ SV164 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1909,plain,
! [SV12: $i,SV164: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY369 @ SV164 @ SV12 ) @ ( sK15_SY377 @ SV12 @ SV164 ) ) @ SV12 )
= $true )
| ( ( subset @ SV12 @ SV164 )
= $true )
| ( ( relation @ SV164 )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1910,plain,
! [SV190: $i,SV16: $i,SV188: $i] :
( ( ~ ~ ( ~ ( in @ SV188 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SV190 @ SV188 ) )
| ( in @ SV190 @ ( sK5_SY224 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(1911,plain,
! [SV16: $i,SV184: $i] :
( ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false )
| ( ( ~ ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY375: $i] :
( ~ ( subset @ SY375 @ SV184 )
| ( in @ SY375 @ SY374 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1912,plain,
! [SV16: $i,SV178: $i] :
( ( ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(1913,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) )
= $false )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $false )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1914,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( ~ ( subrelstr @ SV176 @ SV165 )
| ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) ) )
= $true )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(1915,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( empty_carrier @ SV23 )
= $true )
| ( ( ~ ( one_sorted_str @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(1916,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( empty_carrier @ SV48 )
| ~ ( one_sorted_str @ SV48 ) )
= $true )
| ( ( ~ ~ ( empty_carrier @ SV119 ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(1917,plain,
! [SV51: $i,SV183: $i] :
( ( ( empty_carrier @ SV183 )
= $true )
| ( ( ~ ( net_str @ SV183 @ SV51 ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SY372 @ SY373 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SY372 )
| ( is_eventually_in @ SV51 @ SV183 @ SY373 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SY372 )
| ( is_often_in @ SV51 @ SV183 @ SY373 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1918,plain,
! [SV191: $i,SV55: $i,SV189: $i] :
( ( ~ ~ ( ~ ( in @ SV189 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SV191 @ SV189 ) )
| ( in @ SV191 @ ( sK6_SY282 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(1919,plain,
! [SV55: $i,SV180: $i] :
( ( ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1920,plain,
! [SV65: $i,SV170: $i] :
( ( ( subset @ ( the_InternalRel @ SV170 ) @ ( the_InternalRel @ SV65 ) )
= $false )
| ( ( subset @ ( the_carrier @ SV170 ) @ ( the_carrier @ SV65 ) )
= $false )
| ( ( subrelstr @ SV170 @ SV65 )
= $true )
| ( ( rel_str @ SV170 )
= $false )
| ( ( rel_str @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1921,plain,
! [SV135: $i,SV73: $i] :
( ( ( ~ ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 ) )
= $false )
| ( ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(1922,plain,
! [SV135: $i,SV73: $i] :
( ( ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
= $false )
| ( ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(1923,plain,
! [SV135: $i,SV73: $i] :
( ( ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
= $true )
| ( ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
= $false )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1906]) ).
thf(1924,plain,
! [SV190: $i,SV16: $i,SV188: $i] :
( ( ( ~ ~ ( ~ ( in @ SV188 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SV190 @ SV188 ) ) )
= $true )
| ( ( in @ SV190 @ ( sK5_SY224 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(1925,plain,
! [SV184: $i,SV16: $i] :
( ( ( ! [SY374: $i] :
~ ~ ( ~ ( in @ SY374 @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY375: $i] :
( ~ ( subset @ SY375 @ SV184 )
| ( in @ SY375 @ SY374 ) ) ) )
= $false )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1926,plain,
! [SV16: $i,SV178: $i] :
( ( ( ~ ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $false )
| ( ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $false )
| ( ( ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(1927,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( ~ ( subrelstr @ SV176 @ SV165 ) )
= $false )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $false )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1913]) ).
thf(1928,plain,
! [SV165: $i,SV176: $i,SV20: $i] :
( ( ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) )
= $false )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $false )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1913]) ).
