%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU321+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 : n017.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 10:43:57 AM UTC 2026
% Result : Theorem 19.81s 3.52s
% Output : CNFRefutation 19.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 93
% Syntax : Number of formulae : 1851 ( 530 unt; 0 typ; 0 def)
% Number of atoms : 16673 (6598 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 35783 (10356 ~;6030 |; 148 &;18981 @)
% ( 91 <=>; 177 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 172 ( 169 usr; 9 con; 0-6 aty)
% Number of variables : 5149 ( 0 ^;5110 !; 39 ?;5149 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_apply_binary,type,
apply_binary: $i > $i > $i > $i ).
thf(tp_apply_binary_as_element,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_below,type,
below: $i > $i > $i > $o ).
thf(tp_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_subset,type,
cast_to_subset: $i > $i ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_carrier_subset,type,
empty_carrier_subset: $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_equipotent,type,
equipotent: $i > $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_join,type,
join: $i > $i > $i > $i ).
thf(tp_join_commut,type,
join_commut: $i > $i > $i > $i ).
thf(tp_join_commutative,type,
join_commutative: $i > $o ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_meet,type,
meet: $i > $i > $i > $i ).
thf(tp_meet_absorbing,type,
meet_absorbing: $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_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_open_subset,type,
open_subset: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $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_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $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_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_as_subset,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SY311,type,
sK10_SY311: $i ).
thf(tp_sK11_SY281,type,
sK11_SY281: $i > $i > $i ).
thf(tp_sK12_SY338,type,
sK12_SY338: $i > $i ).
thf(tp_sK13_SY302,type,
sK13_SY302: $i > $i > $i ).
thf(tp_sK14_SY342,type,
sK14_SY342: $i > $i ).
thf(tp_sK15_SY345,type,
sK15_SY345: $i > $i ).
thf(tp_sK16_SY239,type,
sK16_SY239: $i > $i ).
thf(tp_sK17_SY348,type,
sK17_SY348: $i > $i ).
thf(tp_sK18_SY181,type,
sK18_SY181: $i > $i ).
thf(tp_sK19_SY230,type,
sK19_SY230: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY279,type,
sK20_SY279: $i > $i > $i ).
thf(tp_sK21_SY283,type,
sK21_SY283: $i > $i > $i ).
thf(tp_sK22_SY350,type,
sK22_SY350: $i > $i ).
thf(tp_sK23_SY295,type,
sK23_SY295: $i > $i > $i ).
thf(tp_sK24_SY316,type,
sK24_SY316: $i > $i > $i ).
thf(tp_sK25_SY325,type,
sK25_SY325: $i > $i > $i ).
thf(tp_sK26_SY193,type,
sK26_SY193: $i > $i ).
thf(tp_sK27_SY245,type,
sK27_SY245: $i > $i ).
thf(tp_sK28_SY331,type,
sK28_SY331: $i > $i > $i > $i ).
thf(tp_sK29_SY333,type,
sK29_SY333: $i > $i > $i > $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK30_SY335,type,
sK30_SY335: $i > $i > $i > $i ).
thf(tp_sK31_SY337,type,
sK31_SY337: $i > $i > $i > $i ).
thf(tp_sK32_SY183,type,
sK32_SY183: $i > $i ).
thf(tp_sK33_SY341,type,
sK33_SY341: $i > $i > $i > $i > $i ).
thf(tp_sK34_SY289,type,
sK34_SY289: $i > $i > $i ).
thf(tp_sK35_SY193,type,
sK35_SY193: $i > $i ).
thf(tp_sK36_SY347,type,
sK36_SY347: $i > $i > $i > $i ).
thf(tp_sK37_SY245,type,
sK37_SY245: $i > $i ).
thf(tp_sK38_SY352,type,
sK38_SY352: $i > $i > $i > $i ).
thf(tp_sK39_SY193,type,
sK39_SY193: $i > $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK40_SY245,type,
sK40_SY245: $i > $i ).
thf(tp_sK41_SY362,type,
sK41_SY362: $i > $i > $i ).
thf(tp_sK42_SY355,type,
sK42_SY355: $i > $i > $i ).
thf(tp_sK43_SY364,type,
sK43_SY364: $i > $i > $i ).
thf(tp_sK44_SY193,type,
sK44_SY193: $i > $i ).
thf(tp_sK45_SY193,type,
sK45_SY193: $i > $i ).
thf(tp_sK46_SY245,type,
sK46_SY245: $i > $i ).
thf(tp_sK47_SY245,type,
sK47_SY245: $i > $i ).
thf(tp_sK48_SY372,type,
sK48_SY372: $i > $i > $i ).
thf(tp_sK49_SY374,type,
sK49_SY374: $i > $i > $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK50_SY355,type,
sK50_SY355: $i > $i > $i > $i ).
thf(tp_sK51_SY382,type,
sK51_SY382: $i > $i > $i ).
thf(tp_sK52_SY384,type,
sK52_SY384: $i > $i > $i ).
thf(tp_sK53_SY398,type,
sK53_SY398: $i > $i > $i ).
thf(tp_sK54_SY400,type,
sK54_SY400: $i > $i > $i ).
thf(tp_sK55_SY402,type,
sK55_SY402: $i > $i > $i ).
thf(tp_sK56_SY404,type,
sK56_SY404: $i > $i > $i ).
thf(tp_sK5_SY211,type,
sK5_SY211: $i > $i ).
thf(tp_sK6_SY237,type,
sK6_SY237: $i > $i ).
thf(tp_sK7_SY240,type,
sK7_SY240: $i > $i ).
thf(tp_sK8_SY190,type,
sK8_SY190: $i > $i ).
thf(tp_sK9_SX1,type,
sK9_SX1: $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_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_succ,type,
succ: $i > $i ).
thf(tp_the_L_join,type,
the_L_join: $i > $i ).
thf(tp_the_L_meet,type,
the_L_meet: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_topology,type,
the_topology: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $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_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(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(20,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
thf(27,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( in @ D @ A )
& ( C
= ( singleton @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
thf(46,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(48,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(54,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(61,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(119,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(120,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(137,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(141,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(145,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(149,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(150,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(152,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(153,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(154,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(155,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(156,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(168,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(169,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(170,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(174,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(175,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(177,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(179,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(180,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(182,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(183,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(184,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(185,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(186,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(190,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(191,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(193,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(194,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(195,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(196,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(197,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(198,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(199,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(201,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(202,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(203,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(204,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(239,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(241,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(242,axiom,
! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(254,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(255,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(298,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(312,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(323,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(364,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(423,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(472,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(481,axiom,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(491,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(512,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(523,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) )
<=> ~ ( in @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
thf(524,negated_conjecture,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) )
<=> ~ ( in @ C @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[523]) ).
thf(525,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) )
<=> ~ ( in @ C @ B ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[524]) ).
thf(526,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(527,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(528,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(529,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(530,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(534,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(535,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( in @ D @ A )
& ( C
= ( singleton @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(536,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(537,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(538,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(539,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(542,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(543,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(544,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(545,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(546,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(547,plain,
$true = $true,
inference(unfold_def,[status(thm)],[145]) ).
thf(548,plain,
$true = $true,
inference(unfold_def,[status(thm)],[149]) ).
thf(549,plain,
$true = $true,
inference(unfold_def,[status(thm)],[150]) ).
thf(550,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(551,plain,
$true = $true,
inference(unfold_def,[status(thm)],[153]) ).
thf(552,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(553,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(554,plain,
$true = $true,
inference(unfold_def,[status(thm)],[156]) ).
thf(555,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(556,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(557,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(558,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(559,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(560,plain,
$true = $true,
inference(unfold_def,[status(thm)],[168]) ).
thf(561,plain,
$true = $true,
inference(unfold_def,[status(thm)],[169]) ).
thf(562,plain,
$true = $true,
inference(unfold_def,[status(thm)],[170]) ).
thf(563,plain,
$true = $true,
inference(unfold_def,[status(thm)],[174]) ).
thf(564,plain,
$true = $true,
inference(unfold_def,[status(thm)],[175]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(566,plain,
$true = $true,
inference(unfold_def,[status(thm)],[177]) ).
thf(567,plain,
$true = $true,
inference(unfold_def,[status(thm)],[179]) ).
thf(568,plain,
$true = $true,
inference(unfold_def,[status(thm)],[180]) ).
thf(569,plain,
$true = $true,
inference(unfold_def,[status(thm)],[182]) ).
thf(570,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(571,plain,
$true = $true,
inference(unfold_def,[status(thm)],[184]) ).
thf(572,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(573,plain,
$true = $true,
inference(unfold_def,[status(thm)],[186]) ).
thf(574,plain,
$true = $true,
inference(unfold_def,[status(thm)],[190]) ).
thf(575,plain,
$true = $true,
inference(unfold_def,[status(thm)],[191]) ).
thf(576,plain,
$true = $true,
inference(unfold_def,[status(thm)],[193]) ).
thf(577,plain,
$true = $true,
inference(unfold_def,[status(thm)],[194]) ).
thf(578,plain,
$true = $true,
inference(unfold_def,[status(thm)],[195]) ).
thf(579,plain,
$true = $true,
inference(unfold_def,[status(thm)],[196]) ).
thf(580,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(581,plain,
$true = $true,
inference(unfold_def,[status(thm)],[198]) ).
thf(582,plain,
$true = $true,
inference(unfold_def,[status(thm)],[199]) ).
thf(583,plain,
$true = $true,
inference(unfold_def,[status(thm)],[201]) ).
thf(584,plain,
$true = $true,
inference(unfold_def,[status(thm)],[202]) ).
thf(585,plain,
$true = $true,
inference(unfold_def,[status(thm)],[203]) ).
thf(586,plain,
$true = $true,
inference(unfold_def,[status(thm)],[204]) ).
thf(587,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(588,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(589,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(590,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(591,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(592,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(593,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(594,plain,
( ( ! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(595,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(596,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(597,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(598,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(599,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(600,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(601,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(602,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(603,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(604,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(605,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(606,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(607,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(608,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(609,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(610,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(611,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(612,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(613,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(614,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(615,plain,
( ( ! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(616,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(617,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(618,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( one_sorted_str @ sK1_A ) )
=> ! [SY163: $i] :
( ( element @ SY163 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ! [SY164: $i] :
( ( element @ SY164 @ ( the_carrier @ sK1_A ) )
=> ( ( in @ SY164 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY163 ) )
<=> ~ ( in @ SY164 @ SY163 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[525]) ).
thf(619,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[618]) ).
thf(620,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[618]) ).
thf(621,plain,
( ( ! [SY163: $i] :
( ( element @ SY163 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ! [SY164: $i] :
( ( element @ SY164 @ ( the_carrier @ sK1_A ) )
=> ( ( in @ SY164 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY163 ) )
<=> ~ ( in @ SY164 @ SY163 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[618]) ).
thf(622,plain,
( ( ~ ! [SY163: $i] :
( ( element @ SY163 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ! [SY164: $i] :
( ( element @ SY164 @ ( the_carrier @ sK1_A ) )
=> ( ( in @ SY164 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY163 ) )
<=> ~ ( in @ SY164 @ SY163 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[621]) ).
thf(623,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(624,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(625,plain,
( ( ! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(626,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(627,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(628,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(629,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(630,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(631,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(632,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(633,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(634,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(635,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(636,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(637,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(638,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(639,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(640,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(641,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(642,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(643,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(644,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(645,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(646,plain,
( ( ! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(647,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(648,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(649,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(650,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(651,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(652,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(653,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(654,plain,
$true = $true,
inference(copy,[status(thm)],[586]) ).
thf(655,plain,
$true = $true,
inference(copy,[status(thm)],[585]) ).
thf(656,plain,
$true = $true,
inference(copy,[status(thm)],[584]) ).
thf(657,plain,
$true = $true,
inference(copy,[status(thm)],[583]) ).
thf(658,plain,
$true = $true,
inference(copy,[status(thm)],[582]) ).
thf(659,plain,
$true = $true,
inference(copy,[status(thm)],[581]) ).
thf(660,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(661,plain,
$true = $true,
inference(copy,[status(thm)],[579]) ).
thf(662,plain,
$true = $true,
inference(copy,[status(thm)],[578]) ).
thf(663,plain,
$true = $true,
inference(copy,[status(thm)],[577]) ).
thf(664,plain,
$true = $true,
inference(copy,[status(thm)],[576]) ).
thf(665,plain,
$true = $true,
inference(copy,[status(thm)],[575]) ).
thf(666,plain,
$true = $true,
inference(copy,[status(thm)],[574]) ).
thf(667,plain,
$true = $true,
inference(copy,[status(thm)],[573]) ).
thf(668,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(669,plain,
$true = $true,
inference(copy,[status(thm)],[571]) ).
thf(670,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(671,plain,
$true = $true,
inference(copy,[status(thm)],[569]) ).
thf(672,plain,
$true = $true,
inference(copy,[status(thm)],[568]) ).
thf(673,plain,
$true = $true,
inference(copy,[status(thm)],[567]) ).
thf(674,plain,
$true = $true,
inference(copy,[status(thm)],[566]) ).
thf(675,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(676,plain,
$true = $true,
inference(copy,[status(thm)],[564]) ).
thf(677,plain,
$true = $true,
inference(copy,[status(thm)],[563]) ).
thf(678,plain,
$true = $true,
inference(copy,[status(thm)],[562]) ).
thf(679,plain,
$true = $true,
inference(copy,[status(thm)],[561]) ).
thf(680,plain,
$true = $true,
inference(copy,[status(thm)],[560]) ).
thf(681,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(682,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(683,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(684,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(685,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(686,plain,
$true = $true,
inference(copy,[status(thm)],[554]) ).
thf(687,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(688,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(689,plain,
$true = $true,
inference(copy,[status(thm)],[551]) ).
thf(690,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(691,plain,
$true = $true,
inference(copy,[status(thm)],[549]) ).
thf(692,plain,
$true = $true,
inference(copy,[status(thm)],[548]) ).
thf(693,plain,
$true = $true,
inference(copy,[status(thm)],[547]) ).
thf(694,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(695,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(696,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(697,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(698,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(699,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(700,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(701,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(702,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(703,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(704,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(705,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( in @ D @ A )
& ( C
= ( singleton @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(706,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(707,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(708,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(709,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(710,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(711,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(712,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(713,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(714,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(715,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(716,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(717,plain,
( ( ~ ! [SY163: $i] :
( ( element @ SY163 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ! [SY164: $i] :
( ( element @ SY164 @ ( the_carrier @ sK1_A ) )
=> ( ( in @ SY164 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY163 ) )
<=> ~ ( in @ SY164 @ SY163 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(718,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[714]) ).
thf(719,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) )
| ~ ( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(720,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ SX1 )
= ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(721,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(722,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)],[648]) ).
thf(723,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[711]) ).
thf(724,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(725,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ~ ( in @ SX1 @ SX2 ) )
| ~ ( ( SX1 != SX2 ) ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ~ ( in @ SX1 @ SX2 ) )
| ~ ( ( SX1 != SX2 ) ) )
| ~ ~ ( in @ SX2 @ SX1 ) )
| ( epsilon_connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(726,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(727,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != empty_set ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( subset_complement @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(728,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( in @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(729,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( complements_of_subsets @ SX0 @ ( complements_of_subsets @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(730,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(731,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( SX2
!= ( singleton @ SX1 ) ) )
| ~ ( in @ SX1 @ SX0 ) )
| ( SX3
!= ( singleton @ SX1 ) ) )
| ( SX2 = SX3 ) )
| ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX0 ) )
| ( SX2
!= ( singleton @ SX3 ) ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX0 ) )
| ( SX2
!= ( singleton @ SX3 ) ) )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[705]) ).
thf(732,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( meet_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(733,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_difference @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(734,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_intersection2 @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(735,plain,
( ( ~ ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(736,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(737,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(738,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( empty_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(739,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[713]) ).
thf(740,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(741,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[712]) ).
thf(742,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(743,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(744,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(745,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(746,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)],[710]) ).
thf(747,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(748,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX0 @ SX1 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(749,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( SX3
!= ( unordered_triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX4: $i] :
~ ( ~ ( ~ ( in @ SX4 @ SX3 )
| ~ ~ ( ~ ~ ( ~ ( ( SX4 != SX0 ) )
| ~ ( ( SX4 != SX1 ) ) )
| ~ ( ( SX4 != SX2 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SX4 != SX0 ) )
| ~ ( ( SX4 != SX1 ) ) )
| ~ ( ( SX4 != SX2 ) ) )
| ( in @ SX4 @ SX3 ) ) ) )
| ~ ( ~ ! [SX4: $i] :
~ ( ~ ( ~ ( in @ SX4 @ SX3 )
| ~ ~ ( ~ ~ ( ~ ( ( SX4 != SX0 ) )
| ~ ( ( SX4 != SX1 ) ) )
| ~ ( ( SX4 != SX2 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SX4 != SX0 ) )
| ~ ( ( SX4 != SX1 ) ) )
| ~ ( ( SX4 != SX2 ) ) )
| ( in @ SX4 @ SX3 ) ) )
| ( SX3
= ( unordered_triple @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(750,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(751,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(752,plain,
( ( ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(753,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(754,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( empty @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(755,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(756,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ( ( SX2
!= ( complements_of_subsets @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) )
| ( SX2
= ( complements_of_subsets @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(757,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( ordinal @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( ordinal @ SX2 ) )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(758,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(759,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(760,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(761,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX1 != SX2 )
| ~ ( ordinal @ SX2 ) )
| ( SX1 != SX3 ) )
| ~ ( ordinal @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX3 != SX2 ) )
| ~ ( ordinal @ SX2 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX3 != SX2 ) )
| ~ ( ordinal @ SX2 ) )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(762,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX2 )
= ( subset_intersection2 @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(763,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(764,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( ~ ( in @ SX1 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[717]) ).
thf(765,plain,
( ( ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(766,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(767,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(768,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(769,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(770,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( complements_of_subsets @ SX0 @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(771,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)],[642]) ).
thf(772,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[707]) ).
thf(773,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(774,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(775,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(776,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(777,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(778,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( cast_as_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(779,plain,
! [SV1: $i] :
( ( in @ SV1 @ ( succ @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(780,plain,
! [SV2: $i] :
( ( ( union @ ( powerset @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(781,plain,
! [SV3: $i] :
( ( element @ ( cast_to_subset @ SV3 ) @ ( powerset @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(782,plain,
! [SV4: $i] :
( ( ~ ( empty @ ( powerset @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(783,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(784,plain,
! [SV5: $i] :
( ( ! [SY165: $i] :
~ ~ ( ~ ( in @ SV5 @ SY165 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY165 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY165 )
| ~ ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(785,plain,
! [SV6: $i] :
( ( ! [SY168: $i] :
~ ( ~ ( ~ ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SY168 @ SV6 )
| ( in @ SY168 @ SV6 ) )
| ~ ( ~ ( in @ SY168 @ SV6 )
| ( element @ SY168 @ SV6 ) ) ) )
| ~ ( ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SY168 @ SV6 )
| ( empty @ SY168 ) )
| ~ ( ~ ( empty @ SY168 )
| ( element @ SY168 @ SV6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(786,plain,
! [SV7: $i] :
( ( ! [SY169: $i] :
( ~ ( element @ SY169 @ ( powerset @ SV7 ) )
| ( ( subset_complement @ SV7 @ SY169 )
= ( set_difference @ SV7 @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(787,plain,
! [SV8: $i] :
( ( ! [SY170: $i] :
( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV8 )
| ( in @ SY171 @ SY170 ) )
| ~ ( ~ ( in @ SY171 @ SY170 )
| ( in @ SY171 @ SV8 ) ) )
| ( SV8 = SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(788,plain,
! [SV9: $i] :
( ( ! [SY172: $i] :
~ ( ~ ( ~ ( subset @ SV9 @ SY172 )
| ! [SY173: $i] :
( ~ ( in @ SY173 @ SV9 )
| ( in @ SY173 @ SY172 ) ) )
| ~ ( ~ ! [SY174: $i] :
( ~ ( in @ SY174 @ SV9 )
| ( in @ SY174 @ SY172 ) )
| ( subset @ SV9 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(789,plain,
! [SV10: $i] :
( ( ! [SY175: $i,SY176: $i] :
( ~ ~ ( ~ ( in @ SV10 @ SY175 )
| ~ ( element @ SY175 @ ( powerset @ SY176 ) ) )
| ( element @ SV10 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(790,plain,
! [SV11: $i] :
( ( ! [SY177: $i,SY178: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SY177 )
| ~ ( in @ SY177 @ SY178 ) )
| ~ ( in @ SY178 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(791,plain,
! [SV12: $i] :
( ( ~ ( ~ ( ~ ( epsilon_connected @ SV12 )
| ! [SY179: $i,SY180: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY179 @ SV12 )
| ~ ( in @ SY180 @ SV12 ) )
| ~ ~ ( in @ SY179 @ SY180 ) )
| ~ ( ( SY179 != SY180 ) ) )
| ~ ~ ( in @ SY180 @ SY179 ) ) )
| ~ ( ~ ! [SY181: $i,SY182: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY181 @ SV12 )
| ~ ( in @ SY182 @ SV12 ) )
| ~ ~ ( in @ SY181 @ SY182 ) )
| ~ ( ( SY181 != SY182 ) ) )
| ~ ~ ( in @ SY182 @ SY181 ) )
| ( epsilon_connected @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(792,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV13 )
| ~ ( one_sorted_str @ SV13 ) )
| ~ ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(793,plain,
! [SV14: $i] :
( ( ~ ( ( SV14 != empty_set ) )
| ! [SY184: $i] :
( ~ ( element @ SY184 @ ( powerset @ SV14 ) )
| ! [SY185: $i] :
( ~ ( element @ SY185 @ SV14 )
| ~ ~ ( in @ SY185 @ SY184 )
| ( in @ SY185 @ ( subset_complement @ SV14 @ SY184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(794,plain,
! [SV15: $i] :
( ( ! [SY186: $i,SY187: $i] :
( ~ ( element @ SY187 @ ( powerset @ SV15 ) )
| ~ ~ ( ~ ( in @ SY186 @ ( subset_complement @ SV15 @ SY187 ) )
| ~ ( in @ SY186 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(795,plain,
! [SV16: $i] :
( ( ! [SY188: $i] :
( ~ ( element @ SY188 @ ( powerset @ ( powerset @ SV16 ) ) )
| ( ( complements_of_subsets @ SV16 @ ( complements_of_subsets @ SV16 @ SY188 ) )
= SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(796,plain,
! [SV17: $i] :
( ( ! [SY189: $i] :
( ~ ( element @ SV17 @ SY189 )
| ( empty @ SY189 )
| ( in @ SV17 @ SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(797,plain,
! [SV18: $i] :
( ( ~ ! [SY190: $i,SY191: $i,SY192: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV18 )
| ( SY191
!= ( singleton @ SY190 ) ) )
| ~ ( in @ SY190 @ SV18 ) )
| ( SY192
!= ( singleton @ SY190 ) ) )
| ( SY191 = SY192 ) )
| ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(798,plain,
! [SV19: $i] :
( ( ! [SY197: $i] :
( ~ ( element @ SY197 @ ( powerset @ ( powerset @ SV19 ) ) )
| ( element @ ( meet_of_subsets @ SV19 @ SY197 ) @ ( powerset @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(799,plain,
! [SV20: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ~ ~ ( ~ ( element @ SY198 @ ( powerset @ SV20 ) )
| ~ ( element @ SY199 @ ( powerset @ SV20 ) ) )
| ( element @ ( subset_difference @ SV20 @ SY198 @ SY199 ) @ ( powerset @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(800,plain,
! [SV21: $i] :
( ( ! [SY200: $i,SY201: $i] :
( ~ ~ ( ~ ( element @ SY200 @ ( powerset @ SV21 ) )
| ~ ( element @ SY201 @ ( powerset @ SV21 ) ) )
| ( element @ ( subset_intersection2 @ SV21 @ SY200 @ SY201 ) @ ( powerset @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(801,plain,
( ( ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(802,plain,
! [SV22: $i] :
( ( ! [SY202: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV22 @ SY202 )
| ~ ! [SY203: $i] :
~ ~ ( ~ ( in @ SY203 @ SV22 )
| ~ ( in @ SY203 @ SY202 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY204: $i] :
~ ~ ( ~ ( in @ SY204 @ SV22 )
| ~ ( in @ SY204 @ SY202 ) )
| ~ ( disjoint @ SV22 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(803,plain,
! [SV23: $i] :
( ( ~ ( v1_membered @ SV23 )
| ! [SY205: $i] :
( ~ ( element @ SY205 @ ( powerset @ SV23 ) )
| ( v1_membered @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(804,plain,
! [SV24: $i] :
( ( ~ ( one_sorted_str @ SV24 )
| ( element @ ( empty_carrier_subset @ SV24 ) @ ( powerset @ ( the_carrier @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(805,plain,
! [SV25: $i] :
( ( ! [SY206: $i] :
~ ~ ( ~ ( in @ SV25 @ SY206 )