thf(1929,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( ~ ( subrelstr @ SV176 @ SV165 ) )
= $true )
| ( ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) )
= $true )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(1930,plain,
! [SV149: $i,SV102: $i,SV23: $i] :
( ( ( one_sorted_str @ SV23 )
= $false )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( ~ ( element @ SV102 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(1931,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ~ ( empty_carrier @ SV48 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV48 ) )
= $true )
| ( ( ~ ~ ( empty_carrier @ SV119 ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(1932,plain,
! [SV51: $i,SV183: $i] :
( ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SY372 @ SY373 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SY372 )
| ( is_eventually_in @ SV51 @ SV183 @ SY373 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SY372 )
| ( is_often_in @ SV51 @ SV183 @ SY373 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1933,plain,
! [SV191: $i,SV55: $i,SV189: $i] :
( ( ( ~ ~ ( ~ ( in @ SV189 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SV191 @ SV189 ) ) )
= $true )
| ( ( in @ SV191 @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(1934,plain,
! [SV55: $i,SV180: $i] :
( ( ( ~ ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $false )
| ( ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $false )
| ( ( ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1935,plain,
! [SV135: $i,SV73: $i] :
( ( ( subset @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV73 )
= $true )
| ( ( in @ ( sK12_SY348 @ SV73 @ SV135 ) @ SV135 )
= $true )
| ( ( SV135
= ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(1936,plain,
! [SV190: $i,SV16: $i,SV188: $i] :
( ( ( ~ ( ~ ( in @ SV188 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SV190 @ SV188 ) ) )
= $false )
| ( ( in @ SV190 @ ( sK5_SY224 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(1937,plain,
! [SV16: $i,SV184: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY374 @ SV184 @ SV16 ) @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY380: $i] :
( ~ ( subset @ SY380 @ SV184 )
| ( in @ SY380 @ ( sK16_SY374 @ SV184 @ SV16 ) ) ) ) )
= $false )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1925]) ).
thf(1938,plain,
! [SV16: $i,SV178: $i] :
( ( ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $true )
| ( ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $false )
| ( ( ~ ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(1939,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( subrelstr @ SV176 @ SV165 )
= $true )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $false )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(1940,plain,
! [SV165: $i,SV176: $i,SV20: $i] :
( ( ( ( the_mapping @ SV20 @ SV176 )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) )
= $true )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $false )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(1941,plain,
! [SV20: $i,SV165: $i,SV176: $i] :
( ( ( subrelstr @ SV176 @ SV165 )
= $false )
| ( ( ( the_mapping @ SV20 @ SV176 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) )
= $true )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(1942,plain,
! [SV149: $i,SV23: $i,SV102: $i] :
( ( ( element @ SV102 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( one_sorted_str @ SV23 )
= $false )
| ( ( ~ ( element @ SV149 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1943,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( ~ ( empty_carrier @ SV48 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV48 ) )
= $true )
| ( ( ~ ~ ( empty_carrier @ SV119 ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(1944,plain,
! [SV183: $i,SV51: $i,SV192: $i] :
( ( ( ! [SY381: $i] :
( ~ ( subset @ SV192 @ SY381 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SV192 )
| ( is_eventually_in @ SV51 @ SV183 @ SY381 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SV192 )
| ( is_often_in @ SV51 @ SV183 @ SY381 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(1945,plain,
! [SV191: $i,SV55: $i,SV189: $i] :
( ( ( ~ ( ~ ( in @ SV189 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SV191 @ SV189 ) ) )
= $false )
| ( ( in @ SV191 @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(1946,plain,
! [SV55: $i,SV180: $i] :
( ( ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $true )
| ( ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $false )
| ( ( ~ ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1934]) ).
thf(1947,plain,
! [SV190: $i,SV16: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ ( sK5_SY224 @ SV16 ) )
| ~ ( subset @ SV190 @ SV188 ) )
= $true )
| ( ( in @ SV190 @ ( sK5_SY224 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(1948,plain,
! [SV16: $i,SV184: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY374 @ SV184 @ SV16 ) @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY380: $i] :
( ~ ( subset @ SY380 @ SV184 )
| ( in @ SY380 @ ( sK16_SY374 @ SV184 @ SV16 ) ) ) ) )
= $true )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(1949,plain,
! [SV16: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ ( sK5_SY224 @ SV16 ) ) )
= $false )
| ( ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $false )
| ( ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(1950,plain,
! [SV165: $i,SV176: $i,SV20: $i] :
( ( ( ( the_mapping @ SV20 @ SV176 )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV165 ) @ ( the_carrier @ SV20 ) @ ( the_mapping @ SV20 @ SV165 ) @ ( the_carrier @ SV176 ) ) )
= $false )
| ( ( subrelstr @ SV176 @ SV165 )
= $false )
| ( ( subnetstr @ SV176 @ SV20 @ SV165 )
= $true )
| ( ( net_str @ SV176 @ SV20 )
= $false )
| ( ( net_str @ SV165 @ SV20 )
= $false )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1951,plain,
! [SV102: $i,SV23: $i,SV149: $i] :
( ( ( element @ SV149 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( one_sorted_str @ SV23 )
= $false )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( element @ SV102 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( ( unordered_pair_as_carrier_subset @ SV23 @ SV102 @ SV149 )
= ( unordered_pair_as_carrier_subset @ SV23 @ SV149 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(1952,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( empty_carrier @ SV48 )
= $true )
| ( ( ~ ( one_sorted_str @ SV48 ) )
= $true )
| ( ( ~ ~ ( empty_carrier @ SV119 ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(1953,plain,
! [SV183: $i,SV51: $i,SV193: $i,SV192: $i] :
( ( ( ~ ( subset @ SV192 @ SV193 )
| ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SV192 )
| ( is_eventually_in @ SV51 @ SV183 @ SV193 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SV192 )
| ( is_often_in @ SV51 @ SV183 @ SV193 ) ) ) )
= $true )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(1954,plain,
! [SV191: $i,SV55: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ ( sK6_SY282 @ SV55 ) )
| ~ ( subset @ SV191 @ SV189 ) )
= $true )
| ( ( in @ SV191 @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(1955,plain,
! [SV55: $i,SV180: $i] :
( ( ( ~ ( in @ SV180 @ ( sK6_SY282 @ SV55 ) ) )
= $false )
| ( ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $false )
| ( ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(1956,plain,
! [SV190: $i,SV16: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ ( sK5_SY224 @ SV16 ) ) )
= $true )
| ( ( ~ ( subset @ SV190 @ SV188 ) )
= $true )
| ( ( in @ SV190 @ ( sK5_SY224 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(1957,plain,
! [SV16: $i,SV184: $i] :
( ( ( ~ ( in @ ( sK16_SY374 @ SV184 @ SV16 ) @ ( sK5_SY224 @ SV16 ) )
| ~ ! [SY380: $i] :
( ~ ( subset @ SY380 @ SV184 )
| ( in @ SY380 @ ( sK16_SY374 @ SV184 @ SV16 ) ) ) )
= $false )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(1958,plain,
! [SV16: $i,SV178: $i] :
( ( ( in @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $true )
| ( ( subset @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $false )
| ( ( are_equipotent @ SV178 @ ( sK5_SY224 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(1959,plain,
! [SV155: $i,SV119: $i,SV48: $i] :
( ( ( one_sorted_str @ SV48 )
= $false )
| ( ( empty_carrier @ SV48 )
= $true )
| ( ( ~ ~ ( empty_carrier @ SV119 ) )
= $true )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(1960,plain,
! [SV183: $i,SV51: $i,SV193: $i,SV192: $i] :
( ( ( ~ ( subset @ SV192 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SV192 )
| ( is_eventually_in @ SV51 @ SV183 @ SV193 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SV192 )
| ( is_often_in @ SV51 @ SV183 @ SV193 ) ) ) )
= $true )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(1961,plain,
! [SV191: $i,SV55: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ ( sK6_SY282 @ SV55 ) ) )
= $true )
| ( ( ~ ( subset @ SV191 @ SV189 ) )
= $true )