| ~ ( empty @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(806,plain,
! [SV26: $i] :
( ( ! [SY207: $i] :
( ~ ( element @ SY207 @ ( powerset @ SV26 ) )
| ( element @ ( subset_complement @ SV26 @ SY207 ) @ ( powerset @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(807,plain,
! [SV27: $i] :
( ( ! [SY208: $i,SY209: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV27 @ SY208 )
| ~ ( element @ SY208 @ ( powerset @ SY209 ) ) )
| ~ ( empty @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(808,plain,
! [SV28: $i] :
( ( ! [SY210: $i] :
( ~ ( element @ SY210 @ ( powerset @ SV28 ) )
| ( ( subset_complement @ SV28 @ ( subset_complement @ SV28 @ SY210 ) )
= SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(809,plain,
! [SV29: $i] :
( ( ~ ! [SY211: $i] :
~ ( element @ SY211 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(810,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(811,plain,
! [SV30: $i] :
( ( ~ ( finite @ SV30 )
| ! [SY212: $i] :
( ~ ( element @ SY212 @ ( powerset @ SV30 ) )
| ( finite @ SY212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(812,plain,
! [SV31: $i] :
( ( ! [SY213: $i] :
~ ( ~ ( ~ ( element @ SV31 @ ( powerset @ SY213 ) )
| ( subset @ SV31 @ SY213 ) )
| ~ ( ~ ( subset @ SV31 @ SY213 )
| ( element @ SV31 @ ( powerset @ SY213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(813,plain,
! [SV32: $i] :
( ( ! [SY214: $i] :
~ ( ~ ( ( SY214
!= ( union @ SV32 ) )
| ! [SY215: $i] :
~ ( ~ ( ~ ( in @ SY215 @ SY214 )
| ~ ! [SY216: $i] :
~ ~ ( ~ ( in @ SY215 @ SY216 )
| ~ ( in @ SY216 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( in @ SY215 @ SY217 )
| ~ ( in @ SY217 @ SV32 ) )
| ( in @ SY215 @ SY214 ) ) ) )
| ~ ( ~ ! [SY218: $i] :
~ ( ~ ( ~ ( in @ SY218 @ SY214 )
| ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY218 @ SY219 )
| ~ ( in @ SY219 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ( in @ SY218 @ SY220 )
| ~ ( in @ SY220 @ SV32 ) )
| ( in @ SY218 @ SY214 ) ) )
| ( SY214
= ( union @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(814,plain,
! [SV33: $i] :
( ( ! [SY221: $i] :
( ~ ( ordinal @ SY221 )
| ~ ( in @ SV33 @ SY221 )
| ( ordinal @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(815,plain,
! [SV34: $i] :
( ( ! [SY222: $i,SY223: $i,SY224: $i] :
~ ( ~ ( ( SY224
!= ( unordered_triple @ SV34 @ SY222 @ SY223 ) )
| ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SY224 )
| ~ ~ ( ~ ~ ( ~ ( ( SY225 != SV34 ) )
| ~ ( ( SY225 != SY222 ) ) )
| ~ ( ( SY225 != SY223 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY225 != SV34 ) )
| ~ ( ( SY225 != SY222 ) ) )
| ~ ( ( SY225 != SY223 ) ) )
| ( in @ SY225 @ SY224 ) ) ) )
| ~ ( ~ ! [SY226: $i] :
~ ( ~ ( ~ ( in @ SY226 @ SY224 )
| ~ ~ ( ~ ~ ( ~ ( ( SY226 != SV34 ) )
| ~ ( ( SY226 != SY222 ) ) )
| ~ ( ( SY226 != SY223 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY226 != SV34 ) )
| ~ ( ( SY226 != SY222 ) ) )
| ~ ( ( SY226 != SY223 ) ) )
| ( in @ SY226 @ SY224 ) ) )
| ( SY224
= ( unordered_triple @ SV34 @ SY222 @ SY223 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(816,plain,
! [SV35: $i] :
( ( ! [SY227: $i] :
( ~ ! [SY228: $i] :
( ~ ( in @ SY228 @ SV35 )
| ( in @ SY228 @ SY227 ) )
| ( element @ SV35 @ ( powerset @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(817,plain,
! [SV36: $i] :
( ( ~ ( ~ ( ( SV36 != empty_set )
| ! [SY229: $i] :
~ ( in @ SY229 @ SV36 ) )
| ~ ( ~ ! [SY230: $i] :
~ ( in @ SY230 @ SV36 )
| ( SV36 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(818,plain,
! [SV37: $i] :
( ( ~ ( meet_semilatt_str @ SV37 )
| ( one_sorted_str @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(819,plain,
! [SV38: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ~ ~ ( ~ ( element @ SY231 @ ( powerset @ SV38 ) )
| ~ ( element @ SY232 @ ( powerset @ SV38 ) ) )
| ( ( subset_intersection2 @ SV38 @ SY231 @ SY231 )
= SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(820,plain,
! [SV39: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV39 )
| ~ ( one_sorted_str @ SV39 ) )
| ~ ( empty @ ( the_carrier @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(821,plain,
! [SV40: $i] :
( ( ~ ( top_str @ SV40 )
| ( one_sorted_str @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(822,plain,
! [SV41: $i] :
( ( ! [SY233: $i] :
( ~ ( element @ SY233 @ ( powerset @ ( powerset @ SV41 ) ) )
| ! [SY234: $i] :
( ~ ( element @ SY234 @ ( powerset @ ( powerset @ SV41 ) ) )
| ~ ( ~ ( ( SY234
!= ( complements_of_subsets @ SV41 @ SY233 ) )
| ! [SY235: $i] :
( ~ ( element @ SY235 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY235 @ SY234 )
| ( in @ ( subset_complement @ SV41 @ SY235 ) @ SY233 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY235 ) @ SY233 )
| ( in @ SY235 @ SY234 ) ) ) ) )
| ~ ( ~ ! [SY236: $i] :
( ~ ( element @ SY236 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY236 @ SY234 )
| ( in @ ( subset_complement @ SV41 @ SY236 ) @ SY233 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY236 ) @ SY233 )
| ( in @ SY236 @ SY234 ) ) ) )
| ( SY234
= ( complements_of_subsets @ SV41 @ SY233 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(823,plain,
! [SV42: $i] :
( ( ~ ! [SY237: $i] :
~ ! [SY238: $i] :
~ ( ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( ~ ( in @ SY238 @ SV42 )
| ~ ( ordinal @ SY238 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY238 @ SV42 )
| ~ ( ordinal @ SY238 ) )
| ( in @ SY238 @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(824,plain,
! [SV43: $i] :
( ( ~ ~ ( empty @ SV43 )
| ~ ! [SY239: $i] :
~ ~ ( ~ ( element @ SY239 @ ( powerset @ SV43 ) )
| ~ ~ ( empty @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(825,plain,
! [SV44: $i] :
( ( ~ ! [SY240: $i] :
~ ~ ( ~ ( element @ SY240 @ ( powerset @ SV44 ) )
| ~ ( empty @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(826,plain,
! [SV45: $i] :
( ( ~ ( ordinal @ SV45 )
| ! [SY241: $i] :
( ~ ( ordinal @ SY241 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SV45 @ SY241 )
| ~ ( ( SV45 != SY241 ) ) )
| ~ ~ ( in @ SY241 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(827,plain,
! [SV46: $i] :
( ( ~ ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX1 != SX2 )
| ~ ( ordinal @ SX2 ) )
| ( SX1 != SX3 ) )
| ~ ( ordinal @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(828,plain,
! [SV47: $i] :
( ( ! [SY249: $i,SY250: $i] :
( ~ ~ ( ~ ( element @ SY249 @ ( powerset @ SV47 ) )
| ~ ( element @ SY250 @ ( powerset @ SV47 ) ) )
| ( ( subset_intersection2 @ SV47 @ SY249 @ SY250 )
= ( subset_intersection2 @ SV47 @ SY250 @ SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(829,plain,
! [SV48: $i] :
( ( ! [SY251: $i,SY252: $i] :
~ ( ~ ( ( SY252
!= ( unordered_pair @ SV48 @ SY251 ) )
| ! [SY253: $i] :
~ ( ~ ( ~ ( in @ SY253 @ SY252 )
| ( SY253 = SV48 )
| ( SY253 = SY251 ) )
| ~ ( ~ ( ( SY253 = SV48 )
| ( SY253 = SY251 ) )
| ( in @ SY253 @ SY252 ) ) ) )
| ~ ( ~ ! [SY254: $i] :
~ ( ~ ( ~ ( in @ SY254 @ SY252 )
| ( SY254 = SV48 )
| ( SY254 = SY251 ) )
| ~ ( ~ ( ( SY254 = SV48 )
| ( SY254 = SY251 ) )
| ( in @ SY254 @ SY252 ) ) )
| ( SY252
= ( unordered_pair @ SV48 @ SY251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(830,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( ~ ( in @ SX1 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(831,plain,
! [SV49: $i] :
( ( ~ ( join_semilatt_str @ SV49 )
| ( one_sorted_str @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(832,plain,
! [SV50: $i] :
( ( ~ ( one_sorted_str @ SV50 )
| ( ( cast_as_carrier_subset @ SV50 )
= ( the_carrier @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(833,plain,
! [SV51: $i] :
( ( ! [SY255: $i,SY256: $i] :
~ ( ~ ( ( SY256
!= ( set_intersection2 @ SV51 @ SY255 ) )
| ! [SY257: $i] :
~ ( ~ ( ~ ( in @ SY257 @ SY256 )
| ~ ( ~ ( in @ SY257 @ SV51 )
| ~ ( in @ SY257 @ SY255 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY257 @ SV51 )
| ~ ( in @ SY257 @ SY255 ) )
| ( in @ SY257 @ SY256 ) ) ) )
| ~ ( ~ ! [SY258: $i] :
~ ( ~ ( ~ ( in @ SY258 @ SY256 )
| ~ ( ~ ( in @ SY258 @ SV51 )
| ~ ( in @ SY258 @ SY255 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY258 @ SV51 )
| ~ ( in @ SY258 @ SY255 ) )
| ( in @ SY258 @ SY256 ) ) )
| ( SY256
= ( set_intersection2 @ SV51 @ SY255 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(834,plain,
! [SV52: $i] :
( ( ! [SY259: $i] :
( ~ ( in @ SV52 @ SY259 )
| ~ ( in @ SY259 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(835,plain,
! [SV53: $i] :
( ( ! [SY260: $i] :
( ~ ( element @ SY260 @ ( powerset @ ( powerset @ SV53 ) ) )
| ( element @ ( union_of_subsets @ SV53 @ SY260 ) @ ( powerset @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(836,plain,
! [SV54: $i] :
( ( ! [SY261: $i] :
( ~ ( element @ SY261 @ ( powerset @ ( powerset @ SV54 ) ) )
| ( element @ ( complements_of_subsets @ SV54 @ SY261 ) @ ( powerset @ ( powerset @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(837,plain,
! [SV55: $i] :
( ( ! [SY262: $i] :
~ ( ~ ( ( SY262
!= ( powerset @ SV55 ) )
| ! [SY263: $i] :
~ ( ~ ( ~ ( in @ SY263 @ SY262 )
| ( subset @ SY263 @ SV55 ) )
| ~ ( ~ ( subset @ SY263 @ SV55 )
| ( in @ SY263 @ SY262 ) ) ) )
| ~ ( ~ ! [SY264: $i] :
~ ( ~ ( ~ ( in @ SY264 @ SY262 )
| ( subset @ SY264 @ SV55 ) )
| ~ ( ~ ( subset @ SY264 @ SV55 )
| ( in @ SY264 @ SY262 ) ) )
| ( SY262
= ( powerset @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(838,plain,
! [SV56: $i] :
( ( ! [SY265: $i] :
( ~ ( in @ SV56 @ SY265 )
| ( element @ SV56 @ SY265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(839,plain,
! [SV57: $i] :
( ( ! [SY266: $i] :
( ~ ( element @ SY266 @ ( powerset @ SV57 ) )
| ! [SY267: $i] :
( ~ ( in @ SY267 @ SY266 )
| ( in @ SY267 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(840,plain,
! [SV58: $i] :
( ( ! [SY268: $i,SY269: $i] :
~ ( ~ ( ( SY269
!= ( set_difference @ SV58 @ SY268 ) )
| ! [SY270: $i] :
~ ( ~ ( ~ ( in @ SY270 @ SY269 )
| ~ ( ~ ( in @ SY270 @ SV58 )
| ~ ~ ( in @ SY270 @ SY268 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY270 @ SV58 )
| ~ ~ ( in @ SY270 @ SY268 ) )
| ( in @ SY270 @ SY269 ) ) ) )
| ~ ( ~ ! [SY271: $i] :
~ ( ~ ( ~ ( in @ SY271 @ SY269 )
| ~ ( ~ ( in @ SY271 @ SV58 )
| ~ ~ ( in @ SY271 @ SY268 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY271 @ SV58 )
| ~ ~ ( in @ SY271 @ SY268 ) )
| ( in @ SY271 @ SY269 ) ) )
| ( SY269
= ( set_difference @ SV58 @ SY268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(841,plain,
! [SV59: $i] :
( ( ! [SY272: $i,SY273: $i] :
~ ( ~ ( ( SY273
!= ( set_union2 @ SV59 @ SY272 ) )
| ! [SY274: $i] :
~ ( ~ ( ~ ( in @ SY274 @ SY273 )
| ( in @ SY274 @ SV59 )
| ( in @ SY274 @ SY272 ) )
| ~ ( ~ ( ( in @ SY274 @ SV59 )
| ( in @ SY274 @ SY272 ) )
| ( in @ SY274 @ SY273 ) ) ) )
| ~ ( ~ ! [SY275: $i] :
~ ( ~ ( ~ ( in @ SY275 @ SY273 )
| ( in @ SY275 @ SV59 )
| ( in @ SY275 @ SY272 ) )
| ~ ( ~ ( ( in @ SY275 @ SV59 )
| ( in @ SY275 @ SY272 ) )
| ( in @ SY275 @ SY273 ) ) )
| ( SY273
= ( set_union2 @ SV59 @ SY272 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(842,plain,
! [SV60: $i] :
( ( ! [SY276: $i] :
~ ( ~ ( ( SY276
!= ( singleton @ SV60 ) )
| ! [SY277: $i] :
~ ( ~ ( ~ ( in @ SY277 @ SY276 )
| ( SY277 = SV60 ) )
| ~ ( ( SY277 != SV60 )
| ( in @ SY277 @ SY276 ) ) ) )
| ~ ( ~ ! [SY278: $i] :
~ ( ~ ( ~ ( in @ SY278 @ SY276 )
| ( SY278 = SV60 ) )
| ~ ( ( SY278 != SV60 )
| ( in @ SY278 @ SY276 ) ) )
| ( SY276
= ( singleton @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(843,plain,
! [SV61: $i] :
( ( ~ ( one_sorted_str @ SV61 )
| ( ( cast_as_carrier_subset @ SV61 )
= ( the_carrier @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(844,plain,
! [SV62: $i] :
( ( ~ ( one_sorted_str @ SV62 )
| ( element @ ( cast_as_carrier_subset @ SV62 ) @ ( powerset @ ( the_carrier @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(845,plain,
! [SV4: $i] :
( ( empty @ ( powerset @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(846,plain,
! [SV63: $i,SV5: $i] :
( ( ~ ~ ( ~ ( in @ SV5 @ SV63 )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV63 )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ SV63 )
| ~ ( in @ SY280 @ SY279 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(847,plain,
! [SV64: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
| ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) ) )
| ~ ( ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) )
| ~ ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(848,plain,
! [SV7: $i,SV65: $i] :
( ( ~ ( element @ SV65 @ ( powerset @ SV7 ) )
| ( ( subset_complement @ SV7 @ SV65 )
= ( set_difference @ SV7 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(849,plain,
! [SV66: $i,SV8: $i] :
( ( ~ ! [SY281: $i] :
~ ( ~ ( ~ ( in @ SY281 @ SV8 )
| ( in @ SY281 @ SV66 ) )
| ~ ( ~ ( in @ SY281 @ SV66 )
| ( in @ SY281 @ SV8 ) ) )
| ( SV8 = SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(850,plain,
! [SV67: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV9 @ SV67 )
| ! [SY282: $i] :
( ~ ( in @ SY282 @ SV9 )
| ( in @ SY282 @ SV67 ) ) )
| ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV9 )
| ( in @ SY283 @ SV67 ) )
| ( subset @ SV9 @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(851,plain,
! [SV68: $i,SV10: $i] :
( ( ! [SY284: $i] :
( ~ ~ ( ~ ( in @ SV10 @ SV68 )
| ~ ( element @ SV68 @ ( powerset @ SY284 ) ) )
| ( element @ SV10 @ SY284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(852,plain,
! [SV69: $i,SV11: $i] :
( ( ! [SY285: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SV69 )
| ~ ( in @ SV69 @ SY285 ) )
| ~ ( in @ SY285 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(853,plain,
! [SV12: $i] :
( ( ~ ( ~ ( epsilon_connected @ SV12 )
| ! [SY179: $i,SY180: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY179 @ SV12 )
| ~ ( in @ SY180 @ SV12 ) )
| ~ ~ ( in @ SY179 @ SY180 ) )
| ~ ( ( SY179 != SY180 ) ) )
| ~ ~ ( in @ SY180 @ SY179 ) ) )
| ~ ( ~ ! [SY181: $i,SY182: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY181 @ SV12 )
| ~ ( in @ SY182 @ SV12 ) )
| ~ ~ ( in @ SY181 @ SY182 ) )
| ~ ( ( SY181 != SY182 ) ) )
| ~ ~ ( in @ SY182 @ SY181 ) )
| ( epsilon_connected @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(854,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV13 )
| ~ ( one_sorted_str @ SV13 ) ) )
= $true )
| ( ( ~ ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(855,plain,
! [SV14: $i] :
( ( ( ~ ( ( SV14 != empty_set ) ) )
= $true )
| ( ( ! [SY184: $i] :
( ~ ( element @ SY184 @ ( powerset @ SV14 ) )
| ! [SY185: $i] :
( ~ ( element @ SY185 @ SV14 )
| ~ ~ ( in @ SY185 @ SY184 )
| ( in @ SY185 @ ( subset_complement @ SV14 @ SY184 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(856,plain,
! [SV70: $i,SV15: $i] :
( ( ! [SY286: $i] :
( ~ ( element @ SY286 @ ( powerset @ SV15 ) )
| ~ ~ ( ~ ( in @ SV70 @ ( subset_complement @ SV15 @ SY286 ) )
| ~ ( in @ SV70 @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(857,plain,
! [SV16: $i,SV71: $i] :
( ( ~ ( element @ SV71 @ ( powerset @ ( powerset @ SV16 ) ) )
| ( ( complements_of_subsets @ SV16 @ ( complements_of_subsets @ SV16 @ SV71 ) )
= SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(858,plain,
! [SV72: $i,SV17: $i] :
( ( ~ ( element @ SV17 @ SV72 )
| ( empty @ SV72 )
| ( in @ SV17 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(859,plain,
! [SV18: $i] :
( ( ( ~ ! [SY190: $i,SY191: $i,SY192: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV18 )
| ( SY191
!= ( singleton @ SY190 ) ) )
| ~ ( in @ SY190 @ SV18 ) )
| ( SY192
!= ( singleton @ SY190 ) ) )
| ( SY191 = SY192 ) ) )
= $true )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(860,plain,
! [SV19: $i,SV73: $i] :
( ( ~ ( element @ SV73 @ ( powerset @ ( powerset @ SV19 ) ) )
| ( element @ ( meet_of_subsets @ SV19 @ SV73 ) @ ( powerset @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(861,plain,
! [SV20: $i,SV74: $i] :
( ( ! [SY287: $i] :
( ~ ~ ( ~ ( element @ SV74 @ ( powerset @ SV20 ) )
| ~ ( element @ SY287 @ ( powerset @ SV20 ) ) )
| ( element @ ( subset_difference @ SV20 @ SV74 @ SY287 ) @ ( powerset @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(862,plain,
! [SV21: $i,SV75: $i] :
( ( ! [SY288: $i] :
( ~ ~ ( ~ ( element @ SV75 @ ( powerset @ SV21 ) )
| ~ ( element @ SY288 @ ( powerset @ SV21 ) ) )
| ( element @ ( subset_intersection2 @ SV21 @ SV75 @ SY288 ) @ ( powerset @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(863,plain,
( ( ~ ( one_sorted_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[801]) ).
thf(864,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV22 @ SV76 )
| ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) )
| ~ ( disjoint @ SV22 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(865,plain,
! [SV23: $i] :
( ( ( ~ ( v1_membered @ SV23 ) )
= $true )
| ( ( ! [SY205: $i] :
( ~ ( element @ SY205 @ ( powerset @ SV23 ) )
| ( v1_membered @ SY205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(866,plain,
! [SV24: $i] :
( ( ( ~ ( one_sorted_str @ SV24 ) )
= $true )
| ( ( element @ ( empty_carrier_subset @ SV24 ) @ ( powerset @ ( the_carrier @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(867,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ~ ( ~ ( in @ SV25 @ SV77 )
| ~ ( empty @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(868,plain,
! [SV26: $i,SV78: $i] :
( ( ~ ( element @ SV78 @ ( powerset @ SV26 ) )
| ( element @ ( subset_complement @ SV26 @ SV78 ) @ ( powerset @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(869,plain,
! [SV79: $i,SV27: $i] :
( ( ! [SY291: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV27 @ SV79 )
| ~ ( element @ SV79 @ ( powerset @ SY291 ) ) )
| ~ ( empty @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(870,plain,
! [SV28: $i,SV80: $i] :
( ( ~ ( element @ SV80 @ ( powerset @ SV28 ) )
| ( ( subset_complement @ SV28 @ ( subset_complement @ SV28 @ SV80 ) )
= SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(871,plain,
! [SV29: $i] :
( ( ! [SY211: $i] :
~ ( element @ SY211 @ SV29 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(872,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[810]) ).
thf(873,plain,
! [SV30: $i] :
( ( ( ~ ( finite @ SV30 ) )
= $true )
| ( ( ! [SY212: $i] :
( ~ ( element @ SY212 @ ( powerset @ SV30 ) )
| ( finite @ SY212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(874,plain,
! [SV81: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( element @ SV31 @ ( powerset @ SV81 ) )
| ( subset @ SV31 @ SV81 ) )
| ~ ( ~ ( subset @ SV31 @ SV81 )
| ( element @ SV31 @ ( powerset @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(875,plain,
! [SV32: $i,SV82: $i] :
( ( ~ ( ~ ( ( SV82
!= ( union @ SV32 ) )
| ! [SY292: $i] :
~ ( ~ ( ~ ( in @ SY292 @ SV82 )
| ~ ! [SY216: $i] :
~ ~ ( ~ ( in @ SY292 @ SY216 )
| ~ ( in @ SY216 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( in @ SY292 @ SY217 )
| ~ ( in @ SY217 @ SV32 ) )
| ( in @ SY292 @ SV82 ) ) ) )
| ~ ( ~ ! [SY295: $i] :
~ ( ~ ( ~ ( in @ SY295 @ SV82 )
| ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY295 @ SY219 )
| ~ ( in @ SY219 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ( in @ SY295 @ SY220 )
| ~ ( in @ SY220 @ SV32 ) )
| ( in @ SY295 @ SV82 ) ) )
| ( SV82
= ( union @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(876,plain,
! [SV33: $i,SV83: $i] :
( ( ~ ( ordinal @ SV83 )
| ~ ( in @ SV33 @ SV83 )
| ( ordinal @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(877,plain,
! [SV84: $i,SV34: $i] :
( ( ! [SY298: $i,SY299: $i] :
~ ( ~ ( ( SY299
!= ( unordered_triple @ SV34 @ SV84 @ SY298 ) )
| ! [SY300: $i] :
~ ( ~ ( ~ ( in @ SY300 @ SY299 )
| ~ ~ ( ~ ~ ( ~ ( ( SY300 != SV34 ) )
| ~ ( ( SY300 != SV84 ) ) )
| ~ ( ( SY300 != SY298 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY300 != SV34 ) )
| ~ ( ( SY300 != SV84 ) ) )
| ~ ( ( SY300 != SY298 ) ) )
| ( in @ SY300 @ SY299 ) ) ) )
| ~ ( ~ ! [SY301: $i] :
~ ( ~ ( ~ ( in @ SY301 @ SY299 )
| ~ ~ ( ~ ~ ( ~ ( ( SY301 != SV34 ) )
| ~ ( ( SY301 != SV84 ) ) )
| ~ ( ( SY301 != SY298 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY301 != SV34 ) )
| ~ ( ( SY301 != SV84 ) ) )
| ~ ( ( SY301 != SY298 ) ) )
| ( in @ SY301 @ SY299 ) ) )
| ( SY299
= ( unordered_triple @ SV34 @ SV84 @ SY298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(878,plain,
! [SV85: $i,SV35: $i] :
( ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SV35 )
| ( in @ SY302 @ SV85 ) )
| ( element @ SV35 @ ( powerset @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(879,plain,
! [SV36: $i] :
( ( ~ ( ( SV36 != empty_set )
| ! [SY229: $i] :
~ ( in @ SY229 @ SV36 ) )
| ~ ( ~ ! [SY230: $i] :
~ ( in @ SY230 @ SV36 )
| ( SV36 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(880,plain,
! [SV37: $i] :
( ( ( ~ ( meet_semilatt_str @ SV37 ) )
= $true )
| ( ( one_sorted_str @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(881,plain,
! [SV38: $i,SV86: $i] :
( ( ! [SY303: $i] :
( ~ ~ ( ~ ( element @ SV86 @ ( powerset @ SV38 ) )
| ~ ( element @ SY303 @ ( powerset @ SV38 ) ) )
| ( ( subset_intersection2 @ SV38 @ SV86 @ SV86 )
= SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(882,plain,
! [SV39: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV39 )
| ~ ( one_sorted_str @ SV39 ) ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(883,plain,
! [SV40: $i] :
( ( ( ~ ( top_str @ SV40 ) )
= $true )
| ( ( one_sorted_str @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(884,plain,
! [SV41: $i,SV87: $i] :
( ( ~ ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
| ! [SY304: $i] :
( ~ ( element @ SY304 @ ( powerset @ ( powerset @ SV41 ) ) )
| ~ ( ~ ( ( SY304
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY305: $i] :
( ~ ( element @ SY305 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY305 @ SY304 )
| ( in @ ( subset_complement @ SV41 @ SY305 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY305 ) @ SV87 )
| ( in @ SY305 @ SY304 ) ) ) ) )
| ~ ( ~ ! [SY306: $i] :
( ~ ( element @ SY306 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY306 @ SY304 )
| ( in @ ( subset_complement @ SV41 @ SY306 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY306 ) @ SV87 )
| ( in @ SY306 @ SY304 ) ) ) )
| ( SY304
= ( complements_of_subsets @ SV41 @ SV87 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(885,plain,
! [SV42: $i] :
( ( ! [SY237: $i] :
~ ! [SY238: $i] :
~ ( ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( ~ ( in @ SY238 @ SV42 )
| ~ ( ordinal @ SY238 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY238 @ SV42 )
| ~ ( ordinal @ SY238 ) )
| ( in @ SY238 @ SY237 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(886,plain,
! [SV43: $i] :
( ( ( ~ ~ ( empty @ SV43 ) )
= $true )
| ( ( ~ ! [SY239: $i] :
~ ~ ( ~ ( element @ SY239 @ ( powerset @ SV43 ) )
| ~ ~ ( empty @ SY239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(887,plain,
! [SV44: $i] :
( ( ! [SY240: $i] :
~ ~ ( ~ ( element @ SY240 @ ( powerset @ SV44 ) )
| ~ ( empty @ SY240 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(888,plain,
! [SV45: $i] :
( ( ( ~ ( ordinal @ SV45 ) )
= $true )
| ( ( ! [SY241: $i] :
( ~ ( ordinal @ SY241 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SV45 @ SY241 )
| ~ ( ( SV45 != SY241 ) ) )
| ~ ~ ( in @ SY241 @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(889,plain,
! [SV46: $i] :
( ( ( ~ ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX1 != SX2 )
| ~ ( ordinal @ SX2 ) )
| ( SX1 != SX3 ) )
| ~ ( ordinal @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(890,plain,
! [SV47: $i,SV88: $i] :
( ( ! [SY307: $i] :
( ~ ~ ( ~ ( element @ SV88 @ ( powerset @ SV47 ) )
| ~ ( element @ SY307 @ ( powerset @ SV47 ) ) )
| ( ( subset_intersection2 @ SV47 @ SV88 @ SY307 )
= ( subset_intersection2 @ SV47 @ SY307 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(891,plain,
! [SV89: $i,SV48: $i] :
( ( ! [SY308: $i] :
~ ( ~ ( ( SY308
!= ( unordered_pair @ SV48 @ SV89 ) )
| ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SY308 )
| ( SY309 = SV48 )
| ( SY309 = SV89 ) )
| ~ ( ~ ( ( SY309 = SV48 )
| ( SY309 = SV89 ) )
| ( in @ SY309 @ SY308 ) ) ) )
| ~ ( ~ ! [SY310: $i] :
~ ( ~ ( ~ ( in @ SY310 @ SY308 )
| ( SY310 = SV48 )
| ( SY310 = SV89 ) )
| ~ ( ~ ( ( SY310 = SV48 )
| ( SY310 = SV89 ) )
| ( in @ SY310 @ SY308 ) ) )
| ( SY308
= ( unordered_pair @ SV48 @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(892,plain,
( ( ~ ( element @ sK4_SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ! [SY311: $i] :
( ~ ( element @ SY311 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( ~ ( in @ SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
| ~ ( in @ SY311 @ sK4_SX0 ) )
| ~ ( ~ ~ ( in @ SY311 @ sK4_SX0 )
| ( in @ SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[830]) ).
thf(893,plain,
! [SV49: $i] :
( ( ( ~ ( join_semilatt_str @ SV49 ) )
= $true )
| ( ( one_sorted_str @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(894,plain,
! [SV50: $i] :
( ( ( ~ ( one_sorted_str @ SV50 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV50 )
= ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(895,plain,
! [SV90: $i,SV51: $i] :
( ( ! [SY312: $i] :
~ ( ~ ( ( SY312
!= ( set_intersection2 @ SV51 @ SV90 ) )
| ! [SY313: $i] :
~ ( ~ ( ~ ( in @ SY313 @ SY312 )
| ~ ( ~ ( in @ SY313 @ SV51 )
| ~ ( in @ SY313 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY313 @ SV51 )
| ~ ( in @ SY313 @ SV90 ) )
| ( in @ SY313 @ SY312 ) ) ) )
| ~ ( ~ ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SY312 )
| ~ ( ~ ( in @ SY314 @ SV51 )
| ~ ( in @ SY314 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY314 @ SV51 )
| ~ ( in @ SY314 @ SV90 ) )
| ( in @ SY314 @ SY312 ) ) )
| ( SY312
= ( set_intersection2 @ SV51 @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(896,plain,
! [SV91: $i,SV52: $i] :
( ( ~ ( in @ SV52 @ SV91 )
| ~ ( in @ SV91 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(897,plain,
! [SV53: $i,SV92: $i] :
( ( ~ ( element @ SV92 @ ( powerset @ ( powerset @ SV53 ) ) )
| ( element @ ( union_of_subsets @ SV53 @ SV92 ) @ ( powerset @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(898,plain,
! [SV54: $i,SV93: $i] :
( ( ~ ( element @ SV93 @ ( powerset @ ( powerset @ SV54 ) ) )
| ( element @ ( complements_of_subsets @ SV54 @ SV93 ) @ ( powerset @ ( powerset @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(899,plain,
! [SV55: $i,SV94: $i] :
( ( ~ ( ~ ( ( SV94
!= ( powerset @ SV55 ) )
| ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( subset @ SY315 @ SV55 ) )
| ~ ( ~ ( subset @ SY315 @ SV55 )
| ( in @ SY315 @ SV94 ) ) ) )
| ~ ( ~ ! [SY316: $i] :
~ ( ~ ( ~ ( in @ SY316 @ SV94 )
| ( subset @ SY316 @ SV55 ) )
| ~ ( ~ ( subset @ SY316 @ SV55 )
| ( in @ SY316 @ SV94 ) ) )
| ( SV94
= ( powerset @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(900,plain,
! [SV95: $i,SV56: $i] :
( ( ~ ( in @ SV56 @ SV95 )
| ( element @ SV56 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(901,plain,
! [SV57: $i,SV96: $i] :
( ( ~ ( element @ SV96 @ ( powerset @ SV57 ) )
| ! [SY317: $i] :
( ~ ( in @ SY317 @ SV96 )
| ( in @ SY317 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(902,plain,
! [SV97: $i,SV58: $i] :
( ( ! [SY318: $i] :
~ ( ~ ( ( SY318
!= ( set_difference @ SV58 @ SV97 ) )
| ! [SY319: $i] :
~ ( ~ ( ~ ( in @ SY319 @ SY318 )
| ~ ( ~ ( in @ SY319 @ SV58 )
| ~ ~ ( in @ SY319 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY319 @ SV58 )
| ~ ~ ( in @ SY319 @ SV97 ) )
| ( in @ SY319 @ SY318 ) ) ) )
| ~ ( ~ ! [SY320: $i] :
~ ( ~ ( ~ ( in @ SY320 @ SY318 )
| ~ ( ~ ( in @ SY320 @ SV58 )
| ~ ~ ( in @ SY320 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY320 @ SV58 )
| ~ ~ ( in @ SY320 @ SV97 ) )
| ( in @ SY320 @ SY318 ) ) )
| ( SY318
= ( set_difference @ SV58 @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(903,plain,
! [SV98: $i,SV59: $i] :
( ( ! [SY321: $i] :
~ ( ~ ( ( SY321
!= ( set_union2 @ SV59 @ SV98 ) )
| ! [SY322: $i] :
~ ( ~ ( ~ ( in @ SY322 @ SY321 )
| ( in @ SY322 @ SV59 )
| ( in @ SY322 @ SV98 ) )
| ~ ( ~ ( ( in @ SY322 @ SV59 )
| ( in @ SY322 @ SV98 ) )
| ( in @ SY322 @ SY321 ) ) ) )
| ~ ( ~ ! [SY323: $i] :
~ ( ~ ( ~ ( in @ SY323 @ SY321 )
| ( in @ SY323 @ SV59 )
| ( in @ SY323 @ SV98 ) )
| ~ ( ~ ( ( in @ SY323 @ SV59 )
| ( in @ SY323 @ SV98 ) )
| ( in @ SY323 @ SY321 ) ) )
| ( SY321
= ( set_union2 @ SV59 @ SV98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(904,plain,
! [SV60: $i,SV99: $i] :
( ( ~ ( ~ ( ( SV99
!= ( singleton @ SV60 ) )
| ! [SY324: $i] :
~ ( ~ ( ~ ( in @ SY324 @ SV99 )
| ( SY324 = SV60 ) )
| ~ ( ( SY324 != SV60 )
| ( in @ SY324 @ SV99 ) ) ) )
| ~ ( ~ ! [SY325: $i] :
~ ( ~ ( ~ ( in @ SY325 @ SV99 )
| ( SY325 = SV60 ) )
| ~ ( ( SY325 != SV60 )
| ( in @ SY325 @ SV99 ) ) )
| ( SV99
= ( singleton @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(905,plain,
! [SV61: $i] :
( ( ( ~ ( one_sorted_str @ SV61 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV61 )
= ( the_carrier @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(906,plain,
! [SV62: $i] :
( ( ( ~ ( one_sorted_str @ SV62 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV62 ) @ ( powerset @ ( the_carrier @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(907,plain,
! [SV63: $i,SV5: $i] :
( ( ~ ( ~ ( in @ SV5 @ SV63 )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV63 )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ SV63 )
| ~ ( in @ SY280 @ SY279 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(908,plain,
! [SV64: $i,SV6: $i] :
( ( ~ ( ~ ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
| ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) ) )
| ~ ( ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) )
| ~ ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(909,plain,
! [SV7: $i,SV65: $i] :
( ( ( ~ ( element @ SV65 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( ( subset_complement @ SV7 @ SV65 )
= ( set_difference @ SV7 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(910,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ! [SY281: $i] :
~ ( ~ ( ~ ( in @ SY281 @ SV8 )
| ( in @ SY281 @ SV66 ) )
| ~ ( ~ ( in @ SY281 @ SV66 )
| ( in @ SY281 @ SV8 ) ) ) )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(911,plain,
! [SV67: $i,SV9: $i] :
( ( ~ ( ~ ( subset @ SV9 @ SV67 )
| ! [SY282: $i] :
( ~ ( in @ SY282 @ SV9 )
| ( in @ SY282 @ SV67 ) ) )
| ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV9 )
| ( in @ SY283 @ SV67 ) )
| ( subset @ SV9 @ SV67 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(912,plain,
! [SV100: $i,SV68: $i,SV10: $i] :
( ( ~ ~ ( ~ ( in @ SV10 @ SV68 )
| ~ ( element @ SV68 @ ( powerset @ SV100 ) ) )
| ( element @ SV10 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(913,plain,
! [SV101: $i,SV69: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SV69 )
| ~ ( in @ SV69 @ SV101 ) )
| ~ ( in @ SV101 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(914,plain,
! [SV12: $i] :
( ( ~ ( ~ ( epsilon_connected @ SV12 )
| ! [SY179: $i,SY180: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY179 @ SV12 )
| ~ ( in @ SY180 @ SV12 ) )
| ~ ~ ( in @ SY179 @ SY180 ) )
| ~ ( ( SY179 != SY180 ) ) )
| ~ ~ ( in @ SY180 @ SY179 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(915,plain,
! [SV12: $i] :
( ( ~ ( ~ ! [SY181: $i,SY182: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY181 @ SV12 )
| ~ ( in @ SY182 @ SV12 ) )
| ~ ~ ( in @ SY181 @ SY182 ) )
| ~ ( ( SY181 != SY182 ) ) )
| ~ ~ ( in @ SY182 @ SY181 ) )
| ( epsilon_connected @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(916,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV13 )
| ~ ( one_sorted_str @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(917,plain,
! [SV14: $i] :
( ( ( SV14 != empty_set )
= $false )
| ( ( ! [SY184: $i] :
( ~ ( element @ SY184 @ ( powerset @ SV14 ) )
| ! [SY185: $i] :
( ~ ( element @ SY185 @ SV14 )
| ~ ~ ( in @ SY185 @ SY184 )
| ( in @ SY185 @ ( subset_complement @ SV14 @ SY184 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(918,plain,
! [SV70: $i,SV15: $i,SV102: $i] :
( ( ~ ( element @ SV102 @ ( powerset @ SV15 ) )
| ~ ~ ( ~ ( in @ SV70 @ ( subset_complement @ SV15 @ SV102 ) )
| ~ ( in @ SV70 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(919,plain,
! [SV16: $i,SV71: $i] :
( ( ( ~ ( element @ SV71 @ ( powerset @ ( powerset @ SV16 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV16 @ ( complements_of_subsets @ SV16 @ SV71 ) )
= SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(920,plain,
! [SV72: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ SV72 ) )
= $true )
| ( ( ( empty @ SV72 )
| ( in @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(921,plain,
! [SV18: $i] :
( ( ( ! [SY190: $i,SY191: $i,SY192: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV18 )
| ( SY191
!= ( singleton @ SY190 ) ) )
| ~ ( in @ SY190 @ SV18 ) )
| ( SY192
!= ( singleton @ SY190 ) ) )
| ( SY191 = SY192 ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(922,plain,
! [SV19: $i,SV73: $i] :
( ( ( ~ ( element @ SV73 @ ( powerset @ ( powerset @ SV19 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV19 @ SV73 ) @ ( powerset @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(923,plain,
! [SV103: $i,SV20: $i,SV74: $i] :
( ( ~ ~ ( ~ ( element @ SV74 @ ( powerset @ SV20 ) )
| ~ ( element @ SV103 @ ( powerset @ SV20 ) ) )
| ( element @ ( subset_difference @ SV20 @ SV74 @ SV103 ) @ ( powerset @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(924,plain,
! [SV104: $i,SV21: $i,SV75: $i] :
( ( ~ ~ ( ~ ( element @ SV75 @ ( powerset @ SV21 ) )
| ~ ( element @ SV104 @ ( powerset @ SV21 ) ) )
| ( element @ ( subset_intersection2 @ SV21 @ SV75 @ SV104 ) @ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(925,plain,
( ( one_sorted_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(926,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV22 @ SV76 )
| ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) )
| ~ ( disjoint @ SV22 @ SV76 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(927,plain,
! [SV23: $i] :
( ( ( v1_membered @ SV23 )
= $false )
| ( ( ! [SY205: $i] :
( ~ ( element @ SY205 @ ( powerset @ SV23 ) )
| ( v1_membered @ SY205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(928,plain,
! [SV24: $i] :
( ( ( one_sorted_str @ SV24 )
= $false )
| ( ( element @ ( empty_carrier_subset @ SV24 ) @ ( powerset @ ( the_carrier @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(929,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ( ~ ( in @ SV25 @ SV77 )
| ~ ( empty @ SV77 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(930,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV26 @ SV78 ) @ ( powerset @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(931,plain,
! [SV105: $i,SV79: $i,SV27: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV27 @ SV79 )
| ~ ( element @ SV79 @ ( powerset @ SV105 ) ) )
| ~ ( empty @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(932,plain,
! [SV28: $i,SV80: $i] :
( ( ( ~ ( element @ SV80 @ ( powerset @ SV28 ) ) )
= $true )
| ( ( ( subset_complement @ SV28 @ ( subset_complement @ SV28 @ SV80 ) )
= SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(933,plain,
! [SV29: $i] :
( ( ~ ( element @ ( sK5_SY211 @ SV29 ) @ SV29 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[871]) ).
thf(934,plain,
( ( ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(935,plain,
! [SV30: $i] :
( ( ( finite @ SV30 )
= $false )
| ( ( ! [SY212: $i] :
( ~ ( element @ SY212 @ ( powerset @ SV30 ) )
| ( finite @ SY212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(936,plain,
! [SV81: $i,SV31: $i] :
( ( ~ ( ~ ( element @ SV31 @ ( powerset @ SV81 ) )
| ( subset @ SV31 @ SV81 ) )
| ~ ( ~ ( subset @ SV31 @ SV81 )
| ( element @ SV31 @ ( powerset @ SV81 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(937,plain,
! [SV32: $i,SV82: $i] :
( ( ~ ( ( SV82
!= ( union @ SV32 ) )
| ! [SY292: $i] :
~ ( ~ ( ~ ( in @ SY292 @ SV82 )
| ~ ! [SY216: $i] :
~ ~ ( ~ ( in @ SY292 @ SY216 )
| ~ ( in @ SY216 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( in @ SY292 @ SY217 )
| ~ ( in @ SY217 @ SV32 ) )
| ( in @ SY292 @ SV82 ) ) ) )
| ~ ( ~ ! [SY295: $i] :
~ ( ~ ( ~ ( in @ SY295 @ SV82 )
| ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY295 @ SY219 )
| ~ ( in @ SY219 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ( in @ SY295 @ SY220 )
| ~ ( in @ SY220 @ SV32 ) )
| ( in @ SY295 @ SV82 ) ) )
| ( SV82
= ( union @ SV32 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(938,plain,
! [SV33: $i,SV83: $i] :
( ( ( ~ ( ordinal @ SV83 ) )
= $true )
| ( ( ~ ( in @ SV33 @ SV83 )
| ( ordinal @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(939,plain,
! [SV106: $i,SV84: $i,SV34: $i] :
( ( ! [SY326: $i] :
~ ( ~ ( ( SY326
!= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
| ! [SY327: $i] :
~ ( ~ ( ~ ( in @ SY327 @ SY326 )
| ~ ~ ( ~ ~ ( ~ ( ( SY327 != SV34 ) )
| ~ ( ( SY327 != SV84 ) ) )
| ~ ( ( SY327 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY327 != SV34 ) )
| ~ ( ( SY327 != SV84 ) ) )
| ~ ( ( SY327 != SV106 ) ) )
| ( in @ SY327 @ SY326 ) ) ) )
| ~ ( ~ ! [SY328: $i] :
~ ( ~ ( ~ ( in @ SY328 @ SY326 )
| ~ ~ ( ~ ~ ( ~ ( ( SY328 != SV34 ) )
| ~ ( ( SY328 != SV84 ) ) )
| ~ ( ( SY328 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY328 != SV34 ) )
| ~ ( ( SY328 != SV84 ) ) )
| ~ ( ( SY328 != SV106 ) ) )
| ( in @ SY328 @ SY326 ) ) )
| ( SY326
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(940,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SV35 )
| ( in @ SY302 @ SV85 ) ) )
= $true )
| ( ( element @ SV35 @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(941,plain,
! [SV36: $i] :
( ( ~ ( ( SV36 != empty_set )
| ! [SY229: $i] :
~ ( in @ SY229 @ SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(942,plain,
! [SV36: $i] :
( ( ~ ( ~ ! [SY230: $i] :
~ ( in @ SY230 @ SV36 )
| ( SV36 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(943,plain,
! [SV37: $i] :
( ( ( meet_semilatt_str @ SV37 )
= $false )
| ( ( one_sorted_str @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(944,plain,
! [SV107: $i,SV38: $i,SV86: $i] :
( ( ~ ~ ( ~ ( element @ SV86 @ ( powerset @ SV38 ) )
| ~ ( element @ SV107 @ ( powerset @ SV38 ) ) )
| ( ( subset_intersection2 @ SV38 @ SV86 @ SV86 )
= SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(945,plain,
! [SV39: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV39 )
| ~ ( one_sorted_str @ SV39 ) ) )
= $false )
| ( ( ~ ( empty @ ( the_carrier @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(946,plain,
! [SV40: $i] :
( ( ( top_str @ SV40 )
= $false )
| ( ( one_sorted_str @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(947,plain,
! [SV41: $i,SV87: $i] :
( ( ( ~ ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) ) )
= $true )
| ( ( ! [SY304: $i] :
( ~ ( element @ SY304 @ ( powerset @ ( powerset @ SV41 ) ) )
| ~ ( ~ ( ( SY304
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY305: $i] :
( ~ ( element @ SY305 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY305 @ SY304 )
| ( in @ ( subset_complement @ SV41 @ SY305 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY305 ) @ SV87 )
| ( in @ SY305 @ SY304 ) ) ) ) )
| ~ ( ~ ! [SY306: $i] :
( ~ ( element @ SY306 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY306 @ SY304 )
| ( in @ ( subset_complement @ SV41 @ SY306 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY306 ) @ SV87 )
| ( in @ SY306 @ SY304 ) ) ) )
| ( SY304
= ( complements_of_subsets @ SV41 @ SV87 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(948,plain,
! [SV42: $i] :
( ( ~ ! [SY329: $i] :
~ ( ~ ( ~ ( in @ SY329 @ ( sK6_SY237 @ SV42 ) )
| ~ ( ~ ( in @ SY329 @ SV42 )
| ~ ( ordinal @ SY329 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY329 @ SV42 )
| ~ ( ordinal @ SY329 ) )
| ( in @ SY329 @ ( sK6_SY237 @ SV42 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[885]) ).
thf(949,plain,
! [SV43: $i] :
( ( ( ~ ( empty @ SV43 ) )
= $false )
| ( ( ~ ! [SY239: $i] :
~ ~ ( ~ ( element @ SY239 @ ( powerset @ SV43 ) )
| ~ ~ ( empty @ SY239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(950,plain,
! [SV44: $i] :
( ( ~ ~ ( ~ ( element @ ( sK7_SY240 @ SV44 ) @ ( powerset @ SV44 ) )
| ~ ( empty @ ( sK7_SY240 @ SV44 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[887]) ).
thf(951,plain,
! [SV45: $i] :
( ( ( ordinal @ SV45 )
= $false )
| ( ( ! [SY241: $i] :
( ~ ( ordinal @ SY241 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SV45 @ SY241 )
| ~ ( ( SV45 != SY241 ) ) )
| ~ ~ ( in @ SY241 @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(952,plain,
! [SV46: $i] :
( ( ( ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX1 != SX2 )
| ~ ( ordinal @ SX2 ) )
| ( SX1 != SX3 ) )
| ~ ( ordinal @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(953,plain,
! [SV108: $i,SV47: $i,SV88: $i] :
( ( ~ ~ ( ~ ( element @ SV88 @ ( powerset @ SV47 ) )
| ~ ( element @ SV108 @ ( powerset @ SV47 ) ) )
| ( ( subset_intersection2 @ SV47 @ SV88 @ SV108 )
= ( subset_intersection2 @ SV47 @ SV108 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(954,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ~ ( ~ ( ( SV109
!= ( unordered_pair @ SV48 @ SV89 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV109 )
| ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ~ ( ~ ( ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ( in @ SY330 @ SV109 ) ) ) )
| ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV109 )
| ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ~ ( ~ ( ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ( in @ SY331 @ SV109 ) ) )
| ( SV109
= ( unordered_pair @ SV48 @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(955,plain,
( ( ~ ( element @ sK4_SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(956,plain,
( ( ! [SY311: $i] :
( ~ ( element @ SY311 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( ~ ( in @ SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
| ~ ( in @ SY311 @ sK4_SX0 ) )
| ~ ( ~ ~ ( in @ SY311 @ sK4_SX0 )
| ( in @ SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(957,plain,
! [SV49: $i] :
( ( ( join_semilatt_str @ SV49 )
= $false )
| ( ( one_sorted_str @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(958,plain,
! [SV50: $i] :
( ( ( one_sorted_str @ SV50 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV50 )
= ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(959,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ~ ( ~ ( ( SV110
!= ( set_intersection2 @ SV51 @ SV90 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV110 )
| ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) )
| ( in @ SY332 @ SV110 ) ) ) )
| ~ ( ~ ! [SY333: $i] :
~ ( ~ ( ~ ( in @ SY333 @ SV110 )
| ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) )
| ( in @ SY333 @ SV110 ) ) )
| ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(960,plain,
! [SV91: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV91 ) )
= $true )
| ( ( ~ ( in @ SV91 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(961,plain,
! [SV53: $i,SV92: $i] :
( ( ( ~ ( element @ SV92 @ ( powerset @ ( powerset @ SV53 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV53 @ SV92 ) @ ( powerset @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(962,plain,
! [SV54: $i,SV93: $i] :
( ( ( ~ ( element @ SV93 @ ( powerset @ ( powerset @ SV54 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV54 @ SV93 ) @ ( powerset @ ( powerset @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(963,plain,
! [SV55: $i,SV94: $i] :
( ( ~ ( ( SV94
!= ( powerset @ SV55 ) )
| ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( subset @ SY315 @ SV55 ) )
| ~ ( ~ ( subset @ SY315 @ SV55 )
| ( in @ SY315 @ SV94 ) ) ) )
| ~ ( ~ ! [SY316: $i] :
~ ( ~ ( ~ ( in @ SY316 @ SV94 )
| ( subset @ SY316 @ SV55 ) )
| ~ ( ~ ( subset @ SY316 @ SV55 )
| ( in @ SY316 @ SV94 ) ) )
| ( SV94
= ( powerset @ SV55 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(964,plain,
! [SV95: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV95 ) )
= $true )
| ( ( element @ SV56 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(965,plain,
! [SV57: $i,SV96: $i] :
( ( ( ~ ( element @ SV96 @ ( powerset @ SV57 ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ SV96 )
| ( in @ SY317 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(966,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ~ ( ~ ( ( SV111
!= ( set_difference @ SV58 @ SV97 ) )
| ! [SY334: $i] :
~ ( ~ ( ~ ( in @ SY334 @ SV111 )
| ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) )
| ( in @ SY334 @ SV111 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV111 )
| ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) )
| ( in @ SY335 @ SV111 ) ) )
| ( SV111
= ( set_difference @ SV58 @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(967,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ~ ( ~ ( ( SV112
!= ( set_union2 @ SV59 @ SV98 ) )
| ! [SY336: $i] :
~ ( ~ ( ~ ( in @ SY336 @ SV112 )
| ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ~ ( ~ ( ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ( in @ SY336 @ SV112 ) ) ) )
| ~ ( ~ ! [SY337: $i] :
~ ( ~ ( ~ ( in @ SY337 @ SV112 )
| ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ~ ( ~ ( ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ( in @ SY337 @ SV112 ) ) )
| ( SV112
= ( set_union2 @ SV59 @ SV98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(968,plain,
! [SV60: $i,SV99: $i] :
( ( ~ ( ( SV99
!= ( singleton @ SV60 ) )
| ! [SY324: $i] :
~ ( ~ ( ~ ( in @ SY324 @ SV99 )
| ( SY324 = SV60 ) )
| ~ ( ( SY324 != SV60 )
| ( in @ SY324 @ SV99 ) ) ) )
| ~ ( ~ ! [SY325: $i] :
~ ( ~ ( ~ ( in @ SY325 @ SV99 )
| ( SY325 = SV60 ) )
| ~ ( ( SY325 != SV60 )
| ( in @ SY325 @ SV99 ) ) )
| ( SV99
= ( singleton @ SV60 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(969,plain,
! [SV61: $i] :
( ( ( one_sorted_str @ SV61 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV61 )
= ( the_carrier @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(970,plain,
! [SV62: $i] :
( ( ( one_sorted_str @ SV62 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV62 ) @ ( powerset @ ( the_carrier @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(971,plain,
! [SV63: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV63 )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV63 )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ SV63 )
| ~ ( in @ SY280 @ SY279 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(972,plain,
! [SV64: $i,SV6: $i] :
( ( ~ ( ~ ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
| ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(973,plain,
! [SV64: $i,SV6: $i] :
( ( ~ ( ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) )
| ~ ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(974,plain,
! [SV7: $i,SV65: $i] :
( ( ( element @ SV65 @ ( powerset @ SV7 ) )
= $false )
| ( ( ( subset_complement @ SV7 @ SV65 )
= ( set_difference @ SV7 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(975,plain,
! [SV66: $i,SV8: $i] :
( ( ( ! [SY281: $i] :
~ ( ~ ( ~ ( in @ SY281 @ SV8 )
| ( in @ SY281 @ SV66 ) )
| ~ ( ~ ( in @ SY281 @ SV66 )
| ( in @ SY281 @ SV8 ) ) ) )
= $false )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(976,plain,
! [SV67: $i,SV9: $i] :
( ( ~ ( ~ ( subset @ SV9 @ SV67 )
| ! [SY282: $i] :
( ~ ( in @ SY282 @ SV9 )
| ( in @ SY282 @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(977,plain,
! [SV67: $i,SV9: $i] :
( ( ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV9 )
| ( in @ SY283 @ SV67 ) )
| ( subset @ SV9 @ SV67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(978,plain,
! [SV100: $i,SV68: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ SV10 @ SV68 )
| ~ ( element @ SV68 @ ( powerset @ SV100 ) ) ) )
= $true )
| ( ( element @ SV10 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(979,plain,
! [SV101: $i,SV69: $i,SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV11 @ SV69 )
| ~ ( in @ SV69 @ SV101 ) )
| ~ ( in @ SV101 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(980,plain,
! [SV12: $i] :
( ( ~ ( epsilon_connected @ SV12 )
| ! [SY179: $i,SY180: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY179 @ SV12 )
| ~ ( in @ SY180 @ SV12 ) )
| ~ ~ ( in @ SY179 @ SY180 ) )
| ~ ( ( SY179 != SY180 ) ) )
| ~ ~ ( in @ SY180 @ SY179 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(981,plain,
! [SV12: $i] :
( ( ~ ! [SY181: $i,SY182: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY181 @ SV12 )
| ~ ( in @ SY182 @ SV12 ) )
| ~ ~ ( in @ SY181 @ SY182 ) )
| ~ ( ( SY181 != SY182 ) ) )
| ~ ~ ( in @ SY182 @ SY181 ) )
| ( epsilon_connected @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[915]) ).
thf(982,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty_carrier @ SV13 )
| ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ~ ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(983,plain,
! [SV14: $i] :
( ( ( SV14 = empty_set )
= $true )
| ( ( ! [SY184: $i] :
( ~ ( element @ SY184 @ ( powerset @ SV14 ) )
| ! [SY185: $i] :
( ~ ( element @ SY185 @ SV14 )
| ~ ~ ( in @ SY185 @ SY184 )
| ( in @ SY185 @ ( subset_complement @ SV14 @ SY184 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(984,plain,
! [SV70: $i,SV15: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV70 @ ( subset_complement @ SV15 @ SV102 ) )
| ~ ( in @ SV70 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(985,plain,
! [SV16: $i,SV71: $i] :
( ( ( element @ SV71 @ ( powerset @ ( powerset @ SV16 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV16 @ ( complements_of_subsets @ SV16 @ SV71 ) )
= SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(986,plain,
! [SV72: $i,SV17: $i] :
( ( ( element @ SV17 @ SV72 )
= $false )
| ( ( ( empty @ SV72 )
| ( in @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(987,plain,
! [SV18: $i] :
( ( ( ! [SY338: $i,SY339: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( SY338
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
| ( SY339
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ( SY338 = SY339 ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[921]) ).
thf(988,plain,
! [SV19: $i,SV73: $i] :
( ( ( element @ SV73 @ ( powerset @ ( powerset @ SV19 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV19 @ SV73 ) @ ( powerset @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(989,plain,
! [SV103: $i,SV20: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ( element @ SV74 @ ( powerset @ SV20 ) )
| ~ ( element @ SV103 @ ( powerset @ SV20 ) ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV20 @ SV74 @ SV103 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(990,plain,
! [SV104: $i,SV21: $i,SV75: $i] :
( ( ( ~ ~ ( ~ ( element @ SV75 @ ( powerset @ SV21 ) )
| ~ ( element @ SV104 @ ( powerset @ SV21 ) ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV75 @ SV104 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(991,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV22 @ SV76 )
| ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(992,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) )
| ~ ( disjoint @ SV22 @ SV76 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(993,plain,
! [SV23: $i,SV113: $i] :
( ( ( ~ ( element @ SV113 @ ( powerset @ SV23 ) )
| ( v1_membered @ SV113 ) )
= $true )
| ( ( v1_membered @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(994,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ( in @ SV25 @ SV77 )
| ~ ( empty @ SV77 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(995,plain,
! [SV26: $i,SV78: $i] :
( ( ( element @ SV78 @ ( powerset @ SV26 ) )
= $false )
| ( ( element @ ( subset_complement @ SV26 @ SV78 ) @ ( powerset @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(996,plain,
! [SV105: $i,SV79: $i,SV27: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV27 @ SV79 )
| ~ ( element @ SV79 @ ( powerset @ SV105 ) ) )
| ~ ( empty @ SV105 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(997,plain,
! [SV28: $i,SV80: $i] :
( ( ( element @ SV80 @ ( powerset @ SV28 ) )
= $false )
| ( ( ( subset_complement @ SV28 @ ( subset_complement @ SV28 @ SV80 ) )
= SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(998,plain,
! [SV29: $i] :
( ( element @ ( sK5_SY211 @ SV29 ) @ SV29 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[933]) ).
thf(999,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1000,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ( element @ SV114 @ ( powerset @ SV30 ) )
| ( finite @ SV114 ) )
= $true )
| ( ( finite @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1001,plain,
! [SV81: $i,SV31: $i] :
( ( ~ ( ~ ( element @ SV31 @ ( powerset @ SV81 ) )
| ( subset @ SV31 @ SV81 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1002,plain,
! [SV81: $i,SV31: $i] :
( ( ~ ( ~ ( subset @ SV31 @ SV81 )
| ( element @ SV31 @ ( powerset @ SV81 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1003,plain,
! [SV32: $i,SV82: $i] :
( ( ~ ( ( SV82
!= ( union @ SV32 ) )
| ! [SY292: $i] :
~ ( ~ ( ~ ( in @ SY292 @ SV82 )
| ~ ! [SY216: $i] :
~ ~ ( ~ ( in @ SY292 @ SY216 )
| ~ ( in @ SY216 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( in @ SY292 @ SY217 )
| ~ ( in @ SY217 @ SV32 ) )
| ( in @ SY292 @ SV82 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(1004,plain,
! [SV32: $i,SV82: $i] :
( ( ~ ( ~ ! [SY295: $i] :
~ ( ~ ( ~ ( in @ SY295 @ SV82 )
| ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY295 @ SY219 )
| ~ ( in @ SY219 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ( in @ SY295 @ SY220 )
| ~ ( in @ SY220 @ SV32 ) )
| ( in @ SY295 @ SV82 ) ) )
| ( SV82
= ( union @ SV32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(1005,plain,
! [SV33: $i,SV83: $i] :
( ( ( ordinal @ SV83 )
= $false )
| ( ( ~ ( in @ SV33 @ SV83 )
| ( ordinal @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(1006,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ~ ( ~ ( ( SV115
!= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
| ! [SY340: $i] :
~ ( ~ ( ~ ( in @ SY340 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) )
| ( in @ SY340 @ SV115 ) ) ) )
| ~ ( ~ ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) )
| ( in @ SY341 @ SV115 ) ) )
| ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1007,plain,
! [SV85: $i,SV35: $i] :
( ( ( ! [SY302: $i] :
( ~ ( in @ SY302 @ SV35 )
| ( in @ SY302 @ SV85 ) ) )
= $false )
| ( ( element @ SV35 @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1008,plain,
! [SV36: $i] :
( ( ( SV36 != empty_set )
| ! [SY229: $i] :
~ ( in @ SY229 @ SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(1009,plain,
! [SV36: $i] :
( ( ~ ! [SY230: $i] :
~ ( in @ SY230 @ SV36 )
| ( SV36 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1010,plain,
! [SV107: $i,SV38: $i,SV86: $i] :
( ( ( ~ ~ ( ~ ( element @ SV86 @ ( powerset @ SV38 ) )
| ~ ( element @ SV107 @ ( powerset @ SV38 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV38 @ SV86 @ SV86 )
= SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1011,plain,
! [SV39: $i] :
( ( ( ~ ~ ( empty_carrier @ SV39 )
| ~ ( one_sorted_str @ SV39 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(1012,plain,
! [SV41: $i,SV87: $i] :
( ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( ! [SY304: $i] :
( ~ ( element @ SY304 @ ( powerset @ ( powerset @ SV41 ) ) )
| ~ ( ~ ( ( SY304
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY305: $i] :
( ~ ( element @ SY305 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY305 @ SY304 )
| ( in @ ( subset_complement @ SV41 @ SY305 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY305 ) @ SV87 )
| ( in @ SY305 @ SY304 ) ) ) ) )
| ~ ( ~ ! [SY306: $i] :
( ~ ( element @ SY306 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY306 @ SY304 )
| ( in @ ( subset_complement @ SV41 @ SY306 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY306 ) @ SV87 )
| ( in @ SY306 @ SY304 ) ) ) )
| ( SY304
= ( complements_of_subsets @ SV41 @ SV87 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1013,plain,
! [SV42: $i] :
( ( ! [SY329: $i] :
~ ( ~ ( ~ ( in @ SY329 @ ( sK6_SY237 @ SV42 ) )
| ~ ( ~ ( in @ SY329 @ SV42 )
| ~ ( ordinal @ SY329 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY329 @ SV42 )
| ~ ( ordinal @ SY329 ) )
| ( in @ SY329 @ ( sK6_SY237 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1014,plain,
! [SV43: $i] :
( ( ( empty @ SV43 )
= $true )
| ( ( ~ ! [SY239: $i] :
~ ~ ( ~ ( element @ SY239 @ ( powerset @ SV43 ) )
| ~ ~ ( empty @ SY239 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1015,plain,
! [SV44: $i] :
( ( ~ ( ~ ( element @ ( sK7_SY240 @ SV44 ) @ ( powerset @ SV44 ) )
| ~ ( empty @ ( sK7_SY240 @ SV44 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1016,plain,
! [SV45: $i,SV116: $i] :
( ( ( ~ ( ordinal @ SV116 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SV45 @ SV116 )
| ~ ( ( SV45 != SV116 ) ) )
| ~ ~ ( in @ SV116 @ SV45 ) ) )
= $true )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1017,plain,
! [SV46: $i] :
( ( ( ! [SY342: $i,SY343: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= SY342 )
| ~ ( ordinal @ SY342 ) )
| ( ( sK9_SX1 @ SV46 )
!= SY343 ) )
| ~ ( ordinal @ SY343 ) )
| ( SY342 = SY343 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[952]) ).
thf(1018,plain,
! [SV108: $i,SV47: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( element @ SV88 @ ( powerset @ SV47 ) )
| ~ ( element @ SV108 @ ( powerset @ SV47 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV47 @ SV88 @ SV108 )
= ( subset_intersection2 @ SV47 @ SV108 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1019,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ~ ( ( SV109
!= ( unordered_pair @ SV48 @ SV89 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV109 )
| ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ~ ( ~ ( ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ( in @ SY330 @ SV109 ) ) ) )
| ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV109 )
| ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ~ ( ~ ( ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ( in @ SY331 @ SV109 ) ) )
| ( SV109
= ( unordered_pair @ SV48 @ SV89 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1020,plain,
( ( element @ sK4_SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1021,plain,
( ( ~ ( element @ sK10_SY311 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( ~ ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
| ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
| ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[956]) ).
thf(1022,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ~ ( ( SV110
!= ( set_intersection2 @ SV51 @ SV90 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV110 )
| ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) )
| ( in @ SY332 @ SV110 ) ) ) )
| ~ ( ~ ! [SY333: $i] :
~ ( ~ ( ~ ( in @ SY333 @ SV110 )
| ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) )
| ( in @ SY333 @ SV110 ) ) )
| ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1023,plain,
! [SV91: $i,SV52: $i] :
( ( ( in @ SV52 @ SV91 )
= $false )
| ( ( ~ ( in @ SV91 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1024,plain,
! [SV53: $i,SV92: $i] :
( ( ( element @ SV92 @ ( powerset @ ( powerset @ SV53 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV53 @ SV92 ) @ ( powerset @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1025,plain,
! [SV54: $i,SV93: $i] :
( ( ( element @ SV93 @ ( powerset @ ( powerset @ SV54 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV54 @ SV93 ) @ ( powerset @ ( powerset @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1026,plain,
! [SV55: $i,SV94: $i] :
( ( ~ ( ( SV94
!= ( powerset @ SV55 ) )
| ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( subset @ SY315 @ SV55 ) )
| ~ ( ~ ( subset @ SY315 @ SV55 )
| ( in @ SY315 @ SV94 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(1027,plain,
! [SV55: $i,SV94: $i] :
( ( ~ ( ~ ! [SY316: $i] :
~ ( ~ ( ~ ( in @ SY316 @ SV94 )
| ( subset @ SY316 @ SV55 ) )
| ~ ( ~ ( subset @ SY316 @ SV55 )
| ( in @ SY316 @ SV94 ) ) )
| ( SV94
= ( powerset @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(1028,plain,
! [SV95: $i,SV56: $i] :
( ( ( in @ SV56 @ SV95 )
= $false )
| ( ( element @ SV56 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1029,plain,
! [SV57: $i,SV96: $i] :
( ( ( element @ SV96 @ ( powerset @ SV57 ) )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( in @ SY317 @ SV96 )
| ( in @ SY317 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1030,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ~ ( ( SV111
!= ( set_difference @ SV58 @ SV97 ) )
| ! [SY334: $i] :
~ ( ~ ( ~ ( in @ SY334 @ SV111 )
| ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) )
| ( in @ SY334 @ SV111 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV111 )
| ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) )
| ( in @ SY335 @ SV111 ) ) )
| ( SV111
= ( set_difference @ SV58 @ SV97 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1031,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ~ ( ( SV112
!= ( set_union2 @ SV59 @ SV98 ) )
| ! [SY336: $i] :
~ ( ~ ( ~ ( in @ SY336 @ SV112 )
| ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ~ ( ~ ( ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ( in @ SY336 @ SV112 ) ) ) )
| ~ ( ~ ! [SY337: $i] :
~ ( ~ ( ~ ( in @ SY337 @ SV112 )
| ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ~ ( ~ ( ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ( in @ SY337 @ SV112 ) ) )
| ( SV112
= ( set_union2 @ SV59 @ SV98 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1032,plain,
! [SV60: $i,SV99: $i] :
( ( ~ ( ( SV99
!= ( singleton @ SV60 ) )
| ! [SY324: $i] :
~ ( ~ ( ~ ( in @ SY324 @ SV99 )
| ( SY324 = SV60 ) )
| ~ ( ( SY324 != SV60 )
| ( in @ SY324 @ SV99 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(1033,plain,
! [SV60: $i,SV99: $i] :
( ( ~ ( ~ ! [SY325: $i] :
~ ( ~ ( ~ ( in @ SY325 @ SV99 )
| ( SY325 = SV60 ) )
| ~ ( ( SY325 != SV60 )
| ( in @ SY325 @ SV99 ) ) )
| ( SV99
= ( singleton @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(1034,plain,
! [SV63: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV63 ) )
= $true )
| ( ( ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV63 )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ SV63 )
| ~ ( in @ SY280 @ SY279 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1035,plain,
! [SV64: $i,SV6: $i] :
( ( ~ ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
| ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1036,plain,
! [SV64: $i,SV6: $i] :
( ( ~ ( empty @ SV6 )
| ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) )
| ~ ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1037,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 ) )
| ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) ) ) )
= $false )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[975]) ).
thf(1038,plain,
! [SV67: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV67 )
| ! [SY282: $i] :
( ~ ( in @ SY282 @ SV9 )
| ( in @ SY282 @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1039,plain,
! [SV67: $i,SV9: $i] :
( ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV9 )
| ( in @ SY283 @ SV67 ) )
| ( subset @ SV9 @ SV67 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(1040,plain,
! [SV100: $i,SV68: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV68 )
| ~ ( element @ SV68 @ ( powerset @ SV100 ) ) ) )
= $false )
| ( ( element @ SV10 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1041,plain,
! [SV101: $i,SV69: $i,SV11: $i] :
( ( ~ ~ ( ~ ( in @ SV11 @ SV69 )
| ~ ( in @ SV69 @ SV101 ) )
| ~ ( in @ SV101 @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1042,plain,
! [SV12: $i] :
( ( ( ~ ( epsilon_connected @ SV12 ) )
= $true )
| ( ( ! [SY179: $i,SY180: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY179 @ SV12 )
| ~ ( in @ SY180 @ SV12 ) )
| ~ ~ ( in @ SY179 @ SY180 ) )
| ~ ( ( SY179 != SY180 ) ) )
| ~ ~ ( in @ SY180 @ SY179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1043,plain,
! [SV12: $i] :
( ( ( ~ ! [SY181: $i,SY182: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY181 @ SV12 )
| ~ ( in @ SY182 @ SV12 ) )
| ~ ~ ( in @ SY181 @ SY182 ) )
| ~ ( ( SY181 != SY182 ) ) )
| ~ ~ ( in @ SY182 @ SY181 ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1044,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty_carrier @ SV13 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ~ ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1045,plain,
! [SV14: $i,SV117: $i] :
( ( ( ~ ( element @ SV117 @ ( powerset @ SV14 ) )
| ! [SY344: $i] :
( ~ ( element @ SY344 @ SV14 )
| ~ ~ ( in @ SY344 @ SV117 )
| ( in @ SY344 @ ( subset_complement @ SV14 @ SV117 ) ) ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1046,plain,
! [SV70: $i,SV15: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV15 ) )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV70 @ ( subset_complement @ SV15 @ SV102 ) )
| ~ ( in @ SV70 @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1047,plain,
! [SV17: $i,SV72: $i] :
( ( ( empty @ SV72 )
= $true )
| ( ( in @ SV17 @ SV72 )
= $true )
| ( ( element @ SV17 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1048,plain,
! [SV18: $i] :
( ( ( ! [SY345: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
| ( SY345
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ( ( sK12_SY338 @ SV18 )
= SY345 ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[987]) ).
thf(1049,plain,
! [SV103: $i,SV20: $i,SV74: $i] :
( ( ( ~ ( ~ ( element @ SV74 @ ( powerset @ SV20 ) )
| ~ ( element @ SV103 @ ( powerset @ SV20 ) ) ) )
= $false )
| ( ( element @ ( subset_difference @ SV20 @ SV74 @ SV103 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1050,plain,
! [SV104: $i,SV21: $i,SV75: $i] :
( ( ( ~ ( ~ ( element @ SV75 @ ( powerset @ SV21 ) )
| ~ ( element @ SV104 @ ( powerset @ SV21 ) ) ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV75 @ SV104 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1051,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV22 @ SV76 )
| ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1052,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ~ ( ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) )
| ~ ( disjoint @ SV22 @ SV76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1053,plain,
! [SV23: $i,SV113: $i] :
( ( ( ~ ( element @ SV113 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( v1_membered @ SV113 )
= $true )
| ( ( v1_membered @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1054,plain,
! [SV77: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV77 ) )
= $true )
| ( ( ~ ( empty @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1055,plain,
! [SV105: $i,SV79: $i,SV27: $i] :
( ( ~ ~ ( ~ ( in @ SV27 @ SV79 )
| ~ ( element @ SV79 @ ( powerset @ SV105 ) ) )
| ~ ( empty @ SV105 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1056,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1057,plain,
( ( ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1058,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ( element @ SV114 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( finite @ SV114 )
= $true )
| ( ( finite @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1059,plain,
! [SV81: $i,SV31: $i] :
( ( ~ ( element @ SV31 @ ( powerset @ SV81 ) )
| ( subset @ SV31 @ SV81 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1060,plain,
! [SV81: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV81 )
| ( element @ SV31 @ ( powerset @ SV81 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1061,plain,
! [SV32: $i,SV82: $i] :
( ( ( SV82
!= ( union @ SV32 ) )
| ! [SY292: $i] :
~ ( ~ ( ~ ( in @ SY292 @ SV82 )
| ~ ! [SY216: $i] :
~ ~ ( ~ ( in @ SY292 @ SY216 )
| ~ ( in @ SY216 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( in @ SY292 @ SY217 )
| ~ ( in @ SY217 @ SV32 ) )
| ( in @ SY292 @ SV82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1062,plain,
! [SV32: $i,SV82: $i] :
( ( ~ ! [SY295: $i] :
~ ( ~ ( ~ ( in @ SY295 @ SV82 )
| ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY295 @ SY219 )
| ~ ( in @ SY219 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ( in @ SY295 @ SY220 )
| ~ ( in @ SY220 @ SV32 ) )
| ( in @ SY295 @ SV82 ) ) )
| ( SV82
= ( union @ SV32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1063,plain,
! [SV83: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV83 ) )
= $true )
| ( ( ordinal @ SV33 )
= $true )
| ( ( ordinal @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1064,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ~ ( ( SV115
!= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
| ! [SY340: $i] :
~ ( ~ ( ~ ( in @ SY340 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) )
| ( in @ SY340 @ SV115 ) ) ) )
| ~ ( ~ ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) )
| ( in @ SY341 @ SV115 ) ) )
| ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1065,plain,
! [SV35: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK13_SY302 @ SV85 @ SV35 ) @ SV35 )
| ( in @ ( sK13_SY302 @ SV85 @ SV35 ) @ SV85 ) )
= $false )
| ( ( element @ SV35 @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1007]) ).
thf(1066,plain,
! [SV36: $i] :
( ( ( SV36 != empty_set )
= $true )
| ( ( ! [SY229: $i] :
~ ( in @ SY229 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1067,plain,
! [SV36: $i] :
( ( ( ~ ! [SY230: $i] :
~ ( in @ SY230 @ SV36 ) )
= $true )
| ( ( SV36 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1068,plain,
! [SV107: $i,SV38: $i,SV86: $i] :
( ( ( ~ ( ~ ( element @ SV86 @ ( powerset @ SV38 ) )
| ~ ( element @ SV107 @ ( powerset @ SV38 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV38 @ SV86 @ SV86 )
= SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1069,plain,
! [SV39: $i] :
( ( ( ~ ~ ( empty_carrier @ SV39 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV39 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1070,plain,
! [SV87: $i,SV41: $i,SV118: $i] :
( ( ( ~ ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
| ~ ( ~ ( ( SV118
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY346: $i] :
( ~ ( element @ SY346 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY346 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 )
| ( in @ SY346 @ SV118 ) ) ) ) )
| ~ ( ~ ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY347 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 )
| ( in @ SY347 @ SV118 ) ) ) )
| ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) ) ) ) )
= $true )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1071,plain,
! [SV42: $i,SV119: $i] :
( ( ~ ( ~ ( ~ ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
| ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) )
| ( in @ SV119 @ ( sK6_SY237 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1072,plain,
! [SV43: $i] :
( ( ( ! [SY239: $i] :
~ ~ ( ~ ( element @ SY239 @ ( powerset @ SV43 ) )
| ~ ~ ( empty @ SY239 ) ) )
= $false )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1073,plain,
! [SV44: $i] :
( ( ~ ( element @ ( sK7_SY240 @ SV44 ) @ ( powerset @ SV44 ) )
| ~ ( empty @ ( sK7_SY240 @ SV44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1074,plain,
! [SV45: $i,SV116: $i] :
( ( ( ~ ( ordinal @ SV116 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( in @ SV45 @ SV116 )
| ~ ( ( SV45 != SV116 ) ) )
| ~ ~ ( in @ SV116 @ SV45 ) ) )
= $true )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1075,plain,
! [SV46: $i] :
( ( ( ! [SY348: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
| ( ( sK9_SX1 @ SV46 )
!= SY348 ) )
| ~ ( ordinal @ SY348 ) )
| ( ( sK14_SY342 @ SV46 )
= SY348 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1017]) ).
thf(1076,plain,
! [SV108: $i,SV47: $i,SV88: $i] :
( ( ( ~ ( ~ ( element @ SV88 @ ( powerset @ SV47 ) )
| ~ ( element @ SV108 @ ( powerset @ SV47 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV47 @ SV88 @ SV108 )
= ( subset_intersection2 @ SV47 @ SV108 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1077,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ~ ( ( SV109
!= ( unordered_pair @ SV48 @ SV89 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV109 )
| ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ~ ( ~ ( ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ( in @ SY330 @ SV109 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1078,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV109 )
| ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ~ ( ~ ( ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ( in @ SY331 @ SV109 ) ) )
| ( SV109
= ( unordered_pair @ SV48 @ SV89 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1079,plain,
( ( ~ ( element @ sK10_SY311 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1021]) ).
thf(1080,plain,
( ( ~ ( ~ ( ~ ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
| ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
| ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1021]) ).