| ( ( in @ SV191 @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(1962,plain,
! [SV55: $i,SV180: $i] :
( ( ( in @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $true )
| ( ( subset @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $false )
| ( ( are_equipotent @ SV180 @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(1963,plain,
! [SV190: $i,SV16: $i,SV188: $i] :
( ( ( in @ SV188 @ ( sK5_SY224 @ SV16 ) )
= $false )
| ( ( ~ ( subset @ SV190 @ SV188 ) )
= $true )
| ( ( in @ SV190 @ ( sK5_SY224 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(1964,plain,
! [SV16: $i,SV184: $i] :
( ( ( ~ ( in @ ( sK16_SY374 @ SV184 @ SV16 ) @ ( sK5_SY224 @ SV16 ) ) )
= $false )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(1965,plain,
! [SV16: $i,SV184: $i] :
( ( ( ~ ! [SY380: $i] :
( ~ ( subset @ SY380 @ SV184 )
| ( in @ SY380 @ ( sK16_SY374 @ SV184 @ SV16 ) ) ) )
= $false )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(1966,plain,
! [SV155: $i,SV48: $i,SV119: $i] :
( ( ( ~ ( empty_carrier @ SV119 ) )
= $false )
| ( ( empty_carrier @ SV48 )
= $true )
| ( ( one_sorted_str @ SV48 )
= $false )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(1967,plain,
! [SV183: $i,SV51: $i,SV193: $i,SV192: $i] :
( ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( ~ ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SV192 )
| ( is_eventually_in @ SV51 @ SV183 @ SV193 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SV192 )
| ( is_often_in @ SV51 @ SV183 @ SV193 ) ) ) )
= $true )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(1968,plain,
! [SV191: $i,SV55: $i,SV189: $i] :
( ( ( in @ SV189 @ ( sK6_SY282 @ SV55 ) )
= $false )
| ( ( ~ ( subset @ SV191 @ SV189 ) )
= $true )
| ( ( in @ SV191 @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(1969,plain,
! [SV16: $i,SV188: $i,SV190: $i] :
( ( ( subset @ SV190 @ SV188 )
= $false )
| ( ( in @ SV188 @ ( sK5_SY224 @ SV16 ) )
= $false )
| ( ( in @ SV190 @ ( sK5_SY224 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(1970,plain,
! [SV16: $i,SV184: $i] :
( ( ( in @ ( sK16_SY374 @ SV184 @ SV16 ) @ ( sK5_SY224 @ SV16 ) )
= $true )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1964]) ).
thf(1971,plain,
! [SV16: $i,SV184: $i] :
( ( ( ! [SY380: $i] :
( ~ ( subset @ SY380 @ SV184 )
| ( in @ SY380 @ ( sK16_SY374 @ SV184 @ SV16 ) ) ) )
= $true )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(1972,plain,
! [SV155: $i,SV48: $i,SV119: $i] :
( ( ( empty_carrier @ SV119 )
= $true )
| ( ( empty_carrier @ SV48 )
= $true )
| ( ( one_sorted_str @ SV48 )
= $false )
| ( ( ~ ( net_str @ SV119 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(1973,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SV192 )
| ( is_eventually_in @ SV51 @ SV183 @ SV193 ) )
| ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SV192 )
| ( is_often_in @ SV51 @ SV183 @ SV193 ) ) )
= $false )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(1974,plain,
! [SV55: $i,SV189: $i,SV191: $i] :
( ( ( subset @ SV191 @ SV189 )
= $false )
| ( ( in @ SV189 @ ( sK6_SY282 @ SV55 ) )
= $false )
| ( ( in @ SV191 @ ( sK6_SY282 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(1975,plain,
! [SV16: $i,SV184: $i,SV194: $i] :
( ( ( ~ ( subset @ SV194 @ SV184 )
| ( in @ SV194 @ ( sK16_SY374 @ SV184 @ SV16 ) ) )
= $true )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(1976,plain,
! [SV155: $i,SV48: $i,SV119: $i] :
( ( ( net_str @ SV119 @ SV48 )
= $false )
| ( ( one_sorted_str @ SV48 )
= $false )
| ( ( empty_carrier @ SV48 )
= $true )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( ~ ( element @ SV155 @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(1977,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( ~ ( ~ ( is_eventually_in @ SV51 @ SV183 @ SV192 )
| ( is_eventually_in @ SV51 @ SV183 @ SV193 ) ) )
= $false )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(1978,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( ~ ( ~ ( is_often_in @ SV51 @ SV183 @ SV192 )
| ( is_often_in @ SV51 @ SV183 @ SV193 ) ) )
= $false )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(1979,plain,
! [SV16: $i,SV184: $i,SV194: $i] :
( ( ( ~ ( subset @ SV194 @ SV184 ) )
= $true )
| ( ( in @ SV194 @ ( sK16_SY374 @ SV184 @ SV16 ) )
= $true )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(1980,plain,