thf(1081,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ~ ( ( SV110
!= ( set_intersection2 @ SV51 @ SV90 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV110 )
| ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) )
| ( in @ SY332 @ SV110 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1082,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ~ ( ~ ! [SY333: $i] :
~ ( ~ ( ~ ( in @ SY333 @ SV110 )
| ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) )
| ( in @ SY333 @ SV110 ) ) )
| ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1083,plain,
! [SV52: $i,SV91: $i] :
( ( ( in @ SV91 @ SV52 )
= $false )
| ( ( in @ SV52 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1084,plain,
! [SV55: $i,SV94: $i] :
( ( ( SV94
!= ( powerset @ SV55 ) )
| ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( subset @ SY315 @ SV55 ) )
| ~ ( ~ ( subset @ SY315 @ SV55 )
| ( in @ SY315 @ SV94 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1085,plain,
! [SV55: $i,SV94: $i] :
( ( ~ ! [SY316: $i] :
~ ( ~ ( ~ ( in @ SY316 @ SV94 )
| ( subset @ SY316 @ SV55 ) )
| ~ ( ~ ( subset @ SY316 @ SV55 )
| ( in @ SY316 @ SV94 ) ) )
| ( SV94
= ( powerset @ SV55 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1086,plain,
! [SV57: $i,SV96: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV96 )
| ( in @ SV120 @ SV57 ) )
= $true )
| ( ( element @ SV96 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1087,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ~ ( ( SV111
!= ( set_difference @ SV58 @ SV97 ) )
| ! [SY334: $i] :
~ ( ~ ( ~ ( in @ SY334 @ SV111 )
| ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) )
| ( in @ SY334 @ SV111 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1088,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV111 )
| ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) )
| ( in @ SY335 @ SV111 ) ) )
| ( SV111
= ( set_difference @ SV58 @ SV97 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1089,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ~ ( ( SV112
!= ( set_union2 @ SV59 @ SV98 ) )
| ! [SY336: $i] :
~ ( ~ ( ~ ( in @ SY336 @ SV112 )
| ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ~ ( ~ ( ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ( in @ SY336 @ SV112 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1090,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ~ ( ~ ! [SY337: $i] :
~ ( ~ ( ~ ( in @ SY337 @ SV112 )
| ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ~ ( ~ ( ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ( in @ SY337 @ SV112 ) ) )
| ( SV112
= ( set_union2 @ SV59 @ SV98 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1091,plain,
! [SV60: $i,SV99: $i] :
( ( ( SV99
!= ( singleton @ SV60 ) )
| ! [SY324: $i] :
~ ( ~ ( ~ ( in @ SY324 @ SV99 )
| ( SY324 = SV60 ) )
| ~ ( ( SY324 != SV60 )
| ( in @ SY324 @ SV99 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1092,plain,
! [SV60: $i,SV99: $i] :
( ( ~ ! [SY325: $i] :
~ ( ~ ( ~ ( in @ SY325 @ SV99 )
| ( SY325 = SV60 ) )
| ~ ( ( SY325 != SV60 )
| ( in @ SY325 @ SV99 ) ) )
| ( SV99
= ( singleton @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1093,plain,
! [SV63: $i,SV5: $i] :
( ( ( in @ SV5 @ SV63 )
= $false )
| ( ( ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV63 )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ SV63 )
| ~ ( in @ SY280 @ SY279 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1094,plain,
! [SV64: $i,SV6: $i] :
( ( ( ~ ~ ( empty @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
| ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1095,plain,
! [SV64: $i,SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) )
| ~ ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1096,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 ) )
| ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1097,plain,
! [SV67: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV67 ) )
= $true )
| ( ( ! [SY282: $i] :
( ~ ( in @ SY282 @ SV9 )
| ( in @ SY282 @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1098,plain,
! [SV67: $i,SV9: $i] :
( ( ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV9 )
| ( in @ SY283 @ SV67 ) ) )
= $true )
| ( ( subset @ SV9 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1099,plain,
! [SV100: $i,SV68: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV68 )
| ~ ( element @ SV68 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( element @ SV10 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1100,plain,
! [SV101: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ SV11 @ SV69 )
| ~ ( in @ SV69 @ SV101 ) ) )
= $true )
| ( ( ~ ( in @ SV101 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1101,plain,
! [SV12: $i] :
( ( ( epsilon_connected @ SV12 )
= $false )
| ( ( ! [SY179: $i,SY180: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY179 @ SV12 )
| ~ ( in @ SY180 @ SV12 ) )
| ~ ~ ( in @ SY179 @ SY180 ) )
| ~ ( ( SY179 != SY180 ) ) )
| ~ ~ ( in @ SY180 @ SY179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1102,plain,
! [SV12: $i] :
( ( ( ! [SY181: $i,SY182: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY181 @ SV12 )
| ~ ( in @ SY182 @ SV12 ) )
| ~ ~ ( in @ SY181 @ SY182 ) )
| ~ ( ( SY181 != SY182 ) ) )
| ~ ~ ( in @ SY182 @ SY181 ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1103,plain,
! [SV13: $i] :
( ( ( ~ ( empty_carrier @ SV13 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ~ ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1104,plain,
! [SV14: $i,SV117: $i] :
( ( ( ~ ( element @ SV117 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ! [SY344: $i] :
( ~ ( element @ SY344 @ SV14 )
| ~ ~ ( in @ SY344 @ SV117 )
| ( in @ SY344 @ ( subset_complement @ SV14 @ SV117 ) ) ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1105,plain,
! [SV102: $i,SV15: $i,SV70: $i] :
( ( ( ~ ( ~ ( in @ SV70 @ ( subset_complement @ SV15 @ SV102 ) )
| ~ ( in @ SV70 @ SV102 ) ) )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1106,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
| ( ( sK15_SY345 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1048]) ).
thf(1107,plain,
! [SV103: $i,SV20: $i,SV74: $i] :
( ( ( ~ ( element @ SV74 @ ( powerset @ SV20 ) )
| ~ ( element @ SV103 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV20 @ SV74 @ SV103 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1108,plain,
! [SV104: $i,SV21: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ ( powerset @ SV21 ) )
| ~ ( element @ SV104 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV75 @ SV104 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1050]) ).
thf(1109,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV22 @ SV76 )
| ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1110,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ( ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) )
| ~ ( disjoint @ SV22 @ SV76 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1111,plain,
! [SV23: $i,SV113: $i] :
( ( ( element @ SV113 @ ( powerset @ SV23 ) )
= $false )
| ( ( v1_membered @ SV113 )
= $true )
| ( ( v1_membered @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1112,plain,
! [SV77: $i,SV25: $i] :
( ( ( in @ SV25 @ SV77 )
= $false )
| ( ( ~ ( empty @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1113,plain,
! [SV105: $i,SV79: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ SV79 )
| ~ ( element @ SV79 @ ( powerset @ SV105 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1114,plain,
( ( one_sorted_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1115,plain,
( ( ~ ( empty_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1116,plain,
! [SV30: $i,SV114: $i] :
( ( ( element @ SV114 @ ( powerset @ SV30 ) )
= $false )
| ( ( finite @ SV114 )
= $true )
| ( ( finite @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1117,plain,
! [SV81: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( subset @ SV31 @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1118,plain,
! [SV81: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV81 ) )
= $true )
| ( ( element @ SV31 @ ( powerset @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1119,plain,
! [SV32: $i,SV82: $i] :
( ( ( SV82
!= ( union @ SV32 ) )
= $true )
| ( ( ! [SY292: $i] :
~ ( ~ ( ~ ( in @ SY292 @ SV82 )
| ~ ! [SY216: $i] :
~ ~ ( ~ ( in @ SY292 @ SY216 )
| ~ ( in @ SY216 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( in @ SY292 @ SY217 )
| ~ ( in @ SY217 @ SV32 ) )
| ( in @ SY292 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1120,plain,
! [SV32: $i,SV82: $i] :
( ( ( ~ ! [SY295: $i] :
~ ( ~ ( ~ ( in @ SY295 @ SV82 )
| ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY295 @ SY219 )
| ~ ( in @ SY219 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ( in @ SY295 @ SY220 )
| ~ ( in @ SY220 @ SV32 ) )
| ( in @ SY295 @ SV82 ) ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1121,plain,
! [SV83: $i,SV33: $i] :
( ( ( in @ SV33 @ SV83 )
= $false )
| ( ( ordinal @ SV33 )
= $true )
| ( ( ordinal @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1122,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ~ ( ( SV115
!= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
| ! [SY340: $i] :
~ ( ~ ( ~ ( in @ SY340 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) )
| ( in @ SY340 @ SV115 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1123,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ~ ( ~ ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) )
| ( in @ SY341 @ SV115 ) ) )
| ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1124,plain,
! [SV35: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK13_SY302 @ SV85 @ SV35 ) @ SV35 ) )
= $false )
| ( ( element @ SV35 @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1125,plain,
! [SV35: $i,SV85: $i] :
( ( ( in @ ( sK13_SY302 @ SV85 @ SV35 ) @ SV85 )
= $false )
| ( ( element @ SV35 @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1126,plain,
! [SV36: $i] :
( ( ( SV36 = empty_set )
= $false )
| ( ( ! [SY229: $i] :
~ ( in @ SY229 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1127,plain,
! [SV36: $i] :
( ( ( ! [SY230: $i] :
~ ( in @ SY230 @ SV36 ) )
= $false )
| ( ( SV36 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1128,plain,
! [SV107: $i,SV38: $i,SV86: $i] :
( ( ( ~ ( element @ SV86 @ ( powerset @ SV38 ) )
| ~ ( element @ SV107 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV38 @ SV86 @ SV86 )
= SV86 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1129,plain,
! [SV39: $i] :
( ( ( ~ ( empty_carrier @ SV39 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV39 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1130,plain,
! [SV87: $i,SV41: $i,SV118: $i] :
( ( ( ~ ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV118
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY346: $i] :
( ~ ( element @ SY346 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY346 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 )
| ( in @ SY346 @ SV118 ) ) ) ) )
| ~ ( ~ ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY347 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 )
| ( in @ SY347 @ SV118 ) ) ) )
| ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) ) ) ) )
= $true )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1131,plain,
! [SV42: $i,SV119: $i] :
( ( ~ ( ~ ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
| ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) )
| ( in @ SV119 @ ( sK6_SY237 @ SV42 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1132,plain,
! [SV43: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK16_SY239 @ SV43 ) @ ( powerset @ SV43 ) )
| ~ ~ ( empty @ ( sK16_SY239 @ SV43 ) ) ) )
= $false )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1072]) ).
thf(1133,plain,
! [SV44: $i] :
( ( ~ ( element @ ( sK7_SY240 @ SV44 ) @ ( powerset @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1134,plain,
! [SV44: $i] :
( ( ~ ( empty @ ( sK7_SY240 @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1135,plain,
! [SV45: $i,SV116: $i] :
( ( ( ordinal @ SV116 )
= $false )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( in @ SV45 @ SV116 )
| ~ ( ( SV45 != SV116 ) ) )
| ~ ~ ( in @ SV116 @ SV45 ) ) )
= $true )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1136,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
| ( ( sK9_SX1 @ SV46 )
!= ( sK17_SY348 @ SV46 ) ) )
| ~ ( ordinal @ ( sK17_SY348 @ SV46 ) ) )
| ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1075]) ).
thf(1137,plain,
! [SV108: $i,SV47: $i,SV88: $i] :
( ( ( ~ ( element @ SV88 @ ( powerset @ SV47 ) )
| ~ ( element @ SV108 @ ( powerset @ SV47 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV47 @ SV88 @ SV108 )
= ( subset_intersection2 @ SV47 @ SV108 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1138,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ( SV109
!= ( unordered_pair @ SV48 @ SV89 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV109 )
| ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ~ ( ~ ( ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ( in @ SY330 @ SV109 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1139,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV109 )
| ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ~ ( ~ ( ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ( in @ SY331 @ SV109 ) ) )
| ( SV109
= ( unordered_pair @ SV48 @ SV89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1140,plain,
( ( element @ sK10_SY311 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1141,plain,
( ( ~ ( ~ ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
| ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
| ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1142,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ( SV110
!= ( set_intersection2 @ SV51 @ SV90 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV110 )
| ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) )
| ( in @ SY332 @ SV110 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1143,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ~ ! [SY333: $i] :
~ ( ~ ( ~ ( in @ SY333 @ SV110 )
| ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) )
| ( in @ SY333 @ SV110 ) ) )
| ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1144,plain,
! [SV55: $i,SV94: $i] :
( ( ( SV94
!= ( powerset @ SV55 ) )
= $true )
| ( ( ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( subset @ SY315 @ SV55 ) )
| ~ ( ~ ( subset @ SY315 @ SV55 )
| ( in @ SY315 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1145,plain,
! [SV55: $i,SV94: $i] :
( ( ( ~ ! [SY316: $i] :
~ ( ~ ( ~ ( in @ SY316 @ SV94 )
| ( subset @ SY316 @ SV55 ) )
| ~ ( ~ ( subset @ SY316 @ SV55 )
| ( in @ SY316 @ SV94 ) ) ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1146,plain,
! [SV57: $i,SV96: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV96 ) )
= $true )
| ( ( in @ SV120 @ SV57 )
= $true )
| ( ( element @ SV96 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1147,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ( SV111
!= ( set_difference @ SV58 @ SV97 ) )
| ! [SY334: $i] :
~ ( ~ ( ~ ( in @ SY334 @ SV111 )
| ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) )
| ( in @ SY334 @ SV111 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1148,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV111 )
| ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) )
| ( in @ SY335 @ SV111 ) ) )
| ( SV111
= ( set_difference @ SV58 @ SV97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1149,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ( SV112
!= ( set_union2 @ SV59 @ SV98 ) )
| ! [SY336: $i] :
~ ( ~ ( ~ ( in @ SY336 @ SV112 )
| ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ~ ( ~ ( ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ( in @ SY336 @ SV112 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1150,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ~ ! [SY337: $i] :
~ ( ~ ( ~ ( in @ SY337 @ SV112 )
| ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ~ ( ~ ( ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ( in @ SY337 @ SV112 ) ) )
| ( SV112
= ( set_union2 @ SV59 @ SV98 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1151,plain,
! [SV60: $i,SV99: $i] :
( ( ( SV99
!= ( singleton @ SV60 ) )
= $true )
| ( ( ! [SY324: $i] :
~ ( ~ ( ~ ( in @ SY324 @ SV99 )
| ( SY324 = SV60 ) )
| ~ ( ( SY324 != SV60 )
| ( in @ SY324 @ SV99 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1152,plain,
! [SV60: $i,SV99: $i] :
( ( ( ~ ! [SY325: $i] :
~ ( ~ ( ~ ( in @ SY325 @ SV99 )
| ( SY325 = SV60 ) )
| ~ ( ( SY325 != SV60 )
| ( in @ SY325 @ SV99 ) ) ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1153,plain,
! [SV5: $i,SV63: $i] :
( ( ( ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV63 )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ SV63 )
| ~ ( in @ SY280 @ SY279 ) ) ) )
= $false )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1154,plain,
! [SV64: $i,SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
| ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1155,plain,
! [SV64: $i,SV6: $i] :
( ( ( empty @ SV6 )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) )
| ~ ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1156,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1157,plain,
! [SV67: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV67 )
= $false )
| ( ( ! [SY282: $i] :
( ~ ( in @ SY282 @ SV9 )
| ( in @ SY282 @ SV67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1158,plain,
! [SV67: $i,SV9: $i] :
( ( ( ! [SY283: $i] :
( ~ ( in @ SY283 @ SV9 )
| ( in @ SY283 @ SV67 ) ) )
= $false )
| ( ( subset @ SV9 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1159,plain,
! [SV100: $i,SV68: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV68 ) )
= $true )
| ( ( ~ ( element @ SV68 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( element @ SV10 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1160,plain,
! [SV101: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ SV11 @ SV69 )
| ~ ( in @ SV69 @ SV101 ) ) )
= $false )
| ( ( ~ ( in @ SV101 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1161,plain,
! [SV12: $i,SV121: $i] :
( ( ( ! [SY349: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SY349 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SY349 ) )
| ~ ( ( SV121 != SY349 ) ) )
| ~ ~ ( in @ SY349 @ SV121 ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1162,plain,
! [SV12: $i] :
( ( ( ! [SY350: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ SY350 @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ SY350 ) )
| ~ ( ( ( sK18_SY181 @ SV12 )
!= SY350 ) ) )
| ~ ~ ( in @ SY350 @ ( sK18_SY181 @ SV12 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1102]) ).
thf(1163,plain,
! [SV13: $i] :
( ( ( empty_carrier @ SV13 )
= $true )
| ( ( ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ~ ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1164,plain,
! [SV14: $i,SV117: $i] :
( ( ( element @ SV117 @ ( powerset @ SV14 ) )
= $false )
| ( ( ! [SY344: $i] :
( ~ ( element @ SY344 @ SV14 )
| ~ ~ ( in @ SY344 @ SV117 )
| ( in @ SY344 @ ( subset_complement @ SV14 @ SV117 ) ) ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1165,plain,
! [SV102: $i,SV15: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( subset_complement @ SV15 @ SV102 ) )
| ~ ( in @ SV70 @ SV102 ) )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1166,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
| ( ( sK15_SY345 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1167,plain,
! [SV18: $i] :
( ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1168,plain,
! [SV103: $i,SV20: $i,SV74: $i] :
( ( ( ~ ( element @ SV74 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( ~ ( element @ SV103 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV20 @ SV74 @ SV103 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1169,plain,
! [SV104: $i,SV21: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( ~ ( element @ SV104 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV75 @ SV104 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1170,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ~ ( disjoint @ SV22 @ SV76 )
| ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1171,plain,
! [SV76: $i,SV22: $i] :
( ( ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) )
| ~ ( disjoint @ SV22 @ SV76 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1172,plain,
! [SV25: $i,SV77: $i] :
( ( ( empty @ SV77 )
= $false )
| ( ( in @ SV25 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1173,plain,
! [SV105: $i,SV79: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ SV79 )
| ~ ( element @ SV79 @ ( powerset @ SV105 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1174,plain,
( ( empty_carrier @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1175,plain,
! [SV81: $i,SV31: $i] :
( ( ( element @ SV31 @ ( powerset @ SV81 ) )
= $false )
| ( ( subset @ SV31 @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1176,plain,
! [SV81: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV81 )
= $false )
| ( ( element @ SV31 @ ( powerset @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1177,plain,
! [SV32: $i,SV82: $i] :
( ( ( SV82
= ( union @ SV32 ) )
= $false )
| ( ( ! [SY292: $i] :
~ ( ~ ( ~ ( in @ SY292 @ SV82 )
| ~ ! [SY216: $i] :
~ ~ ( ~ ( in @ SY292 @ SY216 )
| ~ ( in @ SY216 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ( ~ ( in @ SY292 @ SY217 )
| ~ ( in @ SY217 @ SV32 ) )
| ( in @ SY292 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1178,plain,
! [SV32: $i,SV82: $i] :
( ( ( ! [SY295: $i] :
~ ( ~ ( ~ ( in @ SY295 @ SV82 )
| ~ ! [SY219: $i] :
~ ~ ( ~ ( in @ SY295 @ SY219 )
| ~ ( in @ SY219 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ( in @ SY295 @ SY220 )
| ~ ( in @ SY220 @ SV32 ) )
| ( in @ SY295 @ SV82 ) ) ) )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1179,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ( SV115
!= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
| ! [SY340: $i] :
~ ( ~ ( ~ ( in @ SY340 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) )
| ( in @ SY340 @ SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1180,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ~ ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) )
| ( in @ SY341 @ SV115 ) ) )
| ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1181,plain,
! [SV35: $i,SV85: $i] :
( ( ( in @ ( sK13_SY302 @ SV85 @ SV35 ) @ SV35 )
= $true )
| ( ( element @ SV35 @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1182,plain,
! [SV36: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV36 ) )
= $true )
| ( ( SV36 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1183,plain,
! [SV36: $i] :
( ( ( ~ ( in @ ( sK19_SY230 @ SV36 ) @ SV36 ) )
= $false )
| ( ( SV36 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1127]) ).
thf(1184,plain,
! [SV107: $i,SV38: $i,SV86: $i] :
( ( ( ~ ( element @ SV86 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( ~ ( element @ SV107 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV38 @ SV86 @ SV86 )
= SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1185,plain,
! [SV39: $i] :
( ( ( empty_carrier @ SV39 )
= $true )
| ( ( ~ ( one_sorted_str @ SV39 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1186,plain,
! [SV87: $i,SV41: $i,SV118: $i] :
( ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV118
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY346: $i] :
( ~ ( element @ SY346 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY346 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 )
| ( in @ SY346 @ SV118 ) ) ) ) )
| ~ ( ~ ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY347 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 )
| ( in @ SY347 @ SV118 ) ) ) )
| ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) ) ) ) )
= $true )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1187,plain,
! [SV42: $i,SV119: $i] :
( ( ~ ( ~ ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
| ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1188,plain,
! [SV42: $i,SV119: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) )
| ( in @ SV119 @ ( sK6_SY237 @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1189,plain,
! [SV43: $i] :
( ( ( ~ ( ~ ( element @ ( sK16_SY239 @ SV43 ) @ ( powerset @ SV43 ) )
| ~ ~ ( empty @ ( sK16_SY239 @ SV43 ) ) ) )
= $true )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1132]) ).
thf(1190,plain,
! [SV44: $i] :
( ( element @ ( sK7_SY240 @ SV44 ) @ ( powerset @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1191,plain,
! [SV44: $i] :
( ( empty @ ( sK7_SY240 @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1192,plain,
! [SV116: $i,SV45: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( in @ SV45 @ SV116 )
| ~ ( ( SV45 != SV116 ) ) )
| ~ ~ ( in @ SV116 @ SV45 ) ) )
= $false )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1193,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
| ( ( sK9_SX1 @ SV46 )
!= ( sK17_SY348 @ SV46 ) ) )
| ~ ( ordinal @ ( sK17_SY348 @ SV46 ) ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1194,plain,
! [SV46: $i] :
( ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1195,plain,
! [SV108: $i,SV47: $i,SV88: $i] :
( ( ( ~ ( element @ SV88 @ ( powerset @ SV47 ) ) )
= $true )
| ( ( ~ ( element @ SV108 @ ( powerset @ SV47 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV47 @ SV88 @ SV108 )
= ( subset_intersection2 @ SV47 @ SV108 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1196,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ( SV109
!= ( unordered_pair @ SV48 @ SV89 ) )
= $true )
| ( ( ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV109 )
| ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ~ ( ~ ( ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ( in @ SY330 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1197,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV109 )
| ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ~ ( ~ ( ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ( in @ SY331 @ SV109 ) ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1198,plain,
( ( ( ~ ( ~ ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
| ~ ( in @ sK10_SY311 @ sK4_SX0 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1199,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ( SV110
!= ( set_intersection2 @ SV51 @ SV90 ) )
= $true )
| ( ( ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV110 )
| ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) )
| ( in @ SY332 @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1200,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ( ~ ! [SY333: $i] :
~ ( ~ ( ~ ( in @ SY333 @ SV110 )
| ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) )
| ( in @ SY333 @ SV110 ) ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1201,plain,
! [SV55: $i,SV94: $i] :
( ( ( SV94
= ( powerset @ SV55 ) )
= $false )
| ( ( ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( subset @ SY315 @ SV55 ) )
| ~ ( ~ ( subset @ SY315 @ SV55 )
| ( in @ SY315 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1202,plain,
! [SV55: $i,SV94: $i] :
( ( ( ! [SY316: $i] :
~ ( ~ ( ~ ( in @ SY316 @ SV94 )
| ( subset @ SY316 @ SV55 ) )
| ~ ( ~ ( subset @ SY316 @ SV55 )
| ( in @ SY316 @ SV94 ) ) ) )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1203,plain,
! [SV57: $i,SV96: $i,SV120: $i] :
( ( ( in @ SV120 @ SV96 )
= $false )
| ( ( in @ SV120 @ SV57 )
= $true )
| ( ( element @ SV96 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1204,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ( SV111
!= ( set_difference @ SV58 @ SV97 ) )
= $true )
| ( ( ! [SY334: $i] :
~ ( ~ ( ~ ( in @ SY334 @ SV111 )
| ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) )
| ( in @ SY334 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1205,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV111 )
| ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) )
| ( in @ SY335 @ SV111 ) ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1206,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ( SV112
!= ( set_union2 @ SV59 @ SV98 ) )
= $true )
| ( ( ! [SY336: $i] :
~ ( ~ ( ~ ( in @ SY336 @ SV112 )
| ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ~ ( ~ ( ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ( in @ SY336 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1207,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ( ~ ! [SY337: $i] :
~ ( ~ ( ~ ( in @ SY337 @ SV112 )
| ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ~ ( ~ ( ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ( in @ SY337 @ SV112 ) ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1208,plain,
! [SV60: $i,SV99: $i] :
( ( ( SV99
= ( singleton @ SV60 ) )
= $false )
| ( ( ! [SY324: $i] :
~ ( ~ ( ~ ( in @ SY324 @ SV99 )
| ( SY324 = SV60 ) )
| ~ ( ( SY324 != SV60 )
| ( in @ SY324 @ SV99 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1209,plain,
! [SV60: $i,SV99: $i] :
( ( ( ! [SY325: $i] :
~ ( ~ ( ~ ( in @ SY325 @ SV99 )
| ( SY325 = SV60 ) )
| ~ ( ( SY325 != SV60 )
| ( in @ SY325 @ SV99 ) ) ) )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1210,plain,
! [SV63: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY279 @ SV5 @ SV63 ) @ SV63 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY351 @ SV63 )
| ~ ( in @ SY351 @ ( sK20_SY279 @ SV5 @ SV63 ) ) ) ) )
= $false )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1153]) ).
thf(1211,plain,
! [SV64: $i,SV6: $i] :
( ( ( empty @ SV6 )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
| ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1212,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) )
| ~ ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) ) )
= $false )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1213,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1214,plain,
! [SV67: $i,SV9: $i,SV123: $i] :
( ( ( ~ ( in @ SV123 @ SV9 )
| ( in @ SV123 @ SV67 ) )
= $true )
| ( ( subset @ SV9 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1215,plain,
! [SV9: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK21_SY283 @ SV67 @ SV9 ) @ SV9 )
| ( in @ ( sK21_SY283 @ SV67 @ SV9 ) @ SV67 ) )
= $false )
| ( ( subset @ SV9 @ SV67 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1158]) ).
thf(1216,plain,
! [SV100: $i,SV68: $i,SV10: $i] :
( ( ( in @ SV10 @ SV68 )
= $false )
| ( ( ~ ( element @ SV68 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( element @ SV10 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1217,plain,
! [SV101: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV69 )
| ~ ( in @ SV69 @ SV101 ) )
= $true )
| ( ( ~ ( in @ SV101 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1218,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) )
| ~ ( ( SV121 != SV124 ) ) )
| ~ ~ ( in @ SV124 @ SV121 ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1219,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
| ~ ( ( ( sK18_SY181 @ SV12 )
!= ( sK22_SY350 @ SV12 ) ) ) )
| ~ ~ ( in @ ( sK22_SY350 @ SV12 ) @ ( sK18_SY181 @ SV12 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1162]) ).
thf(1220,plain,
! [SV13: $i] :
( ( ( one_sorted_str @ SV13 )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( ~ ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1221,plain,
! [SV117: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ SV14 )
| ~ ~ ( in @ SV125 @ SV117 )
| ( in @ SV125 @ ( subset_complement @ SV14 @ SV117 ) ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV14 ) )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1222,plain,
! [SV102: $i,SV15: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( subset_complement @ SV15 @ SV102 ) ) )
= $true )
| ( ( ~ ( in @ SV70 @ SV102 ) )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1223,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
| ( ( sK15_SY345 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) ) )
= $true )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1224,plain,
! [SV18: $i] :
( ( ( ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1225,plain,
! [SV103: $i,SV20: $i,SV74: $i] :
( ( ( element @ SV74 @ ( powerset @ SV20 ) )
= $false )
| ( ( ~ ( element @ SV103 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV20 @ SV74 @ SV103 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1226,plain,
! [SV104: $i,SV21: $i,SV75: $i] :
( ( ( element @ SV75 @ ( powerset @ SV21 ) )
= $false )
| ( ( ~ ( element @ SV104 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV75 @ SV104 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1227,plain,
! [SV76: $i,SV22: $i] :
( ( ( ~ ~ ( disjoint @ SV22 @ SV76 ) )
= $true )
| ( ( ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1228,plain,
! [SV76: $i,SV22: $i] :
( ( ( ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1229,plain,
! [SV105: $i,SV79: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV79 )
| ~ ( element @ SV79 @ ( powerset @ SV105 ) ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1230,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV126 @ SV82 )
| ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SV126 @ SY352 )
| ~ ( in @ SY352 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ SV126 @ SY353 )
| ~ ( in @ SY353 @ SV32 ) )
| ( in @ SV126 @ SV82 ) ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1231,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
| ~ ! [SY354: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY354 )
| ~ ( in @ SY354 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) ) )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1178]) ).
thf(1232,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ( SV115
!= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true )
| ( ( ! [SY340: $i] :
~ ( ~ ( ~ ( in @ SY340 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) )
| ( in @ SY340 @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1233,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ( ~ ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) )
| ( in @ SY341 @ SV115 ) ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1234,plain,
! [SV36: $i,SV122: $i] :
( ( ( in @ SV122 @ SV36 )
= $false )
| ( ( SV36 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1235,plain,
! [SV36: $i] :
( ( ( in @ ( sK19_SY230 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1236,plain,
! [SV107: $i,SV38: $i,SV86: $i] :
( ( ( element @ SV86 @ ( powerset @ SV38 ) )
= $false )
| ( ( ~ ( element @ SV107 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV38 @ SV86 @ SV86 )
= SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1237,plain,
! [SV39: $i] :
( ( ( one_sorted_str @ SV39 )
= $false )
| ( ( empty_carrier @ SV39 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1238,plain,
! [SV87: $i,SV41: $i,SV118: $i] :
( ( ( ~ ( ( SV118
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY346: $i] :
( ~ ( element @ SY346 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY346 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 )
| ( in @ SY346 @ SV118 ) ) ) ) )
| ~ ( ~ ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY347 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 )
| ( in @ SY347 @ SV118 ) ) ) )
| ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) ) ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1239,plain,
! [SV42: $i,SV119: $i] :
( ( ~ ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
| ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1240,plain,
! [SV42: $i,SV119: $i] :
( ( ~ ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) )
| ( in @ SV119 @ ( sK6_SY237 @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1241,plain,
! [SV43: $i] :
( ( ( ~ ( element @ ( sK16_SY239 @ SV43 ) @ ( powerset @ SV43 ) )
| ~ ~ ( empty @ ( sK16_SY239 @ SV43 ) ) )
= $false )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1242,plain,
! [SV116: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ~ ( in @ SV45 @ SV116 )
| ~ ( ( SV45 != SV116 ) ) )
| ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1192]) ).
thf(1243,plain,
! [SV46: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
| ( ( sK9_SX1 @ SV46 )
!= ( sK17_SY348 @ SV46 ) ) )
| ~ ( ordinal @ ( sK17_SY348 @ SV46 ) ) ) )
= $true )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1244,plain,
! [SV46: $i] :
( ( ( ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1245,plain,
! [SV108: $i,SV47: $i,SV88: $i] :
( ( ( element @ SV88 @ ( powerset @ SV47 ) )
= $false )
| ( ( ~ ( element @ SV108 @ ( powerset @ SV47 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV47 @ SV88 @ SV108 )
= ( subset_intersection2 @ SV47 @ SV108 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1246,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false )
| ( ( ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV109 )
| ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ~ ( ~ ( ( SY330 = SV48 )
| ( SY330 = SV89 ) )
| ( in @ SY330 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1247,plain,
! [SV89: $i,SV48: $i,SV109: $i] :
( ( ( ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV109 )
| ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ~ ( ~ ( ( SY331 = SV48 )
| ( SY331 = SV89 ) )
| ( in @ SY331 @ SV109 ) ) ) )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1248,plain,
( ( ( ~ ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
| ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1249,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false )
| ( ( ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV110 )
| ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY332 @ SV51 )
| ~ ( in @ SY332 @ SV90 ) )
| ( in @ SY332 @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1250,plain,
! [SV90: $i,SV51: $i,SV110: $i] :
( ( ( ! [SY333: $i] :
~ ( ~ ( ~ ( in @ SY333 @ SV110 )
| ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY333 @ SV51 )
| ~ ( in @ SY333 @ SV90 ) )
| ( in @ SY333 @ SV110 ) ) ) )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1251,plain,
! [SV55: $i,SV94: $i,SV127: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV127 @ SV94 )
| ( subset @ SV127 @ SV55 ) )
| ~ ( ~ ( subset @ SV127 @ SV55 )
| ( in @ SV127 @ SV94 ) ) ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1252,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
| ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 ) )
| ~ ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) ) ) )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1202]) ).
thf(1253,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false )
| ( ( ! [SY334: $i] :
~ ( ~ ( ~ ( in @ SY334 @ SV111 )
| ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV58 )
| ~ ~ ( in @ SY334 @ SV97 ) )
| ( in @ SY334 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1254,plain,
! [SV97: $i,SV58: $i,SV111: $i] :
( ( ( ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV111 )
| ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY335 @ SV58 )
| ~ ~ ( in @ SY335 @ SV97 ) )
| ( in @ SY335 @ SV111 ) ) ) )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1255,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false )
| ( ( ! [SY336: $i] :
~ ( ~ ( ~ ( in @ SY336 @ SV112 )
| ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ~ ( ~ ( ( in @ SY336 @ SV59 )
| ( in @ SY336 @ SV98 ) )
| ( in @ SY336 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1256,plain,
! [SV98: $i,SV59: $i,SV112: $i] :
( ( ( ! [SY337: $i] :
~ ( ~ ( ~ ( in @ SY337 @ SV112 )
| ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ~ ( ~ ( ( in @ SY337 @ SV59 )
| ( in @ SY337 @ SV98 ) )
| ( in @ SY337 @ SV112 ) ) ) )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1257,plain,
! [SV60: $i,SV99: $i,SV128: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV128 @ SV99 )
| ( SV128 = SV60 ) )
| ~ ( ( SV128 != SV60 )
| ( in @ SV128 @ SV99 ) ) ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1258,plain,
! [SV99: $i,SV60: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
| ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 ) )
| ~ ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) ) ) )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1209]) ).
thf(1259,plain,
! [SV63: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY279 @ SV5 @ SV63 ) @ SV63 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY351 @ SV63 )
| ~ ( in @ SY351 @ ( sK20_SY279 @ SV5 @ SV63 ) ) ) ) )
= $true )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1260,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
| ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) )
= $false )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1261,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) ) )
= $false )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1262,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) ) )
= $false )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1263,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1213]) ).
thf(1264,plain,
! [SV8: $i,SV66: $i] :
( ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1213]) ).
thf(1265,plain,
! [SV67: $i,SV9: $i,SV123: $i] :
( ( ( ~ ( in @ SV123 @ SV9 ) )
= $true )
| ( ( in @ SV123 @ SV67 )
= $true )
| ( ( subset @ SV9 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1266,plain,
! [SV9: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK21_SY283 @ SV67 @ SV9 ) @ SV9 ) )
= $false )
| ( ( subset @ SV9 @ SV67 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1215]) ).
thf(1267,plain,
! [SV9: $i,SV67: $i] :
( ( ( in @ ( sK21_SY283 @ SV67 @ SV9 ) @ SV67 )
= $false )
| ( ( subset @ SV9 @ SV67 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1215]) ).
thf(1268,plain,
! [SV10: $i,SV100: $i,SV68: $i] :
( ( ( element @ SV68 @ ( powerset @ SV100 ) )
= $false )
| ( ( in @ SV10 @ SV68 )
= $false )
| ( ( element @ SV10 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1269,plain,
! [SV101: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV69 ) )
= $true )
| ( ( ~ ( in @ SV69 @ SV101 ) )
= $true )
| ( ( ~ ( in @ SV101 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1270,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) )
| ~ ( ( SV121 != SV124 ) ) )
| ~ ~ ( in @ SV124 @ SV121 ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1271,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
| ~ ( ( ( sK18_SY181 @ SV12 )
!= ( sK22_SY350 @ SV12 ) ) ) )
| ~ ~ ( in @ ( sK22_SY350 @ SV12 ) @ ( sK18_SY181 @ SV12 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1272,plain,
! [SV13: $i] :
( ( ( ! [SY183: $i] :
~ ~ ( ~ ( element @ SY183 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY183 ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1273,plain,
! [SV117: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ SV14 ) )
= $true )
| ( ( ~ ~ ( in @ SV125 @ SV117 )
| ( in @ SV125 @ ( subset_complement @ SV14 @ SV117 ) ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV14 ) )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1274,plain,
! [SV102: $i,SV15: $i,SV70: $i] :
( ( ( in @ SV70 @ ( subset_complement @ SV15 @ SV102 ) )
= $false )
| ( ( ~ ( in @ SV70 @ SV102 ) )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1275,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
| ( ( sK15_SY345 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1276,plain,
! [SV18: $i] :
( ( ( ~ ! [SY356: $i] :
~ ( ~ ( ~ ( in @ SY356 @ ( sK26_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY356
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY356
!= ( singleton @ SY196 ) ) )
| ( in @ SY356 @ ( sK26_SY193 @ SV18 ) ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1224]) ).
thf(1277,plain,
! [SV74: $i,SV20: $i,SV103: $i] :
( ( ( element @ SV103 @ ( powerset @ SV20 ) )
= $false )
| ( ( element @ SV74 @ ( powerset @ SV20 ) )
= $false )
| ( ( element @ ( subset_difference @ SV20 @ SV74 @ SV103 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1278,plain,
! [SV75: $i,SV21: $i,SV104: $i] :
( ( ( element @ SV104 @ ( powerset @ SV21 ) )
= $false )
| ( ( element @ SV75 @ ( powerset @ SV21 ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV75 @ SV104 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1279,plain,
! [SV76: $i,SV22: $i] :
( ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $false )
| ( ( ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1280,plain,
! [SV76: $i,SV22: $i] :
( ( ( ~ ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1281,plain,
! [SV105: $i,SV79: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV79 ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( powerset @ SV105 ) ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1282,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ( ~ ( in @ SV126 @ SV82 )
| ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SV126 @ SY352 )
| ~ ( in @ SY352 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ SV126 @ SY353 )
| ~ ( in @ SY353 @ SV32 ) )
| ( in @ SV126 @ SV82 ) ) )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1283,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
| ~ ! [SY354: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY354 )
| ~ ( in @ SY354 @ SV32 ) ) )
| ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1284,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false )
| ( ( ! [SY340: $i] :
~ ( ~ ( ~ ( in @ SY340 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY340 != SV34 ) )
| ~ ( ( SY340 != SV84 ) ) )
| ~ ( ( SY340 != SV106 ) ) )
| ( in @ SY340 @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1285,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i] :
( ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SY341 != SV34 ) )
| ~ ( ( SY341 != SV84 ) ) )
| ~ ( ( SY341 != SV106 ) ) )
| ( in @ SY341 @ SV115 ) ) ) )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1286,plain,
! [SV86: $i,SV38: $i,SV107: $i] :
( ( ( element @ SV107 @ ( powerset @ SV38 ) )
= $false )
| ( ( element @ SV86 @ ( powerset @ SV38 ) )
= $false )
| ( ( ( subset_intersection2 @ SV38 @ SV86 @ SV86 )
= SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1287,plain,
! [SV39: $i] :
( ( ( empty @ ( the_carrier @ SV39 ) )
= $false )
| ( ( empty_carrier @ SV39 )
= $true )
| ( ( one_sorted_str @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1288,plain,
! [SV87: $i,SV41: $i,SV118: $i] :
( ( ( ~ ( ( SV118
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY346: $i] :
( ~ ( element @ SY346 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY346 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 )
| ( in @ SY346 @ SV118 ) ) ) ) ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1289,plain,
! [SV87: $i,SV118: $i,SV41: $i] :
( ( ( ~ ( ~ ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY347 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 )
| ( in @ SY347 @ SV118 ) ) ) )
| ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) ) ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1290,plain,
! [SV42: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ ( sK6_SY237 @ SV42 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1291,plain,
! [SV42: $i,SV119: $i] :
( ( ( ~ ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) ) )
= $true )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1292,plain,
! [SV43: $i] :
( ( ( ~ ( element @ ( sK16_SY239 @ SV43 ) @ ( powerset @ SV43 ) ) )
= $false )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1293,plain,
! [SV43: $i] :
( ( ( ~ ~ ( empty @ ( sK16_SY239 @ SV43 ) ) )
= $false )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1294,plain,
! [SV116: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ~ ( in @ SV45 @ SV116 )
| ~ ( ( SV45 != SV116 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1295,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
| ( ( sK9_SX1 @ SV46 )
!= ( sK17_SY348 @ SV46 ) ) )
| ~ ( ordinal @ ( sK17_SY348 @ SV46 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1296,plain,
! [SV46: $i] :
( ( ( ~ ! [SY359: $i] :
~ ( ~ ( ~ ( in @ SY359 @ ( sK27_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY359 ) )
| ~ ( ordinal @ SY359 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY359 ) )
| ~ ( ordinal @ SY359 ) )
| ( in @ SY359 @ ( sK27_SY245 @ SV46 ) ) ) ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1244]) ).
thf(1297,plain,
! [SV88: $i,SV47: $i,SV108: $i] :
( ( ( element @ SV108 @ ( powerset @ SV47 ) )
= $false )
| ( ( element @ SV88 @ ( powerset @ SV47 ) )
= $false )
| ( ( ( subset_intersection2 @ SV47 @ SV88 @ SV108 )
= ( subset_intersection2 @ SV47 @ SV108 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1298,plain,
! [SV89: $i,SV48: $i,SV109: $i,SV129: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV129 @ SV109 )
| ( SV129 = SV48 )
| ( SV129 = SV89 ) )
| ~ ( ~ ( ( SV129 = SV48 )
| ( SV129 = SV89 ) )
| ( in @ SV129 @ SV109 ) ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1299,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) ) )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1247]) ).
thf(1300,plain,
( ( ( ~ ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1301,plain,
( ( ( ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1302,plain,
! [SV90: $i,SV51: $i,SV110: $i,SV130: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV130 @ SV110 )
| ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) )
| ( in @ SV130 @ SV110 ) ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1303,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
| ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) ) )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1250]) ).
thf(1304,plain,
! [SV55: $i,SV94: $i,SV127: $i] :
( ( ( ~ ( ~ ( in @ SV127 @ SV94 )
| ( subset @ SV127 @ SV55 ) )
| ~ ( ~ ( subset @ SV127 @ SV55 )
| ( in @ SV127 @ SV94 ) ) )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1305,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
| ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 ) )
| ~ ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1306,plain,
! [SV97: $i,SV58: $i,SV111: $i,SV131: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV131 @ SV111 )
| ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) )
| ( in @ SV131 @ SV111 ) ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1307,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
| ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) ) )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1254]) ).
thf(1308,plain,
! [SV98: $i,SV59: $i,SV112: $i,SV132: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV132 @ SV112 )
| ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
| ~ ( ~ ( ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
| ( in @ SV132 @ SV112 ) ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1309,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) ) )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1256]) ).
thf(1310,plain,
! [SV60: $i,SV99: $i,SV128: $i] :
( ( ( ~ ( ~ ( in @ SV128 @ SV99 )
| ( SV128 = SV60 ) )
| ~ ( ( SV128 != SV60 )
| ( in @ SV128 @ SV99 ) ) )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1311,plain,
! [SV99: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
| ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 ) )
| ~ ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1312,plain,
! [SV63: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK20_SY279 @ SV5 @ SV63 ) @ SV63 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY351 @ SV63 )
| ~ ( in @ SY351 @ ( sK20_SY279 @ SV5 @ SV63 ) ) ) )
= $false )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1313,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) ) )
= $false )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1314,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) ) )
= $false )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1315,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ SV6 )
| ( empty @ SV64 ) )
= $true )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1316,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( empty @ SV64 )
| ( element @ SV64 @ SV6 ) )
= $true )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1317,plain,
! [SV8: $i,SV66: $i] :
( ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1318,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
= $false )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1319,plain,
! [SV67: $i,SV9: $i,SV123: $i] :
( ( ( in @ SV123 @ SV9 )
= $false )
| ( ( in @ SV123 @ SV67 )
= $true )
| ( ( subset @ SV9 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1320,plain,
! [SV9: $i,SV67: $i] :
( ( ( in @ ( sK21_SY283 @ SV67 @ SV9 ) @ SV9 )
= $true )
| ( ( subset @ SV9 @ SV67 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1321,plain,
! [SV101: $i,SV69: $i,SV11: $i] :
( ( ( in @ SV11 @ SV69 )
= $false )
| ( ( ~ ( in @ SV69 @ SV101 ) )
= $true )
| ( ( ~ ( in @ SV101 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1322,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) )
| ~ ( ( SV121 != SV124 ) ) )
| ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1270]) ).
thf(1323,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
| ~ ( ( ( sK18_SY181 @ SV12 )
!= ( sK22_SY350 @ SV12 ) ) ) )
| ~ ~ ( in @ ( sK22_SY350 @ SV12 ) @ ( sK18_SY181 @ SV12 ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1324,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK32_SY183 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ ( sK32_SY183 @ SV13 ) ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1272]) ).
thf(1325,plain,
! [SV117: $i,SV14: $i,SV125: $i] :
( ( ( element @ SV125 @ SV14 )
= $false )
| ( ( ~ ~ ( in @ SV125 @ SV117 )
| ( in @ SV125 @ ( subset_complement @ SV14 @ SV117 ) ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV14 ) )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1326,plain,
! [SV15: $i,SV102: $i,SV70: $i] :
( ( ( in @ SV70 @ SV102 )
= $false )
| ( ( in @ SV70 @ ( subset_complement @ SV15 @ SV102 ) )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1327,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1328,plain,
! [SV18: $i] :
( ( ( ( sK15_SY345 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1329,plain,
! [SV18: $i] :
( ( ( ! [SY356: $i] :
~ ( ~ ( ~ ( in @ SY356 @ ( sK26_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY356
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY356
!= ( singleton @ SY196 ) ) )
| ( in @ SY356 @ ( sK26_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1330,plain,
! [SV76: $i,SV22: $i] :
( ( ( disjoint @ SV22 @ SV76 )
= $true )
| ( ( ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1331,plain,
! [SV76: $i,SV22: $i] :
( ( ( ! [SY290: $i] :
~ ~ ( ~ ( in @ SY290 @ SV22 )
| ~ ( in @ SY290 @ SV76 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1280]) ).
thf(1332,plain,
! [SV105: $i,SV79: $i,SV27: $i] :
( ( ( in @ SV27 @ SV79 )
= $false )
| ( ( ~ ( element @ SV79 @ ( powerset @ SV105 ) ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1333,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ( ~ ( in @ SV126 @ SV82 )
| ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SV126 @ SY352 )
| ~ ( in @ SY352 @ SV32 ) ) ) )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1334,plain,
! [SV82: $i,SV32: $i,SV126: $i] :
( ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ SV126 @ SY353 )
| ~ ( in @ SY353 @ SV32 ) )
| ( in @ SV126 @ SV82 ) ) )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1335,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
| ~ ! [SY354: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY354 )
| ~ ( in @ SY354 @ SV32 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1336,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i,SV133: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV133 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) )
| ( in @ SV133 @ SV115 ) ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1337,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) ) )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1285]) ).
thf(1338,plain,
! [SV87: $i,SV41: $i,SV118: $i] :
( ( ( ( SV118
!= ( complements_of_subsets @ SV41 @ SV87 ) )
| ! [SY346: $i] :
( ~ ( element @ SY346 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY346 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 )
| ( in @ SY346 @ SV118 ) ) ) ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1288]) ).
thf(1339,plain,
! [SV87: $i,SV118: $i,SV41: $i] :
( ( ( ~ ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY347 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 )
| ( in @ SY347 @ SV118 ) ) ) )
| ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1289]) ).
thf(1340,plain,
! [SV42: $i,SV119: $i] :
( ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1341,plain,
! [SV42: $i,SV119: $i] :
( ( ( ~ ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) ) )
= $false )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1342,plain,
! [SV43: $i] :
( ( ( element @ ( sK16_SY239 @ SV43 ) @ ( powerset @ SV43 ) )
= $true )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1292]) ).
thf(1343,plain,
! [SV43: $i] :
( ( ( ~ ( empty @ ( sK16_SY239 @ SV43 ) ) )
= $true )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1293]) ).
thf(1344,plain,
! [SV116: $i,SV45: $i] :
( ( ( ~ ( ~ ~ ( in @ SV45 @ SV116 )
| ~ ( ( SV45 != SV116 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1345,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
| ( ( sK9_SX1 @ SV46 )
!= ( sK17_SY348 @ SV46 ) ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1346,plain,
! [SV46: $i] :
( ( ( ~ ( ordinal @ ( sK17_SY348 @ SV46 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1347,plain,
! [SV46: $i] :
( ( ( ! [SY359: $i] :
~ ( ~ ( ~ ( in @ SY359 @ ( sK27_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY359 ) )
| ~ ( ordinal @ SY359 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY359 ) )
| ~ ( ordinal @ SY359 ) )
| ( in @ SY359 @ ( sK27_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1296]) ).
thf(1348,plain,
! [SV89: $i,SV48: $i,SV109: $i,SV129: $i] :
( ( ( ~ ( ~ ( in @ SV129 @ SV109 )
| ( SV129 = SV48 )
| ( SV129 = SV89 ) )
| ~ ( ~ ( ( SV129 = SV48 )
| ( SV129 = SV89 ) )
| ( in @ SV129 @ SV109 ) ) )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1349,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1350,plain,
( ( ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1351,plain,
( ( ( in @ sK10_SY311 @ sK4_SX0 )
= $true )
| ( ( ~ ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1301]) ).
thf(1352,plain,
! [SV90: $i,SV51: $i,SV110: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ SV130 @ SV110 )
| ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) )
| ( in @ SV130 @ SV110 ) ) )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1353,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
| ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1354,plain,
! [SV55: $i,SV94: $i,SV127: $i] :
( ( ( ~ ( ~ ( in @ SV127 @ SV94 )
| ( subset @ SV127 @ SV55 ) ) )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1355,plain,
! [SV94: $i,SV55: $i,SV127: $i] :
( ( ( ~ ( ~ ( subset @ SV127 @ SV55 )
| ( in @ SV127 @ SV94 ) ) )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1356,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
| ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1357,plain,
! [SV97: $i,SV58: $i,SV111: $i,SV131: $i] :
( ( ( ~ ( ~ ( in @ SV131 @ SV111 )
| ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) )
| ( in @ SV131 @ SV111 ) ) )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1358,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
| ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1307]) ).
thf(1359,plain,
! [SV98: $i,SV59: $i,SV112: $i,SV132: $i] :
( ( ( ~ ( ~ ( in @ SV132 @ SV112 )
| ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
| ~ ( ~ ( ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
| ( in @ SV132 @ SV112 ) ) )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1360,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1309]) ).
thf(1361,plain,
! [SV60: $i,SV99: $i,SV128: $i] :
( ( ( ~ ( ~ ( in @ SV128 @ SV99 )
| ( SV128 = SV60 ) ) )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1362,plain,
! [SV99: $i,SV60: $i,SV128: $i] :
( ( ( ~ ( ( SV128 != SV60 )
| ( in @ SV128 @ SV99 ) ) )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1363,plain,
! [SV99: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
| ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 ) ) )
= $true )
| ( ( ~ ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1364,plain,
! [SV63: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK20_SY279 @ SV5 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1365,plain,
! [SV5: $i,SV63: $i] :
( ( ( ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY351 @ SV63 )
| ~ ( in @ SY351 @ ( sK20_SY279 @ SV5 @ SV63 ) ) ) )
= $false )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1366,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ SV6 )
| ( in @ SV64 @ SV6 ) )
= $true )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1367,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV6 )
| ( element @ SV64 @ SV6 ) )
= $true )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1368,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ SV6 ) )
= $true )
| ( ( empty @ SV64 )
= $true )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1369,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( empty @ SV64 ) )
= $true )
| ( ( element @ SV64 @ SV6 )
= $true )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1370,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
| ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1371,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
= $false )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1372,plain,
! [SV8: $i,SV66: $i] :
( ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
= $false )
| ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
= $false )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1373,plain,
! [SV11: $i,SV101: $i,SV69: $i] :
( ( ( in @ SV69 @ SV101 )
= $false )
| ( ( in @ SV11 @ SV69 )
= $false )
| ( ( ~ ( in @ SV101 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1374,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) )
| ~ ( ( SV121 != SV124 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1375,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
| ~ ( ( ( sK18_SY181 @ SV12 )
!= ( sK22_SY350 @ SV12 ) ) ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1376,plain,
! [SV12: $i] :
( ( ( ~ ~ ( in @ ( sK22_SY350 @ SV12 ) @ ( sK18_SY181 @ SV12 ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1377,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( element @ ( sK32_SY183 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ ( sK32_SY183 @ SV13 ) ) ) )
= $true )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1324]) ).
thf(1378,plain,
! [SV14: $i,SV117: $i,SV125: $i] :
( ( ( ~ ~ ( in @ SV125 @ SV117 ) )
= $true )
| ( ( in @ SV125 @ ( subset_complement @ SV14 @ SV117 ) )
= $true )
| ( ( element @ SV125 @ SV14 )
= $false )
| ( ( element @ SV117 @ ( powerset @ SV14 ) )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1379,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1327]) ).
thf(1380,plain,
! [SV18: $i] :
( ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1381,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
| ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY362 @ SV18 )
| ~ ( in @ SY362 @ SV18 ) )
| ( SV134
!= ( singleton @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV18 )
| ~ ( in @ SY363 @ SV18 ) )
| ( SV134
!= ( singleton @ SY363 ) ) )
| ( in @ SV134 @ ( sK26_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1382,plain,
! [SV76: $i,SV22: $i] :
( ( ( ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV22 )
| ~ ( in @ SY289 @ SV76 ) ) )
= $false )
| ( ( disjoint @ SV22 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1383,plain,
! [SV76: $i,SV22: $i,SV135: $i] :
( ( ( ~ ~ ( ~ ( in @ SV135 @ SV22 )
| ~ ( in @ SV135 @ SV76 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1384,plain,
! [SV27: $i,SV105: $i,SV79: $i] :
( ( ( element @ SV79 @ ( powerset @ SV105 ) )
= $false )
| ( ( in @ SV27 @ SV79 )
= $false )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1385,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV82 )
| ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SV126 @ SY352 )
| ~ ( in @ SY352 @ SV32 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1386,plain,
! [SV82: $i,SV32: $i,SV126: $i] :
( ( ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ SV126 @ SY353 )
| ~ ( in @ SY353 @ SV32 ) )
| ( in @ SV126 @ SV82 ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1387,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
| ~ ! [SY354: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY354 )
| ~ ( in @ SY354 @ SV32 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1388,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i,SV133: $i] :
( ( ( ~ ( ~ ( in @ SV133 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) )
| ( in @ SV133 @ SV115 ) ) )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1389,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1337]) ).
thf(1390,plain,
! [SV87: $i,SV41: $i,SV118: $i] :
( ( ( SV118
!= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( ! [SY346: $i] :
( ~ ( element @ SY346 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY346 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 )
| ( in @ SY346 @ SV118 ) ) ) ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1391,plain,
! [SV87: $i,SV118: $i,SV41: $i] :
( ( ( ~ ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY347 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 )
| ( in @ SY347 @ SV118 ) ) ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1392,plain,
! [SV42: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) )
= $false )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1393,plain,
! [SV42: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV42 )
| ~ ( ordinal @ SV119 ) )
= $true )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1341]) ).
thf(1394,plain,
! [SV43: $i] :
( ( ( empty @ ( sK16_SY239 @ SV43 ) )
= $false )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1395,plain,
! [SV116: $i,SV45: $i] :
( ( ( ~ ~ ( in @ SV45 @ SV116 )
| ~ ( ( SV45 != SV116 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1396,plain,
! [SV46: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
| ( ( sK9_SX1 @ SV46 )
!= ( sK17_SY348 @ SV46 ) ) ) )
= $true )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1345]) ).
thf(1397,plain,
! [SV46: $i] :
( ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1398,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
| ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY364 @ SV46 )
| ( SY364 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
| ~ ( ~ ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY365 @ SV46 )
| ( SY365 != SV136 ) )
| ~ ( ordinal @ SV136 ) )
| ( in @ SV136 @ ( sK27_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1399,plain,
! [SV89: $i,SV48: $i,SV109: $i,SV129: $i] :
( ( ( ~ ( ~ ( in @ SV129 @ SV109 )
| ( SV129 = SV48 )
| ( SV129 = SV89 ) ) )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1400,plain,
! [SV109: $i,SV89: $i,SV48: $i,SV129: $i] :
( ( ( ~ ( ~ ( ( SV129 = SV48 )
| ( SV129 = SV89 ) )
| ( in @ SV129 @ SV109 ) ) )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1401,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1402,plain,
( ( ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) )
= $false )
| ( ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1403,plain,
( ( ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 )
| ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) ) )
= $false )
| ( ( in @ sK10_SY311 @ sK4_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1404,plain,
! [SV90: $i,SV51: $i,SV110: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ SV130 @ SV110 )
| ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) ) ) )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1405,plain,
! [SV110: $i,SV90: $i,SV51: $i,SV130: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) )
| ( in @ SV130 @ SV110 ) ) )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1406,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
| ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1407,plain,
! [SV55: $i,SV94: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV94 )
| ( subset @ SV127 @ SV55 ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1408,plain,
! [SV94: $i,SV55: $i,SV127: $i] :
( ( ( ~ ( subset @ SV127 @ SV55 )
| ( in @ SV127 @ SV94 ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1409,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
| ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1410,plain,
! [SV97: $i,SV58: $i,SV111: $i,SV131: $i] :
( ( ( ~ ( ~ ( in @ SV131 @ SV111 )
| ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) ) ) )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1411,plain,
! [SV111: $i,SV97: $i,SV58: $i,SV131: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) )
| ( in @ SV131 @ SV111 ) ) )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1412,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
| ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1413,plain,
! [SV98: $i,SV59: $i,SV112: $i,SV132: $i] :
( ( ( ~ ( ~ ( in @ SV132 @ SV112 )
| ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) ) )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1414,plain,
! [SV112: $i,SV98: $i,SV59: $i,SV132: $i] :
( ( ( ~ ( ~ ( ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
| ( in @ SV132 @ SV112 ) ) )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1415,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1416,plain,
! [SV60: $i,SV99: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV99 )
| ( SV128 = SV60 ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1417,plain,
! [SV99: $i,SV60: $i,SV128: $i] :
( ( ( ( SV128 != SV60 )
| ( in @ SV128 @ SV99 ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1418,plain,
! [SV99: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
| ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 ) )
= $false )
| ( ( ~ ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1419,plain,
! [SV63: $i,SV5: $i] :
( ( ( in @ ( sK20_SY279 @ SV5 @ SV63 ) @ SV63 )
= $true )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1420,plain,
! [SV5: $i,SV63: $i] :
( ( ( ! [SY351: $i] :
~ ~ ( ~ ( in @ SY351 @ SV63 )
| ~ ( in @ SY351 @ ( sK20_SY279 @ SV5 @ SV63 ) ) ) )
= $true )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1421,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ SV6 ) )
= $true )
| ( ( in @ SV64 @ SV6 )
= $true )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1422,plain,
! [SV6: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV6 ) )
= $true )
| ( ( element @ SV64 @ SV6 )
= $true )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1423,plain,
! [SV6: $i,SV64: $i] :
( ( ( element @ SV64 @ SV6 )
= $false )
| ( ( empty @ SV64 )
= $true )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1424,plain,
! [SV6: $i,SV64: $i] :
( ( ( empty @ SV64 )
= $false )
| ( ( element @ SV64 @ SV6 )
= $true )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1425,plain,
! [SV8: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1426,plain,
! [SV8: $i,SV66: $i] :
( ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
= $false )
| ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1427,plain,
! [SV8: $i,SV66: $i] :
( ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
= $true )
| ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
= $false )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1428,plain,
! [SV69: $i,SV11: $i,SV101: $i] :
( ( ( in @ SV101 @ SV11 )
= $false )
| ( ( in @ SV11 @ SV69 )
= $false )
| ( ( in @ SV69 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1429,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) )
| ~ ( ( SV121 != SV124 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1430,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
| ~ ( ( ( sK18_SY181 @ SV12 )
!= ( sK22_SY350 @ SV12 ) ) ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1431,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( sK22_SY350 @ SV12 ) @ ( sK18_SY181 @ SV12 ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1432,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK32_SY183 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ ( sK32_SY183 @ SV13 ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1433,plain,
! [SV14: $i,SV117: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ SV117 ) )
= $false )
| ( ( in @ SV125 @ ( subset_complement @ SV14 @ SV117 ) )
= $true )
| ( ( element @ SV125 @ SV14 )
= $false )
| ( ( element @ SV117 @ ( powerset @ SV14 ) )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1434,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
| ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1435,plain,
! [SV18: $i] :
( ( ( ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1436,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
| ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY362 @ SV18 )
| ~ ( in @ SY362 @ SV18 ) )
| ( SV134
!= ( singleton @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV18 )
| ~ ( in @ SY363 @ SV18 ) )
| ( SV134
!= ( singleton @ SY363 ) ) )
| ( in @ SV134 @ ( sK26_SY193 @ SV18 ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1437,plain,
! [SV22: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV76 ) ) )
= $false )
| ( ( disjoint @ SV22 @ SV76 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1382]) ).
thf(1438,plain,
! [SV76: $i,SV22: $i,SV135: $i] :
( ( ( ~ ( ~ ( in @ SV135 @ SV22 )
| ~ ( in @ SV135 @ SV76 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1439,plain,
! [SV79: $i,SV27: $i,SV105: $i] :
( ( ( empty @ SV105 )
= $false )
| ( ( in @ SV27 @ SV79 )
= $false )
| ( ( element @ SV79 @ ( powerset @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1440,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV82 ) )
= $true )
| ( ( ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SV126 @ SY352 )
| ~ ( in @ SY352 @ SV32 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1441,plain,
! [SV82: $i,SV32: $i,SV126: $i] :
( ( ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ SV126 @ SY353 )
| ~ ( in @ SY353 @ SV32 ) ) )
= $true )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1442,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1443,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ! [SY354: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY354 )
| ~ ( in @ SY354 @ SV32 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1444,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i,SV133: $i] :
( ( ( ~ ( ~ ( in @ SV133 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) ) )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1445,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) )
| ( in @ SV133 @ SV115 ) ) )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1446,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1447,plain,
! [SV87: $i,SV41: $i,SV118: $i] :
( ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( ! [SY346: $i] :
( ~ ( element @ SY346 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY346 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY346 ) @ SV87 )
| ( in @ SY346 @ SV118 ) ) ) ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1448,plain,
! [SV87: $i,SV118: $i,SV41: $i] :
( ( ( ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SY347 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SY347 ) @ SV87 )
| ( in @ SY347 @ SV118 ) ) ) ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1449,plain,
! [SV42: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV42 ) )
= $false )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1450,plain,
! [SV42: $i,SV119: $i] :
( ( ( ~ ( ordinal @ SV119 ) )
= $false )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1451,plain,
! [SV42: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV42 ) )
= $true )
| ( ( ~ ( ordinal @ SV119 ) )
= $true )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1452,plain,
! [SV116: $i,SV45: $i] :
( ( ( ~ ~ ( in @ SV45 @ SV116 ) )
= $true )
| ( ( ~ ( ( SV45 != SV116 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1453,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
| ( ( sK9_SX1 @ SV46 )
!= ( sK17_SY348 @ SV46 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1454,plain,
! [SV46: $i] :
( ( ( ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1455,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
| ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY364 @ SV46 )
| ( SY364 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
| ~ ( ~ ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY365 @ SV46 )
| ( SY365 != SV136 ) )
| ~ ( ordinal @ SV136 ) )
| ( in @ SV136 @ ( sK27_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1456,plain,
! [SV89: $i,SV48: $i,SV109: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ SV109 )
| ( SV129 = SV48 )
| ( SV129 = SV89 ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1457,plain,
! [SV109: $i,SV89: $i,SV48: $i,SV129: $i] :
( ( ( ~ ( ( SV129 = SV48 )
| ( SV129 = SV89 ) )
| ( in @ SV129 @ SV109 ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1458,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1459,plain,
( ( ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
= $false )
| ( ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1460,plain,
( ( ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
= $false )
| ( ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1461,plain,
( ( ( ~ ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
= $false )
| ( ( in @ sK10_SY311 @ sK4_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1462,plain,
( ( ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
= $false )
| ( ( in @ sK10_SY311 @ sK4_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1463,plain,
! [SV90: $i,SV51: $i,SV110: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV110 )
| ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1464,plain,
! [SV110: $i,SV90: $i,SV51: $i,SV130: $i] :
( ( ( ~ ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) )
| ( in @ SV130 @ SV110 ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1465,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
| ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1466,plain,
! [SV55: $i,SV94: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV94 ) )
= $true )
| ( ( subset @ SV127 @ SV55 )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1467,plain,
! [SV94: $i,SV55: $i,SV127: $i] :
( ( ( ~ ( subset @ SV127 @ SV55 ) )
= $true )
| ( ( in @ SV127 @ SV94 )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1468,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1409]) ).
thf(1469,plain,
! [SV94: $i,SV55: $i] :
( ( ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1409]) ).
thf(1470,plain,
! [SV97: $i,SV58: $i,SV111: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ SV111 )
| ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1471,plain,
! [SV111: $i,SV97: $i,SV58: $i,SV131: $i] :
( ( ( ~ ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) )
| ( in @ SV131 @ SV111 ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1472,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
| ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1473,plain,
! [SV98: $i,SV59: $i,SV112: $i,SV132: $i] :
( ( ( ~ ( in @ SV132 @ SV112 )
| ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1474,plain,
! [SV112: $i,SV98: $i,SV59: $i,SV132: $i] :
( ( ( ~ ( ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
| ( in @ SV132 @ SV112 ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1475,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1476,plain,
! [SV60: $i,SV99: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV99 ) )
= $true )
| ( ( SV128 = SV60 )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1477,plain,
! [SV99: $i,SV60: $i,SV128: $i] :
( ( ( SV128 != SV60 )
= $true )
| ( ( in @ SV128 @ SV99 )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1478,plain,
! [SV99: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) )
= $false )
| ( ( ~ ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1479,plain,
! [SV99: $i,SV60: $i] :
( ( ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 )
= $false )
| ( ( ~ ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1480,plain,
! [SV5: $i,SV63: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ( in @ SV137 @ SV63 )
| ~ ( in @ SV137 @ ( sK20_SY279 @ SV5 @ SV63 ) ) ) )
= $true )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1481,plain,
! [SV6: $i,SV64: $i] :
( ( ( element @ SV64 @ SV6 )
= $false )
| ( ( in @ SV64 @ SV6 )
= $true )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1482,plain,
! [SV6: $i,SV64: $i] :
( ( ( in @ SV64 @ SV6 )
= $false )
| ( ( element @ SV64 @ SV6 )
= $true )
| ( ( empty @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1483,plain,
! [SV8: $i,SV66: $i] :
( ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV66 )
= $true )
| ( ( in @ ( sK11_SY281 @ SV66 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8 = SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1484,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) )
| ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1485,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
| ~ ( ( ( sK18_SY181 @ SV12 )
!= ( sK22_SY350 @ SV12 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1486,plain,
! [SV12: $i] :
( ( ( in @ ( sK22_SY350 @ SV12 ) @ ( sK18_SY181 @ SV12 ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1487,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK32_SY183 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1488,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ ( sK32_SY183 @ SV13 ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1489,plain,
! [SV14: $i,SV117: $i,SV125: $i] :
( ( ( in @ SV125 @ SV117 )
= $true )
| ( ( in @ SV125 @ ( subset_complement @ SV14 @ SV117 ) )
= $true )
| ( ( element @ SV125 @ SV14 )
= $false )
| ( ( element @ SV117 @ ( powerset @ SV14 ) )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1490,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1491,plain,
! [SV18: $i] :
( ( ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1492,plain,
! [SV18: $i] :
( ( ( ~ ! [SY366: $i] :
~ ( ~ ( ~ ( in @ SY366 @ ( sK35_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY366
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY366
!= ( singleton @ SY196 ) ) )
| ( in @ SY366 @ ( sK35_SY193 @ SV18 ) ) ) ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1435]) ).
thf(1493,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
| ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY362 @ SV18 )
| ~ ( in @ SY362 @ SV18 ) )
| ( SV134
!= ( singleton @ SY362 ) ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1494,plain,
! [SV134: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ! [SY363: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV18 )
| ~ ( in @ SY363 @ SV18 ) )
| ( SV134
!= ( singleton @ SY363 ) ) )
| ( in @ SV134 @ ( sK26_SY193 @ SV18 ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1495,plain,
! [SV22: $i,SV76: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV76 ) ) )
= $true )
| ( ( disjoint @ SV22 @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1496,plain,
! [SV76: $i,SV22: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV22 )
| ~ ( in @ SV135 @ SV76 ) )
= $true )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1497,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( in @ SV126 @ SV82 )
= $false )
| ( ( ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SV126 @ SY352 )
| ~ ( in @ SY352 @ SV32 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1498,plain,
! [SV82: $i,SV32: $i,SV126: $i] :
( ( ( ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ SV126 @ SY353 )
| ~ ( in @ SY353 @ SV32 ) ) )
= $false )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1499,plain,
! [SV82: $i,SV32: $i] :
( ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1442]) ).