! [SV48: $i,SV119: $i,SV155: $i] :
( ( ( element @ SV155 @ ( the_carrier @ SV119 ) )
= $false )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( empty_carrier @ SV48 )
= $true )
| ( ( one_sorted_str @ SV48 )
= $false )
| ( ( net_str @ SV119 @ SV48 )
= $false )
| ( ( element @ ( apply_netmap @ SV48 @ SV119 @ SV155 ) @ ( the_carrier @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(1981,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( ~ ( is_eventually_in @ SV51 @ SV183 @ SV192 )
| ( is_eventually_in @ SV51 @ SV183 @ SV193 ) )
= $true )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(1982,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( ~ ( is_often_in @ SV51 @ SV183 @ SV192 )
| ( is_often_in @ SV51 @ SV183 @ SV193 ) )
= $true )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(1983,plain,
! [SV16: $i,SV184: $i,SV194: $i] :
( ( ( subset @ SV194 @ SV184 )
= $false )
| ( ( in @ SV194 @ ( sK16_SY374 @ SV184 @ SV16 ) )
= $true )
| ( ( in @ SV184 @ ( sK5_SY224 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(1984,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( ~ ( is_eventually_in @ SV51 @ SV183 @ SV192 ) )
= $true )
| ( ( is_eventually_in @ SV51 @ SV183 @ SV193 )
= $true )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(1985,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( ~ ( is_often_in @ SV51 @ SV183 @ SV192 ) )
= $true )
| ( ( is_often_in @ SV51 @ SV183 @ SV193 )
= $true )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(1986,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( is_eventually_in @ SV51 @ SV183 @ SV192 )
= $false )
| ( ( is_eventually_in @ SV51 @ SV183 @ SV193 )
= $true )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(1987,plain,
! [SV193: $i,SV192: $i,SV183: $i,SV51: $i] :
( ( ( is_often_in @ SV51 @ SV183 @ SV192 )
= $false )
| ( ( is_often_in @ SV51 @ SV183 @ SV193 )
= $true )
| ( ( subset @ SV192 @ SV193 )
= $false )
| ( ( empty_carrier @ SV183 )
= $true )
| ( ( net_str @ SV183 @ SV51 )
= $false )
| ( ( empty_carrier @ SV51 )
= $true )
| ( ( one_sorted_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(1988,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[956,1987,1986,1983,1980,1974,1970,1969,1962,1958,1951,1950,1940,1939,1935,1923,1922,1920,1909,1908,1907,1903,1902,1891,1886,1885,1880,1878,1875,1874,1867,1858,1857,1852,1851,1848,1836,1835,1834,1833,1817,1816,1813,1803,1802,1800,1799,1793,1781,1780,1777,1762,1755,1743,1741,1733,1732,1730,1729,1726,1720,1717,1716,1714,1713,1707,1706,1705,1699,1698,1697,1694,1683,1681,1680,1677,1673,1672,1665,1658,1657,1652,1642,1641,1635,1634,1629,1611,1608,1607,1604,1603,1597,1596,1594,1588,1578,1570,1562,1547,1540,1530,1522,1478,1459,1456,1450,1449,1446,1435,1432,1428,1426,1424,1423,1419,1406,1397,1394,1393,1387,1386,1381,1372,1368,1364,1354,1346,1333,1332,1320,1316,1315,1312,1304,1303,1295,1286,1285,1189,1188,1187,1186,1096,1007,996,993,992,989,985,984,983,982,980,978,977,976,974,973,972,970,969,967,966,965,964,963,961,960,959,958,957]) ).
thf(1989,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU373+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n014.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 15:17:22 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.77/2.32 .......
% 12.77/2.32
% 12.77/2.32 No.of.Axioms: 118
% 12.77/2.32
% 12.77/2.32 Length.of.Defs: 0
% 12.77/2.32
% 12.77/2.32 Contains.Choice.Funs: false
% 12.77/2.32 ...............................................
% 12.77/2.32
% 12.77/2.32 ********************************
% 12.77/2.32 * All subproblems solved! *
% 12.77/2.32 ********************************
% 12.77/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:119,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:1988,loop_count:0,foatp_calls:1,translation:fof_full)
% 12.77/2.32
% 12.77/2.32 %**** Beginning of derivation protocol ****
% 12.77/2.32 % SZS output start CNFRefutation
% See solution above
% 12.77/2.33
% 12.77/2.33 %**** End of derivation protocol ****
% 12.77/2.33 %**** no. of clauses in derivation: 1344 ****
% 12.77/2.33 %**** clause counter: 1988 ****
% 12.77/2.33
% 12.77/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:119,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:1988,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------