thf(1500,plain,
! [SV82: $i,SV32: $i] :
( ( ( ! [SY354: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY354 )
| ~ ( in @ SY354 @ SV32 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1501,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i,SV133: $i] :
( ( ( ~ ( in @ SV133 @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1502,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) )
| ( in @ SV133 @ SV115 ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1445]) ).
thf(1503,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1504,plain,
! [SV87: $i,SV118: $i,SV41: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ SV138 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
| ( in @ SV138 @ SV118 ) ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1505,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( ~ ( element @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( ~ ( ~ ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
| ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) ) ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1448]) ).
thf(1506,plain,
! [SV42: $i,SV119: $i] :
( ( ( in @ SV119 @ SV42 )
= $true )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1507,plain,
! [SV42: $i,SV119: $i] :
( ( ( ordinal @ SV119 )
= $true )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1508,plain,
! [SV42: $i,SV119: $i] :
( ( ( in @ SV119 @ SV42 )
= $false )
| ( ( ~ ( ordinal @ SV119 ) )
= $true )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1509,plain,
! [SV116: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV116 ) )
= $false )
| ( ( ~ ( ( SV45 != SV116 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1510,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1511,plain,
! [SV46: $i] :
( ( ( ( sK9_SX1 @ SV46 )
!= ( sK17_SY348 @ SV46 ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1512,plain,
! [SV46: $i] :
( ( ( ~ ! [SY369: $i] :
~ ( ~ ( ~ ( in @ SY369 @ ( sK37_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY369 ) )
| ~ ( ordinal @ SY369 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY369 ) )
| ~ ( ordinal @ SY369 ) )
| ( in @ SY369 @ ( sK37_SY245 @ SV46 ) ) ) ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1454]) ).
thf(1513,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
| ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY364 @ SV46 )
| ( SY364 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1514,plain,
! [SV136: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY365 @ SV46 )
| ( SY365 != SV136 ) )
| ~ ( ordinal @ SV136 ) )
| ( in @ SV136 @ ( sK27_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1515,plain,
! [SV89: $i,SV48: $i,SV109: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ SV109 ) )
= $true )
| ( ( ( SV129 = SV48 )
| ( SV129 = SV89 ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1516,plain,
! [SV109: $i,SV89: $i,SV48: $i,SV129: $i] :
( ( ( ~ ( ( SV129 = SV48 )
| ( SV129 = SV89 ) ) )
= $true )
| ( ( in @ SV129 @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1517,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1518,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1519,plain,
( ( ( ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
= $true )
| ( ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1520,plain,
( ( ( ~ ( in @ sK10_SY311 @ sK4_SX0 ) )
= $true )
| ( ( in @ sK10_SY311 @ sK4_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1521,plain,
! [SV90: $i,SV51: $i,SV110: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV110 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1522,plain,
! [SV110: $i,SV90: $i,SV51: $i,SV130: $i] :
( ( ( ~ ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) ) )
= $true )
| ( ( in @ SV130 @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1523,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1524,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1525,plain,
! [SV55: $i,SV94: $i,SV127: $i] :
( ( ( in @ SV127 @ SV94 )
= $false )
| ( ( subset @ SV127 @ SV55 )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1526,plain,
! [SV94: $i,SV55: $i,SV127: $i] :
( ( ( subset @ SV127 @ SV55 )
= $false )
| ( ( in @ SV127 @ SV94 )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1527,plain,
! [SV94: $i,SV55: $i] :
( ( ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1528,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) )
= $false )
| ( ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1529,plain,
! [SV97: $i,SV58: $i,SV111: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1530,plain,
! [SV111: $i,SV97: $i,SV58: $i,SV131: $i] :
( ( ( ~ ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) ) )
= $true )
| ( ( in @ SV131 @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1531,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1532,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1533,plain,
! [SV98: $i,SV59: $i,SV112: $i,SV132: $i] :
( ( ( ~ ( in @ SV132 @ SV112 ) )
= $true )
| ( ( ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1534,plain,
! [SV112: $i,SV98: $i,SV59: $i,SV132: $i] :
( ( ( ~ ( ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) ) )
= $true )
| ( ( in @ SV132 @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1535,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1536,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1537,plain,
! [SV60: $i,SV99: $i,SV128: $i] :
( ( ( in @ SV128 @ SV99 )
= $false )
| ( ( SV128 = SV60 )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1538,plain,
! [SV99: $i,SV60: $i,SV128: $i] :
( ( ( SV128 = SV60 )
= $false )
| ( ( in @ SV128 @ SV99 )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1539,plain,
! [SV99: $i,SV60: $i] :
( ( ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
= $true )
| ( ( ~ ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1478]) ).
thf(1540,plain,
! [SV99: $i,SV60: $i] :
( ( ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) )
= $false )
| ( ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1541,plain,
! [SV5: $i,SV63: $i,SV137: $i] :
( ( ( ~ ( ~ ( in @ SV137 @ SV63 )
| ~ ( in @ SV137 @ ( sK20_SY279 @ SV5 @ SV63 ) ) ) )
= $false )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1542,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) ) )
= $true )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1543,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1544,plain,
! [SV12: $i] :
( ( ( ~ ( ( ( sK18_SY181 @ SV12 )
!= ( sK22_SY350 @ SV12 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1545,plain,
! [SV13: $i] :
( ( ( element @ ( sK32_SY183 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1546,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ ( sK32_SY183 @ SV13 ) ) )
= $true )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1547,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) ) )
= $true )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1490]) ).
thf(1548,plain,
! [SV18: $i] :
( ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1549,plain,
! [SV18: $i] :
( ( ( ! [SY366: $i] :
~ ( ~ ( ~ ( in @ SY366 @ ( sK35_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY366
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY366
!= ( singleton @ SY196 ) ) )
| ( in @ SY366 @ ( sK35_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1492]) ).
thf(1550,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
| ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY362 @ SV18 )
| ~ ( in @ SY362 @ SV18 ) )
| ( SV134
!= ( singleton @ SY362 ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1551,plain,
! [SV134: $i,SV18: $i] :
( ( ( ~ ~ ! [SY363: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV18 )
| ~ ( in @ SY363 @ SV18 ) )
| ( SV134
!= ( singleton @ SY363 ) ) )
| ( in @ SV134 @ ( sK26_SY193 @ SV18 ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1552,plain,
! [SV22: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV76 ) )
= $false )
| ( ( disjoint @ SV22 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1553,plain,
! [SV76: $i,SV22: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV22 ) )
= $true )
| ( ( ~ ( in @ SV135 @ SV76 ) )
= $true )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1554,plain,
! [SV82: $i,SV32: $i,SV126: $i] :
( ( ( ! [SY352: $i] :
~ ~ ( ~ ( in @ SV126 @ SY352 )
| ~ ( in @ SY352 @ SV32 ) ) )
= $false )
| ( ( in @ SV126 @ SV82 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1555,plain,
! [SV82: $i,SV32: $i,SV126: $i] :
( ( ( ! [SY353: $i] :
~ ~ ( ~ ( in @ SV126 @ SY353 )
| ~ ( in @ SY353 @ SV32 ) ) )
= $true )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1556,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1557,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
| ~ ( in @ SV139 @ SV32 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1558,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i,SV133: $i] :
( ( ( ~ ( in @ SV133 @ SV115 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1559,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1560,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1503]) ).
thf(1561,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1503]) ).
thf(1562,plain,
! [SV87: $i,SV118: $i,SV41: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV138 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
| ( in @ SV138 @ SV118 ) ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1563,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( ~ ( element @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ ( powerset @ SV41 ) ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1505]) ).
thf(1564,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
| ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) ) ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1505]) ).
thf(1565,plain,
! [SV42: $i,SV119: $i] :
( ( ( ordinal @ SV119 )
= $false )
| ( ( in @ SV119 @ SV42 )
= $false )
| ( ( in @ SV119 @ ( sK6_SY237 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1566,plain,
! [SV116: $i,SV45: $i] :
( ( ( in @ SV45 @ SV116 )
= $true )
| ( ( ~ ( ( SV45 != SV116 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1567,plain,
! [SV46: $i] :
( ( ( ~ ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) ) )
= $true )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1568,plain,
! [SV46: $i] :
( ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1511]) ).
thf(1569,plain,
! [SV46: $i] :
( ( ( ! [SY369: $i] :
~ ( ~ ( ~ ( in @ SY369 @ ( sK37_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY369 ) )
| ~ ( ordinal @ SY369 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY369 ) )
| ~ ( ordinal @ SY369 ) )
| ( in @ SY369 @ ( sK37_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1570,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
| ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY364 @ SV46 )
| ( SY364 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1571,plain,
! [SV136: $i,SV46: $i] :
( ( ( ~ ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY365 @ SV46 )
| ( SY365 != SV136 ) )
| ~ ( ordinal @ SV136 ) )
| ( in @ SV136 @ ( sK27_SY245 @ SV46 ) ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1572,plain,
! [SV89: $i,SV48: $i,SV109: $i,SV129: $i] :
( ( ( in @ SV129 @ SV109 )
= $false )
| ( ( ( SV129 = SV48 )
| ( SV129 = SV89 ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1573,plain,
! [SV109: $i,SV89: $i,SV48: $i,SV129: $i] :
( ( ( ( SV129 = SV48 )
| ( SV129 = SV89 ) )
= $false )
| ( ( in @ SV129 @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1574,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $true )
| ( ( ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1517]) ).
thf(1575,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $false )
| ( ( ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1576,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $false )
| ( ( ~ ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1577,plain,
( ( ( in @ sK10_SY311 @ sK4_SX0 )
= $false )
| ( ( in @ sK10_SY311 @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK4_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1578,plain,
( ( ( in @ sK10_SY311 @ sK4_SX0 )
= $false )
| ( ( in @ sK10_SY311 @ sK4_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1579,plain,
! [SV90: $i,SV51: $i,SV110: $i,SV130: $i] :
( ( ( in @ SV130 @ SV110 )
= $false )
| ( ( ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1580,plain,
! [SV110: $i,SV90: $i,SV51: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) ) )
= $false )
| ( ( in @ SV130 @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1581,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1523]) ).
thf(1582,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1583,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
| ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 ) )
= $false )
| ( ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1584,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 ) )
= $false )
| ( ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1585,plain,
! [SV94: $i,SV55: $i] :
( ( ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
= $false )
| ( ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1586,plain,
! [SV97: $i,SV58: $i,SV111: $i,SV131: $i] :
( ( ( in @ SV131 @ SV111 )
= $false )
| ( ( ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1587,plain,
! [SV111: $i,SV97: $i,SV58: $i,SV131: $i] :
( ( ( ~ ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) ) )
= $false )
| ( ( in @ SV131 @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1588,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1589,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1532]) ).
thf(1590,plain,
! [SV98: $i,SV59: $i,SV112: $i,SV132: $i] :
( ( ( in @ SV132 @ SV112 )
= $false )
| ( ( ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1591,plain,
! [SV112: $i,SV98: $i,SV59: $i,SV132: $i] :
( ( ( ( in @ SV132 @ SV59 )
| ( in @ SV132 @ SV98 ) )
= $false )
| ( ( in @ SV132 @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1592,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1593,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1536]) ).
thf(1594,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1536]) ).
thf(1595,plain,
! [SV99: $i,SV60: $i] :
( ( ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
| ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 ) )
= $false )
| ( ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1596,plain,
! [SV99: $i,SV60: $i] :
( ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
= $false )
| ( ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1597,plain,
! [SV99: $i,SV60: $i] :
( ( ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
= $false )
| ( ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1598,plain,
! [SV5: $i,SV63: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ SV63 )
| ~ ( in @ SV137 @ ( sK20_SY279 @ SV5 @ SV63 ) ) )
= $true )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1599,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) ) )
= $false )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1600,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1601,plain,
! [SV12: $i] :
( ( ( ( sK18_SY181 @ SV12 )
!= ( sK22_SY350 @ SV12 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1602,plain,
! [SV13: $i] :
( ( ( empty @ ( sK32_SY183 @ SV13 ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1603,plain,
! [SV18: $i] :
( ( ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
| ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1604,plain,
! [SV18: $i] :
( ( ( ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1605,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
| ~ ! [SY372: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY372 @ SV18 )
| ~ ( in @ SY372 @ SV18 ) )
| ( SV140
!= ( singleton @ SY372 ) ) ) )
| ~ ( ~ ~ ! [SY373: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY373 @ SV18 )
| ~ ( in @ SY373 @ SV18 ) )
| ( SV140
!= ( singleton @ SY373 ) ) )
| ( in @ SV140 @ ( sK35_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1606,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ ( sK26_SY193 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY362 @ SV18 )
| ~ ( in @ SY362 @ SV18 ) )
| ( SV134
!= ( singleton @ SY362 ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1607,plain,
! [SV134: $i,SV18: $i] :
( ( ( ~ ~ ! [SY363: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV18 )
| ~ ( in @ SY363 @ SV18 ) )
| ( SV134
!= ( singleton @ SY363 ) ) ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1608,plain,
! [SV22: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV22 ) )
= $false )
| ( ( disjoint @ SV22 @ SV76 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1609,plain,
! [SV22: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV76 ) )
= $false )
| ( ( disjoint @ SV22 @ SV76 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1610,plain,
! [SV76: $i,SV22: $i,SV135: $i] :
( ( ( in @ SV135 @ SV22 )
= $false )
| ( ( ~ ( in @ SV135 @ SV76 ) )
= $true )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1611,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ~ ( ~ ( in @ SV126 @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) )
| ~ ( in @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) @ SV32 ) ) )
= $false )
| ( ( in @ SV126 @ SV82 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1554]) ).
thf(1612,plain,
! [SV82: $i,SV32: $i,SV141: $i,SV126: $i] :
( ( ( ~ ~ ( ~ ( in @ SV126 @ SV141 )
| ~ ( in @ SV141 @ SV32 ) ) )
= $true )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1613,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1614,plain,
! [SV82: $i,SV32: $i] :
( ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1615,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
| ~ ( in @ SV139 @ SV32 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1616,plain,
! [SV106: $i,SV84: $i,SV34: $i,SV115: $i,SV133: $i] :
( ( ( in @ SV133 @ SV115 )
= $false )
| ( ( ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1617,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1618,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1619,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1620,plain,
! [SV87: $i,SV118: $i,SV41: $i,SV138: $i] :
( ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV138 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
| ( in @ SV138 @ SV118 ) ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1621,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( element @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ ( powerset @ SV41 ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1622,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
| ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1623,plain,
! [SV116: $i,SV45: $i] :
( ( ( SV45 != SV116 )
= $false )
| ( ( in @ SV45 @ SV116 )
= $true )
| ( ( ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1624,plain,
! [SV46: $i] :
( ( ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
| ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1625,plain,
! [SV46: $i] :
( ( ( ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1626,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
| ~ ! [SY374: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY374 @ SV46 )
| ( SY374 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
| ~ ( ~ ~ ! [SY375: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY375 @ SV46 )
| ( SY375 != SV142 ) )
| ~ ( ordinal @ SV142 ) )
| ( in @ SV142 @ ( sK37_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1627,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ ( sK27_SY245 @ SV46 ) ) )
= $true )
| ( ( ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY364 @ SV46 )
| ( SY364 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1628,plain,
! [SV136: $i,SV46: $i] :
( ( ( ~ ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY365 @ SV46 )
| ( SY365 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1629,plain,
! [SV109: $i,SV89: $i,SV48: $i,SV129: $i] :
( ( ( SV129 = SV48 )
= $true )
| ( ( SV129 = SV89 )
= $true )
| ( ( in @ SV129 @ SV109 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1630,plain,
! [SV89: $i,SV109: $i,SV48: $i,SV129: $i] :
( ( ( SV129 = SV48 )
= $false )
| ( ( in @ SV129 @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1631,plain,
! [SV48: $i,SV109: $i,SV89: $i,SV129: $i] :
( ( ( SV129 = SV89 )
= $false )
| ( ( in @ SV129 @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1632,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) )
= $false )
| ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1633,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) )
= $false )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1634,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
| ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 ) )
= $false )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1635,plain,
! [SV110: $i,SV90: $i,SV51: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) )
= $false )
| ( ( in @ SV130 @ SV110 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1636,plain,
! [SV110: $i,SV90: $i,SV51: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV51 )
| ~ ( in @ SV130 @ SV90 ) )
= $true )
| ( ( in @ SV130 @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1637,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1638,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 ) )
= $true )
| ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1639,plain,
! [SV94: $i,SV55: $i] :
( ( ( ~ ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 ) )
= $false )
| ( ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1640,plain,
! [SV94: $i,SV55: $i] :
( ( ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
= $false )
| ( ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1641,plain,
! [SV94: $i,SV55: $i] :
( ( ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
= $true )
| ( ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
= $false )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1642,plain,
! [SV111: $i,SV97: $i,SV58: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) )
= $false )
| ( ( in @ SV131 @ SV111 )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1643,plain,
! [SV111: $i,SV97: $i,SV58: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ SV58 )
| ~ ~ ( in @ SV131 @ SV97 ) )
= $true )
| ( ( in @ SV131 @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1644,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1645,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1646,plain,
! [SV112: $i,SV98: $i,SV59: $i,SV132: $i] :
( ( ( in @ SV132 @ SV59 )
= $true )
| ( ( in @ SV132 @ SV98 )
= $true )
| ( ( in @ SV132 @ SV112 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1647,plain,
! [SV98: $i,SV112: $i,SV59: $i,SV132: $i] :
( ( ( in @ SV132 @ SV59 )
= $false )
| ( ( in @ SV132 @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1648,plain,
! [SV59: $i,SV112: $i,SV98: $i,SV132: $i] :
( ( ( in @ SV132 @ SV98 )
= $false )
| ( ( in @ SV132 @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1649,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1650,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1651,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1652,plain,
! [SV99: $i,SV60: $i] :
( ( ( ( sK25_SY325 @ SV60 @ SV99 )
!= SV60 )
= $false )
| ( ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1653,plain,
! [SV99: $i,SV60: $i] :
( ( ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
= $false )
| ( ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1654,plain,
! [SV99: $i,SV60: $i] :
( ( ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 )
= $true )
| ( ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 )
= $false )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1655,plain,
! [SV5: $i,SV63: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( sK20_SY279 @ SV5 @ SV63 ) ) )
= $true )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1656,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
| ~ ~ ( in @ SV121 @ SV124 ) )
= $true )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1657,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
| ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1658,plain,
! [SV12: $i] :
( ( ( ( sK18_SY181 @ SV12 )
= ( sK22_SY350 @ SV12 ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1659,plain,
! [SV18: $i] :
( ( ( ~ ( in @ ( sK8_SY190 @ SV18 ) @ SV18 ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1660,plain,
! [SV18: $i] :
( ( ( ( sK12_SY338 @ SV18 )
!= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $false )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1661,plain,
! [SV18: $i] :
( ( ( ~ ! [SY376: $i] :
~ ( ~ ( ~ ( in @ SY376 @ ( sK39_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY376
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY376
!= ( singleton @ SY196 ) ) )
| ( in @ SY376 @ ( sK39_SY193 @ SV18 ) ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1604]) ).
thf(1662,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( ~ ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
| ~ ! [SY372: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY372 @ SV18 )
| ~ ( in @ SY372 @ SV18 ) )
| ( SV140
!= ( singleton @ SY372 ) ) ) )
| ~ ( ~ ~ ! [SY373: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY373 @ SV18 )
| ~ ( in @ SY373 @ SV18 ) )
| ( SV140
!= ( singleton @ SY373 ) ) )
| ( in @ SV140 @ ( sK35_SY193 @ SV18 ) ) ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1663,plain,
! [SV18: $i,SV134: $i] :
( ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY362 @ SV18 )
| ~ ( in @ SY362 @ SV18 ) )
| ( SV134
!= ( singleton @ SY362 ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1664,plain,
! [SV134: $i,SV18: $i] :
( ( ( ~ ! [SY363: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV18 )
| ~ ( in @ SY363 @ SV18 ) )
| ( SV134
!= ( singleton @ SY363 ) ) ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1665,plain,
! [SV22: $i,SV76: $i] :
( ( ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV22 )
= $true )
| ( ( disjoint @ SV22 @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1666,plain,
! [SV22: $i,SV76: $i] :
( ( ( in @ ( sK34_SY289 @ SV76 @ SV22 ) @ SV76 )
= $true )
| ( ( disjoint @ SV22 @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1667,plain,
! [SV22: $i,SV76: $i,SV135: $i] :
( ( ( in @ SV135 @ SV76 )
= $false )
| ( ( in @ SV135 @ SV22 )
= $false )
| ( ( ~ ( disjoint @ SV22 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1668,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ( ~ ( in @ SV126 @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) )
| ~ ( in @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) @ SV32 ) ) )
= $true )
| ( ( in @ SV126 @ SV82 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1669,plain,
! [SV82: $i,SV32: $i,SV141: $i,SV126: $i] :
( ( ( ~ ( ~ ( in @ SV126 @ SV141 )
| ~ ( in @ SV141 @ SV32 ) ) )
= $false )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1670,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) ) )
= $true )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1671,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
| ~ ( in @ SV139 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1672,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
= $false )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1673,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1674,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) )
= $false )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1675,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1676,plain,
! [SV87: $i,SV41: $i,SV118: $i,SV138: $i] :
( ( ( ~ ( ~ ( in @ SV138 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 ) )
| ~ ( ~ ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
| ( in @ SV138 @ SV118 ) ) )
= $false )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1677,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
| ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1678,plain,
! [SV116: $i,SV45: $i] :
( ( ( SV45 = SV116 )
= $true )
| ( ( in @ SV45 @ SV116 )
= $true )
| ( ( ~ ~ ( in @ SV116 @ SV45 ) )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1679,plain,
! [SV46: $i] :
( ( ( ( sK9_SX1 @ SV46 )
!= ( sK14_SY342 @ SV46 ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1680,plain,
! [SV46: $i] :
( ( ( ~ ( ordinal @ ( sK14_SY342 @ SV46 ) ) )
= $false )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1681,plain,
! [SV46: $i] :
( ( ( ~ ! [SY379: $i] :
~ ( ~ ( ~ ( in @ SY379 @ ( sK40_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY379 ) )
| ~ ( ordinal @ SY379 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY379 ) )
| ~ ( ordinal @ SY379 ) )
| ( in @ SY379 @ ( sK40_SY245 @ SV46 ) ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1625]) ).
thf(1682,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
| ~ ! [SY374: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY374 @ SV46 )
| ( SY374 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
| ~ ( ~ ~ ! [SY375: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY375 @ SV46 )
| ( SY375 != SV142 ) )
| ~ ( ordinal @ SV142 ) )
| ( in @ SV142 @ ( sK37_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1683,plain,
! [SV46: $i,SV136: $i] :
( ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY364 @ SV46 )
| ( SY364 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1684,plain,
! [SV136: $i,SV46: $i] :
( ( ( ~ ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY365 @ SV46 )
| ( SY365 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1685,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) ) )
= $false )
| ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1686,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $false )
| ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1687,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) ) )
= $false )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1688,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $false )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1689,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ~ ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) ) )
= $false )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1690,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $false )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1691,plain,
! [SV90: $i,SV110: $i,SV51: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV51 ) )
= $false )
| ( ( in @ SV130 @ SV110 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1692,plain,
! [SV51: $i,SV110: $i,SV90: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV90 ) )
= $false )
| ( ( in @ SV130 @ SV110 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1693,plain,
! [SV110: $i,SV90: $i,SV51: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV51 ) )
= $true )
| ( ( ~ ( in @ SV130 @ SV90 ) )
= $true )
| ( ( in @ SV130 @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1694,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1695,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1696,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1697,plain,
! [SV94: $i,SV55: $i] :
( ( ( subset @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV55 )
= $true )
| ( ( in @ ( sK24_SY316 @ SV55 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( powerset @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1698,plain,
! [SV97: $i,SV111: $i,SV58: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ SV58 ) )
= $false )
| ( ( in @ SV131 @ SV111 )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1699,plain,
! [SV58: $i,SV111: $i,SV97: $i,SV131: $i] :
( ( ( ~ ~ ( in @ SV131 @ SV97 ) )
= $false )
| ( ( in @ SV131 @ SV111 )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1700,plain,
! [SV111: $i,SV97: $i,SV58: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ SV58 ) )
= $true )
| ( ( ~ ~ ( in @ SV131 @ SV97 ) )
= $true )
| ( ( in @ SV131 @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1701,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1702,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1703,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1704,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) ) )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1705,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1706,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) ) )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1707,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1708,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) ) )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1709,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1710,plain,
! [SV99: $i,SV60: $i] :
( ( ( ( sK25_SY325 @ SV60 @ SV99 )
= SV60 )
= $true )
| ( ( in @ ( sK25_SY325 @ SV60 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( singleton @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1711,plain,
! [SV5: $i,SV63: $i,SV137: $i] :
( ( ( in @ SV137 @ SV63 )
= $false )
| ( ( ~ ( in @ SV137 @ ( sK20_SY279 @ SV5 @ SV63 ) ) )
= $true )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1712,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV121 @ SV124 ) )
= $true )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1713,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1714,plain,
! [SV12: $i] :
( ( ( ~ ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1715,plain,
! [SV18: $i] :
( ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1716,plain,
! [SV18: $i] :
( ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1717,plain,
! [SV18: $i] :
( ( ( ! [SY376: $i] :
~ ( ~ ( ~ ( in @ SY376 @ ( sK39_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY376
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY376
!= ( singleton @ SY196 ) ) )
| ( in @ SY376 @ ( sK39_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1718,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( ~ ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
| ~ ! [SY372: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY372 @ SV18 )
| ~ ( in @ SY372 @ SV18 ) )
| ( SV140
!= ( singleton @ SY372 ) ) ) ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1662]) ).
thf(1719,plain,
! [SV140: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ! [SY373: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY373 @ SV18 )
| ~ ( in @ SY373 @ SV18 ) )
| ( SV140
!= ( singleton @ SY373 ) ) )
| ( in @ SV140 @ ( sK35_SY193 @ SV18 ) ) ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1662]) ).
thf(1720,plain,
! [SV134: $i,SV18: $i] :
( ( ( ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY362 @ SV18 )
| ~ ( in @ SY362 @ SV18 ) )
| ( SV134
!= ( singleton @ SY362 ) ) ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1721,plain,
! [SV134: $i,SV18: $i] :
( ( ( ! [SY363: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV18 )
| ~ ( in @ SY363 @ SV18 ) )
| ( SV134
!= ( singleton @ SY363 ) ) ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1722,plain,
! [SV135: $i,SV76: $i,SV22: $i] :
( ( ( disjoint @ SV22 @ SV76 )
= $false )
| ( ( in @ SV135 @ SV22 )
= $false )
| ( ( in @ SV135 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1723,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) )
| ~ ( in @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) @ SV32 ) )
= $false )
| ( ( in @ SV126 @ SV82 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1724,plain,
! [SV82: $i,SV32: $i,SV141: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV141 )
| ~ ( in @ SV141 @ SV32 ) )
= $true )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1725,plain,
! [SV82: $i,SV32: $i] :
( ( ( ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1726,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 ) )
= $true )
| ( ( ~ ( in @ SV139 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1727,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1728,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
| ~ ( ( SV133 != SV106 ) ) )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1729,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1674]) ).
thf(1730,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $false )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1674]) ).
thf(1731,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1732,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1733,plain,
! [SV87: $i,SV41: $i,SV118: $i,SV138: $i] :
( ( ( ~ ( ~ ( in @ SV138 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 ) ) )
= $false )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1734,plain,
! [SV118: $i,SV87: $i,SV138: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
| ( in @ SV138 @ SV118 ) ) )
= $false )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1735,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
| ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1736,plain,
! [SV45: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV45 ) )
= $false )
| ( ( in @ SV45 @ SV116 )
= $true )
| ( ( SV45 = SV116 )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1737,plain,
! [SV46: $i] :
( ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1738,plain,
! [SV46: $i] :
( ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true )
| ( ( ~ ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1739,plain,
! [SV46: $i] :
( ( ( ! [SY379: $i] :
~ ( ~ ( ~ ( in @ SY379 @ ( sK40_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY379 ) )
| ~ ( ordinal @ SY379 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY379 ) )
| ~ ( ordinal @ SY379 ) )
| ( in @ SY379 @ ( sK40_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1740,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
| ~ ! [SY374: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY374 @ SV46 )
| ( SY374 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1741,plain,
! [SV142: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ! [SY375: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY375 @ SV46 )
| ( SY375 != SV142 ) )
| ~ ( ordinal @ SV142 ) )
| ( in @ SV142 @ ( sK37_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1742,plain,
! [SV136: $i,SV46: $i] :
( ( ( ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY364 @ SV46 )
| ( SY364 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1743,plain,
! [SV136: $i,SV46: $i] :
( ( ( ! [SY365: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY365 @ SV46 )
| ( SY365 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1744,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
= $true )
| ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1685]) ).
thf(1745,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
= $true )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1746,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
| ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 ) )
= $true )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1747,plain,
! [SV90: $i,SV110: $i,SV51: $i,SV130: $i] :
( ( ( in @ SV130 @ SV51 )
= $true )
| ( ( in @ SV130 @ SV110 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1748,plain,
! [SV51: $i,SV110: $i,SV90: $i,SV130: $i] :
( ( ( in @ SV130 @ SV90 )
= $true )
| ( ( in @ SV130 @ SV110 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1749,plain,
! [SV110: $i,SV90: $i,SV51: $i,SV130: $i] :
( ( ( in @ SV130 @ SV51 )
= $false )
| ( ( ~ ( in @ SV130 @ SV90 ) )
= $true )
| ( ( in @ SV130 @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1750,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) )
= $true )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1751,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) ) )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1752,plain,
! [SV97: $i,SV111: $i,SV58: $i,SV131: $i] :
( ( ( in @ SV131 @ SV58 )
= $true )
| ( ( in @ SV131 @ SV111 )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1753,plain,
! [SV58: $i,SV111: $i,SV97: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ SV97 ) )
= $true )
| ( ( in @ SV131 @ SV111 )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1754,plain,
! [SV111: $i,SV97: $i,SV58: $i,SV131: $i] :
( ( ( in @ SV131 @ SV58 )
= $false )
| ( ( ~ ~ ( in @ SV131 @ SV97 ) )
= $true )
| ( ( in @ SV131 @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1755,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) )
= $true )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1756,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1757,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1758,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1759,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
| ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 ) )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1760,plain,
! [SV63: $i,SV5: $i,SV137: $i] :
( ( ( in @ SV137 @ ( sK20_SY279 @ SV5 @ SV63 ) )
= $false )
| ( ( in @ SV137 @ SV63 )
= $false )
| ( ( in @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1761,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV121 @ SV124 ) )
= $true )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1762,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1763,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1764,plain,
! [SV18: $i] :
( ( ( ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1765,plain,
! [SV18: $i] :
( ( ( ! [SY193: $i] :
~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SY193 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY194
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY194
!= ( singleton @ SY196 ) ) )
| ( in @ SY194 @ SY193 ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1766,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
| ~ ! [SY382: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY382 @ SV18 )
| ~ ( in @ SY382 @ SV18 ) )
| ( SV143
!= ( singleton @ SY382 ) ) ) )
| ~ ( ~ ~ ! [SY383: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY383 @ SV18 )
| ~ ( in @ SY383 @ SV18 ) )
| ( SV143
!= ( singleton @ SY383 ) ) )
| ( in @ SV143 @ ( sK39_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(1767,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
| ~ ! [SY372: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY372 @ SV18 )
| ~ ( in @ SY372 @ SV18 ) )
| ( SV140
!= ( singleton @ SY372 ) ) ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1768,plain,
! [SV140: $i,SV18: $i] :
( ( ( ~ ~ ! [SY373: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY373 @ SV18 )
| ~ ( in @ SY373 @ SV18 ) )
| ( SV140
!= ( singleton @ SY373 ) ) )
| ( in @ SV140 @ ( sK35_SY193 @ SV18 ) ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1769,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 ) )
| ( SV134
!= ( singleton @ ( sK41_SY362 @ SV134 @ SV18 ) ) ) ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1720]) ).
thf(1770,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV144 @ SV18 )
| ~ ( in @ SV144 @ SV18 ) )
| ( SV134
!= ( singleton @ SV144 ) ) ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1771,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) ) )
= $false )
| ( ( in @ SV126 @ SV82 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1723]) ).
thf(1772,plain,
! [SV126: $i,SV32: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) @ SV32 ) )
= $false )
| ( ( in @ SV126 @ SV82 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1723]) ).
thf(1773,plain,
! [SV82: $i,SV32: $i,SV141: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV141 ) )
= $true )
| ( ( ~ ( in @ SV141 @ SV32 ) )
= $true )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1774,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK42_SY355 @ SV82 @ SV32 ) )
| ~ ( in @ ( sK42_SY355 @ SV82 @ SV32 ) @ SV32 ) ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1725]) ).
thf(1775,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( ~ ( in @ SV139 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1776,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) ) )
= $true )
| ( ( ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1777,plain,
! [SV106: $i,SV115: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) ) )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1728]) ).
thf(1778,plain,
! [SV84: $i,SV34: $i,SV115: $i,SV106: $i,SV133: $i] :
( ( ( ~ ( ( SV133 != SV106 ) ) )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1728]) ).
thf(1779,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1780,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1781,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1732]) ).
thf(1782,plain,
! [SV87: $i,SV41: $i,SV118: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV118 )
| ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 ) )
= $true )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1733]) ).
thf(1783,plain,
! [SV118: $i,SV87: $i,SV138: $i,SV41: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
| ( in @ SV138 @ SV118 ) )
= $true )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1784,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1735]) ).
thf(1785,plain,
! [SV118: $i,SV87: $i,SV41: $i] :
( ( ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
= $false )
| ( ( ~ ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1735]) ).
thf(1786,plain,
! [SV45: $i,SV116: $i] :
( ( ( in @ SV116 @ SV45 )
= $true )
| ( ( in @ SV45 @ SV116 )
= $true )
| ( ( SV45 = SV116 )
= $true )
| ( ( ordinal @ SV116 )
= $false )
| ( ( ordinal @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1787,plain,
! [SV46: $i] :
( ( ( ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1788,plain,
! [SV46: $i] :
( ( ( ! [SY245: $i] :
~ ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY246 ) )
| ~ ( ordinal @ SY246 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY246 ) )
| ~ ( ordinal @ SY246 ) )
| ( in @ SY246 @ SY245 ) ) ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1789,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
| ~ ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY384 @ SV46 )
| ( SY384 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
| ~ ( ~ ~ ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY385 @ SV46 )
| ( SY385 != SV145 ) )
| ~ ( ordinal @ SV145 ) )
| ( in @ SV145 @ ( sK40_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(1790,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
| ~ ! [SY374: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY374 @ SV46 )
| ( SY374 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1791,plain,
! [SV142: $i,SV46: $i] :
( ( ( ~ ~ ! [SY375: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY375 @ SV46 )
| ( SY375 != SV142 ) )
| ~ ( ordinal @ SV142 ) )
| ( in @ SV142 @ ( sK37_SY245 @ SV46 ) ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1741]) ).
thf(1792,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY364 @ SV136 @ SV46 ) @ SV46 )
| ( ( sK43_SY364 @ SV136 @ SV46 )
!= SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1742]) ).
thf(1793,plain,
! [SV136: $i,SV46: $i,SV146: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV146 @ SV46 )
| ( SV146 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(1794,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $true )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $true )
| ( ( in @ ( sK28_SY331 @ SV89 @ SV48 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(1795,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $true )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $true )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(1796,plain,
! [SV109: $i,SV48: $i,SV89: $i] :
( ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV48 )
= $true )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $true )
| ( ( ( sK28_SY331 @ SV89 @ SV48 @ SV109 )
= SV89 )
= $false )
| ( ( SV109
= ( unordered_pair @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1746]) ).
thf(1797,plain,
! [SV110: $i,SV51: $i,SV90: $i,SV130: $i] :
( ( ( in @ SV130 @ SV90 )
= $false )
| ( ( in @ SV130 @ SV51 )
= $false )
| ( ( in @ SV130 @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1798,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1799,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
| ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1800,plain,
! [SV58: $i,SV111: $i,SV97: $i,SV131: $i] :
( ( ( in @ SV131 @ SV97 )
= $false )
| ( ( in @ SV131 @ SV111 )
= $false )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1801,plain,
! [SV111: $i,SV58: $i,SV97: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ SV97 ) )
= $false )
| ( ( in @ SV131 @ SV58 )
= $false )
| ( ( in @ SV131 @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1802,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1803,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1804,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(1805,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1758]) ).
thf(1806,plain,
! [SV112: $i,SV59: $i,SV98: $i] :
( ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV59 )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $true )
| ( ( in @ ( sK31_SY337 @ SV98 @ SV59 @ SV112 ) @ SV98 )
= $false )
| ( ( SV112
= ( set_union2 @ SV59 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1807,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ SV12 )
| ~ ( in @ SV124 @ SV12 ) )
= $true )
| ( ( ~ ~ ( in @ SV121 @ SV124 ) )
= $true )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1808,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1809,plain,
! [SV12: $i] :
( ( ( in @ ( sK18_SY181 @ SV12 ) @ ( sK22_SY350 @ SV12 ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1810,plain,
! [SV18: $i] :
( ( ( ~ ! [SY386: $i] :
~ ( ~ ( ~ ( in @ SY386 @ ( sK44_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY386
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY386
!= ( singleton @ SY196 ) ) )
| ( in @ SY386 @ ( sK44_SY193 @ SV18 ) ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1764]) ).
thf(1811,plain,
! [SV18: $i] :
( ( ( ~ ! [SY389: $i] :
~ ( ~ ( ~ ( in @ SY389 @ ( sK45_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY389
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY389
!= ( singleton @ SY196 ) ) )
| ( in @ SY389 @ ( sK45_SY193 @ SV18 ) ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1765]) ).
thf(1812,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
| ~ ! [SY382: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY382 @ SV18 )
| ~ ( in @ SY382 @ SV18 ) )
| ( SV143
!= ( singleton @ SY382 ) ) ) )
| ~ ( ~ ~ ! [SY383: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY383 @ SV18 )
| ~ ( in @ SY383 @ SV18 ) )
| ( SV143
!= ( singleton @ SY383 ) ) )
| ( in @ SV143 @ ( sK39_SY193 @ SV18 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1813,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ ( sK35_SY193 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY372: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY372 @ SV18 )
| ~ ( in @ SY372 @ SV18 ) )
| ( SV140
!= ( singleton @ SY372 ) ) ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(1814,plain,
! [SV140: $i,SV18: $i] :
( ( ( ~ ~ ! [SY373: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY373 @ SV18 )
| ~ ( in @ SY373 @ SV18 ) )
| ( SV140
!= ( singleton @ SY373 ) ) ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1815,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 ) )
| ( SV134
!= ( singleton @ ( sK41_SY362 @ SV134 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1816,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV144 @ SV18 )
| ~ ( in @ SV144 @ SV18 ) )
| ( SV134
!= ( singleton @ SV144 ) ) ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1817,plain,
! [SV32: $i,SV82: $i,SV126: $i] :
( ( ( in @ SV126 @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) )
= $true )
| ( ( in @ SV126 @ SV82 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1818,plain,
! [SV126: $i,SV32: $i,SV82: $i] :
( ( ( in @ ( sK38_SY352 @ SV82 @ SV32 @ SV126 ) @ SV32 )
= $true )
| ( ( in @ SV126 @ SV82 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1819,plain,
! [SV82: $i,SV32: $i,SV141: $i,SV126: $i] :
( ( ( in @ SV126 @ SV141 )
= $false )
| ( ( ~ ( in @ SV141 @ SV32 ) )
= $true )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1820,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK42_SY355 @ SV82 @ SV32 ) )
| ~ ( in @ ( sK42_SY355 @ SV82 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1821,plain,
! [SV82: $i,SV32: $i,SV139: $i] :
( ( ( in @ SV139 @ SV32 )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( ~ ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1822,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) ) )
= $false )
| ( ( ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1823,plain,
! [SV106: $i,SV115: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1824,plain,
! [SV84: $i,SV34: $i,SV115: $i,SV106: $i,SV133: $i] :
( ( ( SV133 != SV106 )
= $true )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1825,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1826,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1827,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1828,plain,
! [SV87: $i,SV41: $i,SV118: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV118 ) )
= $true )
| ( ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
= $true )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(1829,plain,
! [SV118: $i,SV87: $i,SV138: $i,SV41: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 ) )
= $true )
| ( ( in @ SV138 @ SV118 )
= $true )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(1830,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
= $true )
| ( ( ~ ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1831,plain,
! [SV118: $i,SV87: $i,SV41: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) )
= $false )
| ( ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1832,plain,
! [SV46: $i] :
( ( ( ~ ! [SY392: $i] :
~ ( ~ ( ~ ( in @ SY392 @ ( sK46_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY392 ) )
| ~ ( ordinal @ SY392 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY392 ) )
| ~ ( ordinal @ SY392 ) )
| ( in @ SY392 @ ( sK46_SY245 @ SV46 ) ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1787]) ).
thf(1833,plain,
! [SV46: $i] :
( ( ( ~ ! [SY395: $i] :
~ ( ~ ( ~ ( in @ SY395 @ ( sK47_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY395 ) )
| ~ ( ordinal @ SY395 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY395 ) )
| ~ ( ordinal @ SY395 ) )
| ( in @ SY395 @ ( sK47_SY245 @ SV46 ) ) ) ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1788]) ).
thf(1834,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
| ~ ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY384 @ SV46 )
| ( SY384 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
| ~ ( ~ ~ ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY385 @ SV46 )
| ( SY385 != SV145 ) )
| ~ ( ordinal @ SV145 ) )
| ( in @ SV145 @ ( sK40_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1835,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ ( sK37_SY245 @ SV46 ) ) )
= $true )
| ( ( ~ ! [SY374: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY374 @ SV46 )
| ( SY374 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1836,plain,
! [SV142: $i,SV46: $i] :
( ( ( ~ ~ ! [SY375: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY375 @ SV46 )
| ( SY375 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1837,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK43_SY364 @ SV136 @ SV46 ) @ SV46 )
| ( ( sK43_SY364 @ SV136 @ SV46 )
!= SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1838,plain,
! [SV136: $i,SV46: $i,SV146: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV146 @ SV46 )
| ( SV146 != SV136 ) )
| ~ ( ordinal @ SV136 ) ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1839,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1840,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1841,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1799]) ).
thf(1842,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1799]) ).
thf(1843,plain,
! [SV111: $i,SV58: $i,SV97: $i,SV131: $i] :
( ( ( in @ SV131 @ SV97 )
= $true )
| ( ( in @ SV131 @ SV58 )
= $false )
| ( ( in @ SV131 @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1844,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1802]) ).
thf(1845,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1802]) ).
thf(1846,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
| ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1847,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV124 @ SV12 ) )
= $true )
| ( ( ~ ~ ( in @ SV121 @ SV124 ) )
= $true )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1848,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( sK18_SY181 @ SV12 ) @ SV12 ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1849,plain,
! [SV12: $i] :
( ( ( ~ ( in @ ( sK22_SY350 @ SV12 ) @ SV12 ) )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1850,plain,
! [SV18: $i] :
( ( ( ! [SY386: $i] :
~ ( ~ ( ~ ( in @ SY386 @ ( sK44_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY386
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY386
!= ( singleton @ SY196 ) ) )
| ( in @ SY386 @ ( sK44_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1851,plain,
! [SV18: $i] :
( ( ( ! [SY389: $i] :
~ ( ~ ( ~ ( in @ SY389 @ ( sK45_SY193 @ SV18 ) )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY195 @ SV18 )
| ~ ( in @ SY195 @ SV18 ) )
| ( SY389
!= ( singleton @ SY195 ) ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY196 @ SV18 )
| ~ ( in @ SY196 @ SV18 ) )
| ( SY389
!= ( singleton @ SY196 ) ) )
| ( in @ SY389 @ ( sK45_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1852,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
| ~ ! [SY382: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY382 @ SV18 )
| ~ ( in @ SY382 @ SV18 ) )
| ( SV143
!= ( singleton @ SY382 ) ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1812]) ).
thf(1853,plain,
! [SV143: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ! [SY383: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY383 @ SV18 )
| ~ ( in @ SY383 @ SV18 ) )
| ( SV143
!= ( singleton @ SY383 ) ) )
| ( in @ SV143 @ ( sK39_SY193 @ SV18 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1812]) ).
thf(1854,plain,
! [SV18: $i,SV140: $i] :
( ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ~ ! [SY372: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY372 @ SV18 )
| ~ ( in @ SY372 @ SV18 ) )
| ( SV140
!= ( singleton @ SY372 ) ) ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1855,plain,
! [SV140: $i,SV18: $i] :
( ( ( ~ ! [SY373: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY373 @ SV18 )
| ~ ( in @ SY373 @ SV18 ) )
| ( SV140
!= ( singleton @ SY373 ) ) ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1856,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 ) )
| ( SV134
!= ( singleton @ ( sK41_SY362 @ SV134 @ SV18 ) ) ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1857,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( ~ ~ ( ~ ( in @ SV144 @ SV18 )
| ~ ( in @ SV144 @ SV18 ) )
| ( SV134
!= ( singleton @ SV144 ) ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1858,plain,
! [SV82: $i,SV126: $i,SV32: $i,SV141: $i] :
( ( ( in @ SV141 @ SV32 )
= $false )
| ( ( in @ SV126 @ SV141 )
= $false )
| ( ( in @ SV126 @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1859,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK42_SY355 @ SV82 @ SV32 ) )
| ~ ( in @ ( sK42_SY355 @ SV82 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1860,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) )
| ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1861,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
= $true )
| ( ( ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1862,plain,
! [SV106: $i,SV115: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ( SV133 != SV34 ) )
| ~ ( ( SV133 != SV84 ) ) )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1863,plain,
! [SV84: $i,SV34: $i,SV115: $i,SV106: $i,SV133: $i] :
( ( ( SV133 = SV106 )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1864,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1865,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1866,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1867,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1868,plain,
! [SV87: $i,SV41: $i,SV118: $i,SV138: $i] :
( ( ( in @ SV138 @ SV118 )
= $false )
| ( ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
= $true )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(1869,plain,
! [SV118: $i,SV87: $i,SV138: $i,SV41: $i] :
( ( ( in @ ( subset_complement @ SV41 @ SV138 ) @ SV87 )
= $false )
| ( ( in @ SV138 @ SV118 )
= $true )
| ( ( element @ SV138 @ ( powerset @ SV41 ) )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $false )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1870,plain,
! [SV118: $i,SV87: $i,SV41: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
| ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 ) )
= $false )
| ( ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1871,plain,
! [SV118: $i,SV87: $i,SV41: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 ) )
= $false )
| ( ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1872,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
= $false )
| ( ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1873,plain,
! [SV46: $i] :
( ( ( ! [SY392: $i] :
~ ( ~ ( ~ ( in @ SY392 @ ( sK46_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY392 ) )
| ~ ( ordinal @ SY392 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY392 ) )
| ~ ( ordinal @ SY392 ) )
| ( in @ SY392 @ ( sK46_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1832]) ).
thf(1874,plain,
! [SV46: $i] :
( ( ( ! [SY395: $i] :
~ ( ~ ( ~ ( in @ SY395 @ ( sK47_SY245 @ SV46 ) )
| ~ ! [SY247: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY247 @ SV46 )
| ( SY247 != SY395 ) )
| ~ ( ordinal @ SY395 ) ) )
| ~ ( ~ ~ ! [SY248: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY248 @ SV46 )
| ( SY248 != SY395 ) )
| ~ ( ordinal @ SY395 ) )
| ( in @ SY395 @ ( sK47_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1833]) ).
thf(1875,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
| ~ ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY384 @ SV46 )
| ( SY384 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(1876,plain,
! [SV145: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY385 @ SV46 )
| ( SY385 != SV145 ) )
| ~ ( ordinal @ SV145 ) )
| ( in @ SV145 @ ( sK40_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(1877,plain,
! [SV46: $i,SV142: $i] :
( ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ~ ! [SY374: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY374 @ SV46 )
| ( SY374 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1878,plain,
! [SV142: $i,SV46: $i] :
( ( ( ~ ! [SY375: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY375 @ SV46 )
| ( SY375 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1879,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY364 @ SV136 @ SV46 ) @ SV46 )
| ( ( sK43_SY364 @ SV136 @ SV46 )
!= SV136 ) )
| ~ ( ordinal @ SV136 ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1880,plain,
! [SV136: $i,SV46: $i,SV146: $i] :
( ( ( ~ ~ ( ~ ( in @ SV146 @ SV46 )
| ( SV146 != SV136 ) )
| ~ ( ordinal @ SV136 ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1838]) ).
thf(1881,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $true )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1882,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $true )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(1883,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) ) )
= $true )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(1884,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $true )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(1885,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $true )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(1886,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1846]) ).
thf(1887,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1846]) ).
thf(1888,plain,
! [SV124: $i,SV12: $i,SV121: $i] :
( ( ( in @ SV121 @ SV12 )
= $false )
| ( ( ~ ( in @ SV124 @ SV12 ) )
= $true )
| ( ( ~ ~ ( in @ SV121 @ SV124 ) )
= $true )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1889,plain,
! [SV12: $i] :
( ( ( in @ ( sK18_SY181 @ SV12 ) @ SV12 )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1890,plain,
! [SV12: $i] :
( ( ( in @ ( sK22_SY350 @ SV12 ) @ SV12 )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1891,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
| ~ ! [SY398: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY398 @ SV18 )
| ~ ( in @ SY398 @ SV18 ) )
| ( SV147
!= ( singleton @ SY398 ) ) ) )
| ~ ( ~ ~ ! [SY399: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY399 @ SV18 )
| ~ ( in @ SY399 @ SV18 ) )
| ( SV147
!= ( singleton @ SY399 ) ) )
| ( in @ SV147 @ ( sK44_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(1892,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
| ~ ! [SY400: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY400 @ SV18 )
| ~ ( in @ SY400 @ SV18 ) )
| ( SV148
!= ( singleton @ SY400 ) ) ) )
| ~ ( ~ ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY401 @ SV18 )
| ~ ( in @ SY401 @ SV18 ) )
| ( SV148
!= ( singleton @ SY401 ) ) )
| ( in @ SV148 @ ( sK45_SY193 @ SV18 ) ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(1893,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
| ~ ! [SY382: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY382 @ SV18 )
| ~ ( in @ SY382 @ SV18 ) )
| ( SV143
!= ( singleton @ SY382 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(1894,plain,
! [SV143: $i,SV18: $i] :
( ( ( ~ ~ ! [SY383: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY383 @ SV18 )
| ~ ( in @ SY383 @ SV18 ) )
| ( SV143
!= ( singleton @ SY383 ) ) )
| ( in @ SV143 @ ( sK39_SY193 @ SV18 ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1895,plain,
! [SV140: $i,SV18: $i] :
( ( ( ! [SY372: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY372 @ SV18 )
| ~ ( in @ SY372 @ SV18 ) )
| ( SV140
!= ( singleton @ SY372 ) ) ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1896,plain,
! [SV140: $i,SV18: $i] :
( ( ( ! [SY373: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY373 @ SV18 )
| ~ ( in @ SY373 @ SV18 ) )
| ( SV140
!= ( singleton @ SY373 ) ) ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1897,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 ) ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1856]) ).
thf(1898,plain,
! [SV18: $i,SV134: $i] :
( ( ( SV134
!= ( singleton @ ( sK41_SY362 @ SV134 @ SV18 ) ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1856]) ).
thf(1899,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( ~ ~ ( ~ ( in @ SV144 @ SV18 )
| ~ ( in @ SV144 @ SV18 ) ) )
= $true )
| ( ( SV134
!= ( singleton @ SV144 ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(1900,plain,
! [SV82: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK42_SY355 @ SV82 @ SV32 ) ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1901,plain,
! [SV32: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK42_SY355 @ SV82 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1902,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1860]) ).
thf(1903,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1860]) ).
thf(1904,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ( SV133 != SV34 ) ) )
= $true )
| ( ( ~ ( ( SV133 != SV84 ) ) )
= $true )
| ( ( ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(1905,plain,
! [SV106: $i,SV84: $i,SV115: $i,SV34: $i,SV133: $i] :
( ( ( ~ ( ( SV133 != SV34 ) ) )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1862]) ).
thf(1906,plain,
! [SV106: $i,SV34: $i,SV115: $i,SV84: $i,SV133: $i] :
( ( ( ~ ( ( SV133 != SV84 ) ) )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1862]) ).
thf(1907,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(1908,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(1909,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(1910,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1911,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1912,plain,
! [SV118: $i,SV87: $i,SV41: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 ) )
= $false )
| ( ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1913,plain,
! [SV41: $i,SV118: $i,SV87: $i] :
( ( ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
= $false )
| ( ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1914,plain,
! [SV118: $i,SV87: $i,SV41: $i] :
( ( ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
= $true )
| ( ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
= $false )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1915,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
| ~ ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY402 @ SV46 )
| ( SY402 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
| ~ ( ~ ~ ! [SY403: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY403 @ SV46 )
| ( SY403 != SV149 ) )
| ~ ( ordinal @ SV149 ) )
| ( in @ SV149 @ ( sK46_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(1916,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
| ~ ! [SY404: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY404 @ SV46 )
| ( SY404 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
| ~ ( ~ ~ ! [SY405: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV46 )
| ( SY405 != SV150 ) )
| ~ ( ordinal @ SV150 ) )
| ( in @ SV150 @ ( sK47_SY245 @ SV46 ) ) ) ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(1917,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
| ~ ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY384 @ SV46 )
| ( SY384 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1875]) ).
thf(1918,plain,
! [SV145: $i,SV46: $i] :
( ( ( ~ ~ ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY385 @ SV46 )
| ( SY385 != SV145 ) )
| ~ ( ordinal @ SV145 ) )
| ( in @ SV145 @ ( sK40_SY245 @ SV46 ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1876]) ).
thf(1919,plain,
! [SV142: $i,SV46: $i] :
( ( ( ! [SY374: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY374 @ SV46 )
| ( SY374 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(1920,plain,
! [SV142: $i,SV46: $i] :
( ( ( ! [SY375: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY375 @ SV46 )
| ( SY375 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1921,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY364 @ SV136 @ SV46 ) @ SV46 )
| ( ( sK43_SY364 @ SV136 @ SV46 )
!= SV136 ) ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1922,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( ordinal @ SV136 ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1923,plain,
! [SV136: $i,SV46: $i,SV146: $i] :
( ( ( ~ ~ ( ~ ( in @ SV146 @ SV46 )
| ( SV146 != SV136 ) ) )
= $true )
| ( ( ~ ( ordinal @ SV136 ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(1924,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
| ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1925,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1926,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) ) )
= $true )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1927,plain,
! [SV121: $i,SV12: $i,SV124: $i] :
( ( ( in @ SV124 @ SV12 )
= $false )
| ( ( in @ SV121 @ SV12 )
= $false )
| ( ( ~ ~ ( in @ SV121 @ SV124 ) )
= $true )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1928,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( ~ ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
| ~ ! [SY398: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY398 @ SV18 )
| ~ ( in @ SY398 @ SV18 ) )
| ( SV147
!= ( singleton @ SY398 ) ) ) )
| ~ ( ~ ~ ! [SY399: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY399 @ SV18 )
| ~ ( in @ SY399 @ SV18 ) )
| ( SV147
!= ( singleton @ SY399 ) ) )
| ( in @ SV147 @ ( sK44_SY193 @ SV18 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(1929,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
| ~ ! [SY400: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY400 @ SV18 )
| ~ ( in @ SY400 @ SV18 ) )
| ( SV148
!= ( singleton @ SY400 ) ) ) )
| ~ ( ~ ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY401 @ SV18 )
| ~ ( in @ SY401 @ SV18 ) )
| ( SV148
!= ( singleton @ SY401 ) ) )
| ( in @ SV148 @ ( sK45_SY193 @ SV18 ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(1930,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ ( sK39_SY193 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY382: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY382 @ SV18 )
| ~ ( in @ SY382 @ SV18 ) )
| ( SV143
!= ( singleton @ SY382 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(1931,plain,
! [SV143: $i,SV18: $i] :
( ( ( ~ ~ ! [SY383: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY383 @ SV18 )
| ~ ( in @ SY383 @ SV18 ) )
| ( SV143
!= ( singleton @ SY383 ) ) ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(1932,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 ) )
| ( SV140
!= ( singleton @ ( sK48_SY372 @ SV140 @ SV18 ) ) ) ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1895]) ).
thf(1933,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV151 @ SV18 )
| ~ ( in @ SV151 @ SV18 ) )
| ( SV140
!= ( singleton @ SV151 ) ) ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(1934,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(1935,plain,
! [SV18: $i,SV134: $i] :
( ( ( SV134
= ( singleton @ ( sK41_SY362 @ SV134 @ SV18 ) ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(1936,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( ~ ( ~ ( in @ SV144 @ SV18 )
| ~ ( in @ SV144 @ SV18 ) ) )
= $false )
| ( ( SV134
!= ( singleton @ SV144 ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(1937,plain,
! [SV82: $i,SV32: $i] :
( ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK42_SY355 @ SV82 @ SV32 ) )
= $true )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(1938,plain,
! [SV32: $i,SV82: $i] :
( ( ( in @ ( sK42_SY355 @ SV82 @ SV32 ) @ SV32 )
= $true )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(1939,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) ) )
= $true )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1940,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( SV133 != SV34 )
= $false )
| ( ( ~ ( ( SV133 != SV84 ) ) )
= $true )
| ( ( ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1941,plain,
! [SV106: $i,SV84: $i,SV115: $i,SV34: $i,SV133: $i] :
( ( ( SV133 != SV34 )
= $true )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(1942,plain,
! [SV106: $i,SV34: $i,SV115: $i,SV84: $i,SV133: $i] :
( ( ( SV133 != SV84 )
= $true )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1906]) ).
thf(1943,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $false )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(1944,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1945,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(1946,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(1947,plain,
! [SV118: $i,SV87: $i,SV41: $i] :
( ( ( in @ ( subset_complement @ SV41 @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) ) @ SV87 )
= $true )
| ( ( in @ ( sK36_SY347 @ SV87 @ SV118 @ SV41 ) @ SV118 )
= $true )
| ( ( SV118
= ( complements_of_subsets @ SV41 @ SV87 ) )
= $true )
| ( ( element @ SV118 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false )
| ( ( element @ SV87 @ ( powerset @ ( powerset @ SV41 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1948,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( ~ ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
| ~ ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY402 @ SV46 )
| ( SY402 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
| ~ ( ~ ~ ! [SY403: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY403 @ SV46 )
| ( SY403 != SV149 ) )
| ~ ( ordinal @ SV149 ) )
| ( in @ SV149 @ ( sK46_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(1949,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
| ~ ! [SY404: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY404 @ SV46 )
| ( SY404 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
| ~ ( ~ ~ ! [SY405: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV46 )
| ( SY405 != SV150 ) )
| ~ ( ordinal @ SV150 ) )
| ( in @ SV150 @ ( sK47_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1950,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ ( sK40_SY245 @ SV46 ) ) )
= $true )
| ( ( ~ ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY384 @ SV46 )
| ( SY384 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(1951,plain,
! [SV145: $i,SV46: $i] :
( ( ( ~ ~ ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY385 @ SV46 )
| ( SY385 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(1952,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK49_SY374 @ SV142 @ SV46 ) @ SV46 )
| ( ( sK49_SY374 @ SV142 @ SV46 )
!= SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1919]) ).
thf(1953,plain,
! [SV142: $i,SV46: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV152 @ SV46 )
| ( SV152 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(1954,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY364 @ SV136 @ SV46 ) @ SV46 )
| ( ( sK43_SY364 @ SV136 @ SV46 )
!= SV136 ) ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(1955,plain,
! [SV46: $i,SV136: $i] :
( ( ( ordinal @ SV136 )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1922]) ).
thf(1956,plain,
! [SV136: $i,SV46: $i,SV146: $i] :
( ( ( ~ ( ~ ( in @ SV146 @ SV46 )
| ( SV146 != SV136 ) ) )
= $false )
| ( ( ~ ( ordinal @ SV136 ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(1957,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(1958,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 ) )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(1959,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
| ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1960,plain,
! [SV12: $i,SV124: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ SV124 ) )
= $false )
| ( ( in @ SV121 @ SV12 )
= $false )
| ( ( in @ SV124 @ SV12 )
= $false )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(1961,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( ~ ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
| ~ ! [SY398: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY398 @ SV18 )
| ~ ( in @ SY398 @ SV18 ) )
| ( SV147
!= ( singleton @ SY398 ) ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(1962,plain,
! [SV147: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ! [SY399: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY399 @ SV18 )
| ~ ( in @ SY399 @ SV18 ) )
| ( SV147
!= ( singleton @ SY399 ) ) )
| ( in @ SV147 @ ( sK44_SY193 @ SV18 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(1963,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
| ~ ! [SY400: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY400 @ SV18 )
| ~ ( in @ SY400 @ SV18 ) )
| ( SV148
!= ( singleton @ SY400 ) ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(1964,plain,
! [SV148: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY401 @ SV18 )
| ~ ( in @ SY401 @ SV18 ) )
| ( SV148
!= ( singleton @ SY401 ) ) )
| ( in @ SV148 @ ( sK45_SY193 @ SV18 ) ) ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(1965,plain,
! [SV18: $i,SV143: $i] :
( ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( ~ ! [SY382: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY382 @ SV18 )
| ~ ( in @ SY382 @ SV18 ) )
| ( SV143
!= ( singleton @ SY382 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1966,plain,
! [SV143: $i,SV18: $i] :
( ( ( ~ ! [SY383: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY383 @ SV18 )
| ~ ( in @ SY383 @ SV18 ) )
| ( SV143
!= ( singleton @ SY383 ) ) ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(1967,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 ) )
| ( SV140
!= ( singleton @ ( sK48_SY372 @ SV140 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(1968,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV151 @ SV18 )
| ~ ( in @ SV151 @ SV18 ) )
| ( SV140
!= ( singleton @ SV151 ) ) ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(1969,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(1970,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( ~ ( in @ SV144 @ SV18 )
| ~ ( in @ SV144 @ SV18 ) )
= $true )
| ( ( SV134
!= ( singleton @ SV144 ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(1971,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ! [SY355: $i] :
~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SY355 )
| ~ ( in @ SY355 @ SV32 ) ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(1972,plain,
! [SV115: $i,SV106: $i,SV84: $i,SV34: $i,SV133: $i] :
( ( ( SV133 = SV34 )
= $true )
| ( ( ~ ( ( SV133 != SV84 ) ) )
= $true )
| ( ( ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(1973,plain,
! [SV106: $i,SV84: $i,SV115: $i,SV34: $i,SV133: $i] :
( ( ( SV133 = SV34 )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1974,plain,
! [SV106: $i,SV34: $i,SV115: $i,SV84: $i,SV133: $i] :
( ( ( SV133 = SV84 )
= $false )
| ( ( in @ SV133 @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(1975,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(1976,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(1977,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
| ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(1978,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(1979,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( ~ ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
| ~ ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY402 @ SV46 )
| ( SY402 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(1980,plain,
! [SV149: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ! [SY403: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY403 @ SV46 )
| ( SY403 != SV149 ) )
| ~ ( ordinal @ SV149 ) )
| ( in @ SV149 @ ( sK46_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(1981,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
| ~ ! [SY404: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY404 @ SV46 )
| ( SY404 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(1982,plain,
! [SV150: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ! [SY405: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV46 )
| ( SY405 != SV150 ) )
| ~ ( ordinal @ SV150 ) )
| ( in @ SV150 @ ( sK47_SY245 @ SV46 ) ) ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(1983,plain,
! [SV46: $i,SV145: $i] :
( ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ~ ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY384 @ SV46 )
| ( SY384 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(1984,plain,
! [SV145: $i,SV46: $i] :
( ( ( ~ ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY385 @ SV46 )
| ( SY385 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(1985,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK49_SY374 @ SV142 @ SV46 ) @ SV46 )
| ( ( sK49_SY374 @ SV142 @ SV46 )
!= SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(1986,plain,
! [SV142: $i,SV46: $i,SV152: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV152 @ SV46 )
| ( SV152 != SV142 ) )
| ~ ( ordinal @ SV142 ) ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(1987,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK43_SY364 @ SV136 @ SV46 ) @ SV46 )
| ( ( sK43_SY364 @ SV136 @ SV46 )
!= SV136 ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(1988,plain,
! [SV136: $i,SV46: $i,SV146: $i] :
( ( ( ~ ( in @ SV146 @ SV46 )
| ( SV146 != SV136 ) )
= $true )
| ( ( ~ ( ordinal @ SV136 ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(1989,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $true )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1957]) ).
thf(1990,plain,
! [SV110: $i,SV51: $i,SV90: $i] :
( ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $true )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV51 )
= $false )
| ( ( in @ ( sK29_SY333 @ SV90 @ SV51 @ SV110 ) @ SV90 )
= $false )
| ( ( SV110
= ( set_intersection2 @ SV51 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1958]) ).
thf(1991,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1959]) ).
thf(1992,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1959]) ).
thf(1993,plain,
! [SV12: $i,SV124: $i,SV121: $i] :
( ( ( in @ SV121 @ SV124 )
= $true )
| ( ( in @ SV121 @ SV12 )
= $false )
| ( ( in @ SV124 @ SV12 )
= $false )
| ( ( ~ ( ( SV121 != SV124 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1960]) ).
thf(1994,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
| ~ ! [SY398: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY398 @ SV18 )
| ~ ( in @ SY398 @ SV18 ) )
| ( SV147
!= ( singleton @ SY398 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(1995,plain,
! [SV147: $i,SV18: $i] :
( ( ( ~ ~ ! [SY399: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY399 @ SV18 )
| ~ ( in @ SY399 @ SV18 ) )
| ( SV147
!= ( singleton @ SY399 ) ) )
| ( in @ SV147 @ ( sK44_SY193 @ SV18 ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(1996,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
| ~ ! [SY400: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY400 @ SV18 )
| ~ ( in @ SY400 @ SV18 ) )
| ( SV148
!= ( singleton @ SY400 ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(1997,plain,
! [SV148: $i,SV18: $i] :
( ( ( ~ ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY401 @ SV18 )
| ~ ( in @ SY401 @ SV18 ) )
| ( SV148
!= ( singleton @ SY401 ) ) )
| ( in @ SV148 @ ( sK45_SY193 @ SV18 ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1964]) ).
thf(1998,plain,
! [SV143: $i,SV18: $i] :
( ( ( ! [SY382: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY382 @ SV18 )
| ~ ( in @ SY382 @ SV18 ) )
| ( SV143
!= ( singleton @ SY382 ) ) ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(1999,plain,
! [SV143: $i,SV18: $i] :
( ( ( ! [SY383: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY383 @ SV18 )
| ~ ( in @ SY383 @ SV18 ) )
| ( SV143
!= ( singleton @ SY383 ) ) ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2000,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 ) )
| ( SV140
!= ( singleton @ ( sK48_SY372 @ SV140 @ SV18 ) ) ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2001,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( ~ ~ ( ~ ( in @ SV151 @ SV18 )
| ~ ( in @ SV151 @ SV18 ) )
| ( SV140
!= ( singleton @ SV151 ) ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1968]) ).
thf(2002,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1969]) ).
thf(2003,plain,
! [SV18: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1969]) ).
thf(2004,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( ~ ( in @ SV144 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV144 @ SV18 ) )
= $true )
| ( ( SV134
!= ( singleton @ SV144 ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(2005,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) )
| ~ ( in @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) @ SV32 ) ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1971]) ).
thf(2006,plain,
! [SV115: $i,SV106: $i,SV34: $i,SV84: $i,SV133: $i] :
( ( ( SV133 != SV84 )
= $false )
| ( ( SV133 = SV34 )
= $true )
| ( ( ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2007,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2008,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2009,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2010,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2011,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2012,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2013,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
| ~ ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY402 @ SV46 )
| ( SY402 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1979]) ).
thf(2014,plain,
! [SV149: $i,SV46: $i] :
( ( ( ~ ~ ! [SY403: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY403 @ SV46 )
| ( SY403 != SV149 ) )
| ~ ( ordinal @ SV149 ) )
| ( in @ SV149 @ ( sK46_SY245 @ SV46 ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1980]) ).
thf(2015,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
| ~ ! [SY404: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY404 @ SV46 )
| ( SY404 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1981]) ).
thf(2016,plain,
! [SV150: $i,SV46: $i] :
( ( ( ~ ~ ! [SY405: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV46 )
| ( SY405 != SV150 ) )
| ~ ( ordinal @ SV150 ) )
| ( in @ SV150 @ ( sK47_SY245 @ SV46 ) ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2017,plain,
! [SV145: $i,SV46: $i] :
( ( ( ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY384 @ SV46 )
| ( SY384 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2018,plain,
! [SV145: $i,SV46: $i] :
( ( ( ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY385 @ SV46 )
| ( SY385 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2019,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK49_SY374 @ SV142 @ SV46 ) @ SV46 )
| ( ( sK49_SY374 @ SV142 @ SV46 )
!= SV142 ) )
| ~ ( ordinal @ SV142 ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2020,plain,
! [SV142: $i,SV46: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( in @ SV152 @ SV46 )
| ( SV152 != SV142 ) )
| ~ ( ordinal @ SV142 ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2021,plain,
! [SV46: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK43_SY364 @ SV136 @ SV46 ) @ SV46 ) )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1987]) ).
thf(2022,plain,
! [SV46: $i,SV136: $i] :
( ( ( ( sK43_SY364 @ SV136 @ SV46 )
!= SV136 )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1987]) ).
thf(2023,plain,
! [SV136: $i,SV46: $i,SV146: $i] :
( ( ( ~ ( in @ SV146 @ SV46 ) )
= $true )
| ( ( SV146 != SV136 )
= $true )
| ( ( ~ ( ordinal @ SV136 ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2024,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $true )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2025,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 ) )
= $true )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2026,plain,
! [SV12: $i,SV124: $i,SV121: $i] :
( ( ( SV121 != SV124 )
= $false )
| ( ( in @ SV124 @ SV12 )
= $false )
| ( ( in @ SV121 @ SV12 )
= $false )
| ( ( in @ SV121 @ SV124 )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2027,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( in @ SV147 @ ( sK44_SY193 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY398: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY398 @ SV18 )
| ~ ( in @ SY398 @ SV18 ) )
| ( SV147
!= ( singleton @ SY398 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2028,plain,
! [SV147: $i,SV18: $i] :
( ( ( ~ ~ ! [SY399: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY399 @ SV18 )
| ~ ( in @ SY399 @ SV18 ) )
| ( SV147
!= ( singleton @ SY399 ) ) ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2029,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ ( sK45_SY193 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY400: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY400 @ SV18 )
| ~ ( in @ SY400 @ SV18 ) )
| ( SV148
!= ( singleton @ SY400 ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2030,plain,
! [SV148: $i,SV18: $i] :
( ( ( ~ ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY401 @ SV18 )
| ~ ( in @ SY401 @ SV18 ) )
| ( SV148
!= ( singleton @ SY401 ) ) ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2031,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 ) )
| ( SV143
!= ( singleton @ ( sK51_SY382 @ SV143 @ SV18 ) ) ) ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1998]) ).
thf(2032,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV153 @ SV18 )
| ~ ( in @ SV153 @ SV18 ) )
| ( SV143
!= ( singleton @ SV153 ) ) ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2033,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 ) ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2034,plain,
! [SV18: $i,SV140: $i] :
( ( ( SV140
!= ( singleton @ ( sK48_SY372 @ SV140 @ SV18 ) ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2035,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( ~ ~ ( ~ ( in @ SV151 @ SV18 )
| ~ ( in @ SV151 @ SV18 ) ) )
= $true )
| ( ( SV140
!= ( singleton @ SV151 ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2036,plain,
! [SV18: $i,SV134: $i] :
( ( ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2002]) ).
thf(2037,plain,
! [SV18: $i,SV134: $i] :
( ( ( in @ ( sK41_SY362 @ SV134 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2038,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( in @ SV144 @ SV18 )
= $false )
| ( ( ~ ( in @ SV144 @ SV18 ) )
= $true )
| ( ( SV134
!= ( singleton @ SV144 ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2039,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) )
| ~ ( in @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2040,plain,
! [SV115: $i,SV106: $i,SV34: $i,SV84: $i,SV133: $i] :
( ( ( SV133 = SV84 )
= $true )
| ( ( SV133 = SV34 )
= $true )
| ( ( ~ ( ( SV133 != SV106 ) ) )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2041,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 )
= $false )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2042,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2043,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2044,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2045,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ ( sK46_SY245 @ SV46 ) ) )
= $true )
| ( ( ~ ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY402 @ SV46 )
| ( SY402 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2046,plain,
! [SV149: $i,SV46: $i] :
( ( ( ~ ~ ! [SY403: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY403 @ SV46 )
| ( SY403 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2047,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ ( sK47_SY245 @ SV46 ) ) )
= $true )
| ( ( ~ ! [SY404: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY404 @ SV46 )
| ( SY404 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2048,plain,
! [SV150: $i,SV46: $i] :
( ( ( ~ ~ ! [SY405: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV46 )
| ( SY405 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2049,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK52_SY384 @ SV145 @ SV46 ) @ SV46 )
| ( ( sK52_SY384 @ SV145 @ SV46 )
!= SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2017]) ).
thf(2050,plain,
! [SV145: $i,SV46: $i,SV154: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV154 @ SV46 )
| ( SV154 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2051,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK49_SY374 @ SV142 @ SV46 ) @ SV46 )
| ( ( sK49_SY374 @ SV142 @ SV46 )
!= SV142 ) ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2052,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( ordinal @ SV142 ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2053,plain,
! [SV142: $i,SV46: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( in @ SV152 @ SV46 )
| ( SV152 != SV142 ) ) )
= $true )
| ( ( ~ ( ordinal @ SV142 ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2054,plain,
! [SV46: $i,SV136: $i] :
( ( ( in @ ( sK43_SY364 @ SV136 @ SV46 ) @ SV46 )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2055,plain,
! [SV46: $i,SV136: $i] :
( ( ( ( sK43_SY364 @ SV136 @ SV46 )
= SV136 )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $false )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2056,plain,
! [SV136: $i,SV46: $i,SV146: $i] :
( ( ( in @ SV146 @ SV46 )
= $false )
| ( ( SV146 != SV136 )
= $true )
| ( ( ~ ( ordinal @ SV136 ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2057,plain,
! [SV111: $i,SV58: $i,SV97: $i] :
( ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY335 @ SV97 @ SV58 @ SV111 ) @ SV97 )
= $true )
| ( ( SV111
= ( set_difference @ SV58 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2058,plain,
! [SV12: $i,SV124: $i,SV121: $i] :
( ( ( SV121 = SV124 )
= $true )
| ( ( in @ SV124 @ SV12 )
= $false )
| ( ( in @ SV121 @ SV12 )
= $false )
| ( ( in @ SV121 @ SV124 )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV121 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2059,plain,
! [SV18: $i,SV147: $i] :
( ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( ~ ! [SY398: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY398 @ SV18 )
| ~ ( in @ SY398 @ SV18 ) )
| ( SV147
!= ( singleton @ SY398 ) ) ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2060,plain,
! [SV147: $i,SV18: $i] :
( ( ( ~ ! [SY399: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY399 @ SV18 )
| ~ ( in @ SY399 @ SV18 ) )
| ( SV147
!= ( singleton @ SY399 ) ) ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2061,plain,
! [SV18: $i,SV148: $i] :
( ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ~ ! [SY400: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY400 @ SV18 )
| ~ ( in @ SY400 @ SV18 ) )
| ( SV148
!= ( singleton @ SY400 ) ) ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2062,plain,
! [SV148: $i,SV18: $i] :
( ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY401 @ SV18 )
| ~ ( in @ SY401 @ SV18 ) )
| ( SV148
!= ( singleton @ SY401 ) ) ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2063,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 ) )
| ( SV143
!= ( singleton @ ( sK51_SY382 @ SV143 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2064,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV153 @ SV18 )
| ~ ( in @ SV153 @ SV18 ) )
| ( SV143
!= ( singleton @ SV153 ) ) ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2065,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2066,plain,
! [SV18: $i,SV140: $i] :
( ( ( SV140
= ( singleton @ ( sK48_SY372 @ SV140 @ SV18 ) ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2067,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( ~ ( ~ ( in @ SV151 @ SV18 )
| ~ ( in @ SV151 @ SV18 ) ) )
= $false )
| ( ( SV140
!= ( singleton @ SV151 ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2068,plain,
! [SV134: $i,SV18: $i,SV144: $i] :
( ( ( in @ SV144 @ SV18 )
= $false )
| ( ( in @ SV144 @ SV18 )
= $false )
| ( ( SV134
!= ( singleton @ SV144 ) )
= $true )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2069,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) )
| ~ ( in @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2070,plain,
! [SV115: $i,SV84: $i,SV34: $i,SV106: $i,SV133: $i] :
( ( ( SV133 != SV106 )
= $false )
| ( ( SV133 = SV34 )
= $true )
| ( ( SV133 = SV84 )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2071,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2072,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2073,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) ) )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2074,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $false )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2075,plain,
! [SV46: $i,SV149: $i] :
( ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ~ ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY402 @ SV46 )
| ( SY402 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2076,plain,
! [SV149: $i,SV46: $i] :
( ( ( ~ ! [SY403: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY403 @ SV46 )
| ( SY403 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2077,plain,
! [SV46: $i,SV150: $i] :
( ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ~ ! [SY404: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY404 @ SV46 )
| ( SY404 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2078,plain,
! [SV150: $i,SV46: $i] :
( ( ( ~ ! [SY405: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV46 )
| ( SY405 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2079,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK52_SY384 @ SV145 @ SV46 ) @ SV46 )
| ( ( sK52_SY384 @ SV145 @ SV46 )
!= SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2080,plain,
! [SV145: $i,SV46: $i,SV154: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV154 @ SV46 )
| ( SV154 != SV145 ) )
| ~ ( ordinal @ SV145 ) ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2081,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_SY374 @ SV142 @ SV46 ) @ SV46 )
| ( ( sK49_SY374 @ SV142 @ SV46 )
!= SV142 ) ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2051]) ).
thf(2082,plain,
! [SV46: $i,SV142: $i] :
( ( ( ordinal @ SV142 )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2083,plain,
! [SV142: $i,SV46: $i,SV152: $i] :
( ( ( ~ ( ~ ( in @ SV152 @ SV46 )
| ( SV152 != SV142 ) ) )
= $false )
| ( ( ~ ( ordinal @ SV142 ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2084,plain,
! [SV46: $i,SV136: $i,SV146: $i] :
( ( ( SV146 = SV136 )
= $false )
| ( ( in @ SV146 @ SV46 )
= $false )
| ( ( ~ ( ordinal @ SV136 ) )
= $true )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2085,plain,
! [SV12: $i,SV121: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV121 ) )
= $false )
| ( ( in @ SV121 @ SV124 )
= $true )
| ( ( in @ SV121 @ SV12 )
= $false )
| ( ( in @ SV124 @ SV12 )
= $false )
| ( ( SV121 = SV124 )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2086,plain,
! [SV147: $i,SV18: $i] :
( ( ( ! [SY398: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY398 @ SV18 )
| ~ ( in @ SY398 @ SV18 ) )
| ( SV147
!= ( singleton @ SY398 ) ) ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2087,plain,
! [SV147: $i,SV18: $i] :
( ( ( ! [SY399: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY399 @ SV18 )
| ~ ( in @ SY399 @ SV18 ) )
| ( SV147
!= ( singleton @ SY399 ) ) ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2088,plain,
! [SV148: $i,SV18: $i] :
( ( ( ! [SY400: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY400 @ SV18 )
| ~ ( in @ SY400 @ SV18 ) )
| ( SV148
!= ( singleton @ SY400 ) ) ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2089,plain,
! [SV148: $i,SV18: $i] :
( ( ( ! [SY401: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY401 @ SV18 )
| ~ ( in @ SY401 @ SV18 ) )
| ( SV148
!= ( singleton @ SY401 ) ) ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2090,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 ) )
| ( SV143
!= ( singleton @ ( sK51_SY382 @ SV143 @ SV18 ) ) ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2091,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ( in @ SV153 @ SV18 )
| ~ ( in @ SV153 @ SV18 ) )
| ( SV143
!= ( singleton @ SV153 ) ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2092,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2093,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV18 )
| ~ ( in @ SV151 @ SV18 ) )
= $true )
| ( ( SV140
!= ( singleton @ SV151 ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2094,plain,
! [SV18: $i,SV144: $i,SV134: $i] :
( ( ( SV134
= ( singleton @ SV144 ) )
= $false )
| ( ( in @ SV144 @ SV18 )
= $false )
| ( ( in @ SV144 @ SV18 )
= $false )
| ( ( in @ SV134 @ ( sK26_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( sK15_SY345 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2095,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2096,plain,
! [SV32: $i,SV82: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2097,plain,
! [SV115: $i,SV84: $i,SV34: $i,SV106: $i,SV133: $i] :
( ( ( SV133 = SV106 )
= $true )
| ( ( SV133 = SV34 )
= $true )
| ( ( SV133 = SV84 )
= $true )
| ( ( in @ SV133 @ SV115 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2098,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2099,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2100,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2101,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2102,plain,
! [SV149: $i,SV46: $i] :
( ( ( ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY402 @ SV46 )
| ( SY402 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2103,plain,
! [SV149: $i,SV46: $i] :
( ( ( ! [SY403: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY403 @ SV46 )
| ( SY403 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2104,plain,
! [SV150: $i,SV46: $i] :
( ( ( ! [SY404: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY404 @ SV46 )
| ( SY404 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2105,plain,
! [SV150: $i,SV46: $i] :
( ( ( ! [SY405: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV46 )
| ( SY405 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2106,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK52_SY384 @ SV145 @ SV46 ) @ SV46 )
| ( ( sK52_SY384 @ SV145 @ SV46 )
!= SV145 ) )
| ~ ( ordinal @ SV145 ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2107,plain,
! [SV145: $i,SV46: $i,SV154: $i] :
( ( ( ~ ~ ( ~ ( in @ SV154 @ SV46 )
| ( SV154 != SV145 ) )
| ~ ( ordinal @ SV145 ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2108,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK49_SY374 @ SV142 @ SV46 ) @ SV46 )
| ( ( sK49_SY374 @ SV142 @ SV46 )
!= SV142 ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2109,plain,
! [SV142: $i,SV46: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV46 )
| ( SV152 != SV142 ) )
= $true )
| ( ( ~ ( ordinal @ SV142 ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2110,plain,
! [SV46: $i,SV146: $i,SV136: $i] :
( ( ( ordinal @ SV136 )
= $false )
| ( ( in @ SV146 @ SV46 )
= $false )
| ( ( SV146 = SV136 )
= $false )
| ( ( in @ SV136 @ ( sK27_SY245 @ SV46 ) )
= $true )
| ( ( ( sK14_SY342 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2111,plain,
! [SV12: $i,SV121: $i,SV124: $i] :
( ( ( in @ SV124 @ SV121 )
= $true )
| ( ( in @ SV121 @ SV124 )
= $true )
| ( ( in @ SV121 @ SV12 )
= $false )
| ( ( in @ SV124 @ SV12 )
= $false )
| ( ( SV121 = SV124 )
= $true )
| ( ( epsilon_connected @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2085]) ).
thf(2112,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 ) )
| ( SV147
!= ( singleton @ ( sK53_SY398 @ SV147 @ SV18 ) ) ) ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2086]) ).
thf(2113,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV155 @ SV18 )
| ~ ( in @ SV155 @ SV18 ) )
| ( SV147
!= ( singleton @ SV155 ) ) ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2114,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 ) )
| ( SV148
!= ( singleton @ ( sK54_SY400 @ SV148 @ SV18 ) ) ) ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2088]) ).
thf(2115,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV156 @ SV18 )
| ~ ( in @ SV156 @ SV18 ) )
| ( SV148
!= ( singleton @ SV156 ) ) ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2116,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 ) ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2117,plain,
! [SV18: $i,SV143: $i] :
( ( ( SV143
!= ( singleton @ ( sK51_SY382 @ SV143 @ SV18 ) ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2118,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ( in @ SV153 @ SV18 )
| ~ ( in @ SV153 @ SV18 ) ) )
= $true )
| ( ( SV143
!= ( singleton @ SV153 ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2119,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2120,plain,
! [SV18: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2121,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV151 @ SV18 ) )
= $true )
| ( ( SV140
!= ( singleton @ SV151 ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2122,plain,
! [SV139: $i,SV82: $i,SV32: $i] :
( ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) )
= $true )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2123,plain,
! [SV32: $i,SV82: $i,SV139: $i] :
( ( ( in @ ( sK50_SY355 @ SV139 @ SV82 @ SV32 ) @ SV32 )
= $true )
| ( ( in @ ( sK23_SY295 @ SV32 @ SV82 ) @ SV139 )
= $false )
| ( ( in @ SV139 @ SV32 )
= $false )
| ( ( SV82
= ( union @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2124,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2125,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2126,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2127,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2128,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK55_SY402 @ SV149 @ SV46 ) @ SV46 )
| ( ( sK55_SY402 @ SV149 @ SV46 )
!= SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2102]) ).
thf(2129,plain,
! [SV149: $i,SV46: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV157 @ SV46 )
| ( SV157 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2130,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK56_SY404 @ SV150 @ SV46 ) @ SV46 )
| ( ( sK56_SY404 @ SV150 @ SV46 )
!= SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2104]) ).
thf(2131,plain,
! [SV150: $i,SV46: $i,SV158: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV158 @ SV46 )
| ( SV158 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2132,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK52_SY384 @ SV145 @ SV46 ) @ SV46 )
| ( ( sK52_SY384 @ SV145 @ SV46 )
!= SV145 ) ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2106]) ).
thf(2133,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( ordinal @ SV145 ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2106]) ).
thf(2134,plain,
! [SV145: $i,SV46: $i,SV154: $i] :
( ( ( ~ ~ ( ~ ( in @ SV154 @ SV46 )
| ( SV154 != SV145 ) ) )
= $true )
| ( ( ~ ( ordinal @ SV145 ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2107]) ).
thf(2135,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK49_SY374 @ SV142 @ SV46 ) @ SV46 ) )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2108]) ).
thf(2136,plain,
! [SV46: $i,SV142: $i] :
( ( ( ( sK49_SY374 @ SV142 @ SV46 )
!= SV142 )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2108]) ).
thf(2137,plain,
! [SV142: $i,SV46: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV46 ) )
= $true )
| ( ( SV152 != SV142 )
= $true )
| ( ( ~ ( ordinal @ SV142 ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2138,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 ) )
| ( SV147
!= ( singleton @ ( sK53_SY398 @ SV147 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2139,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV155 @ SV18 )
| ~ ( in @ SV155 @ SV18 ) )
| ( SV147
!= ( singleton @ SV155 ) ) ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2140,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 ) )
| ( SV148
!= ( singleton @ ( sK54_SY400 @ SV148 @ SV18 ) ) ) ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2141,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV156 @ SV18 )
| ~ ( in @ SV156 @ SV18 ) )
| ( SV148
!= ( singleton @ SV156 ) ) ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2142,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2116]) ).
thf(2143,plain,
! [SV18: $i,SV143: $i] :
( ( ( SV143
= ( singleton @ ( sK51_SY382 @ SV143 @ SV18 ) ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2144,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( ~ ( ~ ( in @ SV153 @ SV18 )
| ~ ( in @ SV153 @ SV18 ) ) )
= $false )
| ( ( SV143
!= ( singleton @ SV153 ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2145,plain,
! [SV18: $i,SV140: $i] :
( ( ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2119]) ).
thf(2146,plain,
! [SV18: $i,SV140: $i] :
( ( ( in @ ( sK48_SY372 @ SV140 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $false )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2147,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( in @ SV151 @ SV18 )
= $false )
| ( ( ~ ( in @ SV151 @ SV18 ) )
= $true )
| ( ( SV140
!= ( singleton @ SV151 ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2148,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2149,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $false )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2150,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) ) )
= $false )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2151,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 )
= $false )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2152,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK55_SY402 @ SV149 @ SV46 ) @ SV46 )
| ( ( sK55_SY402 @ SV149 @ SV46 )
!= SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2128]) ).
thf(2153,plain,
! [SV149: $i,SV46: $i,SV157: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV157 @ SV46 )
| ( SV157 != SV149 ) )
| ~ ( ordinal @ SV149 ) ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2154,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK56_SY404 @ SV150 @ SV46 ) @ SV46 )
| ( ( sK56_SY404 @ SV150 @ SV46 )
!= SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2130]) ).
thf(2155,plain,
! [SV150: $i,SV46: $i,SV158: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV158 @ SV46 )
| ( SV158 != SV150 ) )
| ~ ( ordinal @ SV150 ) ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2156,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_SY384 @ SV145 @ SV46 ) @ SV46 )
| ( ( sK52_SY384 @ SV145 @ SV46 )
!= SV145 ) ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2132]) ).
thf(2157,plain,
! [SV46: $i,SV145: $i] :
( ( ( ordinal @ SV145 )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2133]) ).
thf(2158,plain,
! [SV145: $i,SV46: $i,SV154: $i] :
( ( ( ~ ( ~ ( in @ SV154 @ SV46 )
| ( SV154 != SV145 ) ) )
= $false )
| ( ( ~ ( ordinal @ SV145 ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2159,plain,
! [SV46: $i,SV142: $i] :
( ( ( in @ ( sK49_SY374 @ SV142 @ SV46 ) @ SV46 )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2135]) ).
thf(2160,plain,
! [SV46: $i,SV142: $i] :
( ( ( ( sK49_SY374 @ SV142 @ SV46 )
= SV142 )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2161,plain,
! [SV142: $i,SV46: $i,SV152: $i] :
( ( ( in @ SV152 @ SV46 )
= $false )
| ( ( SV152 != SV142 )
= $true )
| ( ( ~ ( ordinal @ SV142 ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2162,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 ) )
| ( SV147
!= ( singleton @ ( sK53_SY398 @ SV147 @ SV18 ) ) ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2163,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( ~ ~ ( ~ ( in @ SV155 @ SV18 )
| ~ ( in @ SV155 @ SV18 ) )
| ( SV147
!= ( singleton @ SV155 ) ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2164,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 ) )
| ( SV148
!= ( singleton @ ( sK54_SY400 @ SV148 @ SV18 ) ) ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2165,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( ~ ~ ( ~ ( in @ SV156 @ SV18 )
| ~ ( in @ SV156 @ SV18 ) )
| ( SV148
!= ( singleton @ SV156 ) ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2166,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2167,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV18 )
| ~ ( in @ SV153 @ SV18 ) )
= $true )
| ( ( SV143
!= ( singleton @ SV153 ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2168,plain,
! [SV140: $i,SV18: $i,SV151: $i] :
( ( ( in @ SV151 @ SV18 )
= $false )
| ( ( in @ SV151 @ SV18 )
= $false )
| ( ( SV140
!= ( singleton @ SV151 ) )
= $true )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2169,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( in @ ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 ) @ SV115 )
= $true )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2170,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2171,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) )
| ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2172,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2173,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK55_SY402 @ SV149 @ SV46 ) @ SV46 )
| ( ( sK55_SY402 @ SV149 @ SV46 )
!= SV149 ) )
| ~ ( ordinal @ SV149 ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2174,plain,
! [SV149: $i,SV46: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ( in @ SV157 @ SV46 )
| ( SV157 != SV149 ) )
| ~ ( ordinal @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2153]) ).
thf(2175,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK56_SY404 @ SV150 @ SV46 ) @ SV46 )
| ( ( sK56_SY404 @ SV150 @ SV46 )
!= SV150 ) )
| ~ ( ordinal @ SV150 ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2176,plain,
! [SV150: $i,SV46: $i,SV158: $i] :
( ( ( ~ ~ ( ~ ( in @ SV158 @ SV46 )
| ( SV158 != SV150 ) )
| ~ ( ordinal @ SV150 ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2155]) ).
thf(2177,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( in @ ( sK52_SY384 @ SV145 @ SV46 ) @ SV46 )
| ( ( sK52_SY384 @ SV145 @ SV46 )
!= SV145 ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2178,plain,
! [SV145: $i,SV46: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ SV46 )
| ( SV154 != SV145 ) )
= $true )
| ( ( ~ ( ordinal @ SV145 ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2158]) ).
thf(2179,plain,
! [SV46: $i,SV142: $i,SV152: $i] :
( ( ( SV152 = SV142 )
= $false )
| ( ( in @ SV152 @ SV46 )
= $false )
| ( ( ~ ( ordinal @ SV142 ) )
= $true )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2180,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 ) ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2162]) ).
thf(2181,plain,
! [SV18: $i,SV147: $i] :
( ( ( SV147
!= ( singleton @ ( sK53_SY398 @ SV147 @ SV18 ) ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2162]) ).
thf(2182,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( ~ ~ ( ~ ( in @ SV155 @ SV18 )
| ~ ( in @ SV155 @ SV18 ) ) )
= $true )
| ( ( SV147
!= ( singleton @ SV155 ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2183,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 ) ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2184,plain,
! [SV18: $i,SV148: $i] :
( ( ( SV148
!= ( singleton @ ( sK54_SY400 @ SV148 @ SV18 ) ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2185,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( ~ ~ ( ~ ( in @ SV156 @ SV18 )
| ~ ( in @ SV156 @ SV18 ) ) )
= $true )
| ( ( SV148
!= ( singleton @ SV156 ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2186,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2166]) ).
thf(2187,plain,
! [SV18: $i,SV143: $i] :
( ( ( ~ ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2166]) ).
thf(2188,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV153 @ SV18 ) )
= $true )
| ( ( SV143
!= ( singleton @ SV153 ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2189,plain,
! [SV18: $i,SV151: $i,SV140: $i] :
( ( ( SV140
= ( singleton @ SV151 ) )
= $false )
| ( ( in @ SV151 @ SV18 )
= $false )
| ( ( in @ SV151 @ SV18 )
= $false )
| ( ( in @ SV140 @ ( sK35_SY193 @ SV18 ) )
= $true )
| ( ( ( sK15_SY345 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2190,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2191,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2192,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2193,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK55_SY402 @ SV149 @ SV46 ) @ SV46 )
| ( ( sK55_SY402 @ SV149 @ SV46 )
!= SV149 ) ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2194,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( ordinal @ SV149 ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2195,plain,
! [SV149: $i,SV46: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ( in @ SV157 @ SV46 )
| ( SV157 != SV149 ) ) )
= $true )
| ( ( ~ ( ordinal @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2196,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK56_SY404 @ SV150 @ SV46 ) @ SV46 )
| ( ( sK56_SY404 @ SV150 @ SV46 )
!= SV150 ) ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2175]) ).
thf(2197,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( ordinal @ SV150 ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2175]) ).
thf(2198,plain,
! [SV150: $i,SV46: $i,SV158: $i] :
( ( ( ~ ~ ( ~ ( in @ SV158 @ SV46 )
| ( SV158 != SV150 ) ) )
= $true )
| ( ( ~ ( ordinal @ SV150 ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2199,plain,
! [SV46: $i,SV145: $i] :
( ( ( ~ ( in @ ( sK52_SY384 @ SV145 @ SV46 ) @ SV46 ) )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2200,plain,
! [SV46: $i,SV145: $i] :
( ( ( ( sK52_SY384 @ SV145 @ SV46 )
!= SV145 )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2201,plain,
! [SV145: $i,SV46: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ SV46 ) )
= $true )
| ( ( SV154 != SV145 )
= $true )
| ( ( ~ ( ordinal @ SV145 ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2202,plain,
! [SV46: $i,SV152: $i,SV142: $i] :
( ( ( ordinal @ SV142 )
= $false )
| ( ( in @ SV152 @ SV46 )
= $false )
| ( ( SV152 = SV142 )
= $false )
| ( ( in @ SV142 @ ( sK37_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2203,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2180]) ).
thf(2204,plain,
! [SV18: $i,SV147: $i] :
( ( ( SV147
= ( singleton @ ( sK53_SY398 @ SV147 @ SV18 ) ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2181]) ).
thf(2205,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( ~ ( ~ ( in @ SV155 @ SV18 )
| ~ ( in @ SV155 @ SV18 ) ) )
= $false )
| ( ( SV147
!= ( singleton @ SV155 ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2206,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2207,plain,
! [SV18: $i,SV148: $i] :
( ( ( SV148
= ( singleton @ ( sK54_SY400 @ SV148 @ SV18 ) ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2184]) ).
thf(2208,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( ~ ( ~ ( in @ SV156 @ SV18 )
| ~ ( in @ SV156 @ SV18 ) ) )
= $false )
| ( ( SV148
!= ( singleton @ SV156 ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2209,plain,
! [SV18: $i,SV143: $i] :
( ( ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2186]) ).
thf(2210,plain,
! [SV18: $i,SV143: $i] :
( ( ( in @ ( sK51_SY382 @ SV143 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2187]) ).
thf(2211,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( in @ SV153 @ SV18 )
= $false )
| ( ( ~ ( in @ SV153 @ SV18 ) )
= $true )
| ( ( SV143
!= ( singleton @ SV153 ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2212,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 )
= $false )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2213,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV34 )
= $false )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2214,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2192]) ).
thf(2215,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( ~ ( in @ ( sK55_SY402 @ SV149 @ SV46 ) @ SV46 )
| ( ( sK55_SY402 @ SV149 @ SV46 )
!= SV149 ) ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2193]) ).
thf(2216,plain,
! [SV46: $i,SV149: $i] :
( ( ( ordinal @ SV149 )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2217,plain,
! [SV149: $i,SV46: $i,SV157: $i] :
( ( ( ~ ( ~ ( in @ SV157 @ SV46 )
| ( SV157 != SV149 ) ) )
= $false )
| ( ( ~ ( ordinal @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2218,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_SY404 @ SV150 @ SV46 ) @ SV46 )
| ( ( sK56_SY404 @ SV150 @ SV46 )
!= SV150 ) ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2196]) ).
thf(2219,plain,
! [SV46: $i,SV150: $i] :
( ( ( ordinal @ SV150 )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2220,plain,
! [SV150: $i,SV46: $i,SV158: $i] :
( ( ( ~ ( ~ ( in @ SV158 @ SV46 )
| ( SV158 != SV150 ) ) )
= $false )
| ( ( ~ ( ordinal @ SV150 ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2221,plain,
! [SV46: $i,SV145: $i] :
( ( ( in @ ( sK52_SY384 @ SV145 @ SV46 ) @ SV46 )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2199]) ).
thf(2222,plain,
! [SV46: $i,SV145: $i] :
( ( ( ( sK52_SY384 @ SV145 @ SV46 )
= SV145 )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2200]) ).
thf(2223,plain,
! [SV145: $i,SV46: $i,SV154: $i] :
( ( ( in @ SV154 @ SV46 )
= $false )
| ( ( SV154 != SV145 )
= $true )
| ( ( ~ ( ordinal @ SV145 ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2224,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2225,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ SV18 )
| ~ ( in @ SV155 @ SV18 ) )
= $true )
| ( ( SV147
!= ( singleton @ SV155 ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2226,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 )
| ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2227,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( ~ ( in @ SV156 @ SV18 )
| ~ ( in @ SV156 @ SV18 ) )
= $true )
| ( ( SV148
!= ( singleton @ SV156 ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2208]) ).
thf(2228,plain,
! [SV143: $i,SV18: $i,SV153: $i] :
( ( ( in @ SV153 @ SV18 )
= $false )
| ( ( in @ SV153 @ SV18 )
= $false )
| ( ( SV143
!= ( singleton @ SV153 ) )
= $true )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2229,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2230,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 ) ) )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2231,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2232,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( in @ ( sK55_SY402 @ SV149 @ SV46 ) @ SV46 )
| ( ( sK55_SY402 @ SV149 @ SV46 )
!= SV149 ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2233,plain,
! [SV149: $i,SV46: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ SV46 )
| ( SV157 != SV149 ) )
= $true )
| ( ( ~ ( ordinal @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2234,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( in @ ( sK56_SY404 @ SV150 @ SV46 ) @ SV46 )
| ( ( sK56_SY404 @ SV150 @ SV46 )
!= SV150 ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2235,plain,
! [SV150: $i,SV46: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ SV46 )
| ( SV158 != SV150 ) )
= $true )
| ( ( ~ ( ordinal @ SV150 ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2236,plain,
! [SV46: $i,SV145: $i,SV154: $i] :
( ( ( SV154 = SV145 )
= $false )
| ( ( in @ SV154 @ SV46 )
= $false )
| ( ( ~ ( ordinal @ SV145 ) )
= $true )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2237,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2238,plain,
! [SV18: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2239,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV155 @ SV18 ) )
= $true )
| ( ( SV147
!= ( singleton @ SV155 ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2240,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2226]) ).
thf(2241,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2226]) ).
thf(2242,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( ~ ( in @ SV156 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV156 @ SV18 ) )
= $true )
| ( ( SV148
!= ( singleton @ SV156 ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2243,plain,
! [SV18: $i,SV153: $i,SV143: $i] :
( ( ( SV143
= ( singleton @ SV153 ) )
= $false )
| ( ( in @ SV153 @ SV18 )
= $false )
| ( ( in @ SV153 @ SV18 )
= $false )
| ( ( in @ SV143 @ ( sK39_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2244,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2245,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV84 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2246,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2231]) ).
thf(2247,plain,
! [SV46: $i,SV149: $i] :
( ( ( ~ ( in @ ( sK55_SY402 @ SV149 @ SV46 ) @ SV46 ) )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2232]) ).
thf(2248,plain,
! [SV46: $i,SV149: $i] :
( ( ( ( sK55_SY402 @ SV149 @ SV46 )
!= SV149 )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2232]) ).
thf(2249,plain,
! [SV149: $i,SV46: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ SV46 ) )
= $true )
| ( ( SV157 != SV149 )
= $true )
| ( ( ~ ( ordinal @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2250,plain,
! [SV46: $i,SV150: $i] :
( ( ( ~ ( in @ ( sK56_SY404 @ SV150 @ SV46 ) @ SV46 ) )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2251,plain,
! [SV46: $i,SV150: $i] :
( ( ( ( sK56_SY404 @ SV150 @ SV46 )
!= SV150 )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2252,plain,
! [SV150: $i,SV46: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ SV46 ) )
= $true )
| ( ( SV158 != SV150 )
= $true )
| ( ( ~ ( ordinal @ SV150 ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2253,plain,
! [SV46: $i,SV154: $i,SV145: $i] :
( ( ( ordinal @ SV145 )
= $false )
| ( ( in @ SV154 @ SV46 )
= $false )
| ( ( SV154 = SV145 )
= $false )
| ( ( in @ SV145 @ ( sK40_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK17_SY348 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2254,plain,
! [SV18: $i,SV147: $i] :
( ( ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2237]) ).
thf(2255,plain,
! [SV18: $i,SV147: $i] :
( ( ( in @ ( sK53_SY398 @ SV147 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2238]) ).
thf(2256,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( in @ SV155 @ SV18 )
= $false )
| ( ( ~ ( in @ SV155 @ SV18 ) )
= $true )
| ( ( SV147
!= ( singleton @ SV155 ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2257,plain,
! [SV18: $i,SV148: $i] :
( ( ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2258,plain,
! [SV18: $i,SV148: $i] :
( ( ( in @ ( sK54_SY400 @ SV148 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $false )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2259,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( in @ SV156 @ SV18 )
= $false )
| ( ( ~ ( in @ SV156 @ SV18 ) )
= $true )
| ( ( SV148
!= ( singleton @ SV156 ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2260,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2261,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ~ ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 ) ) )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2262,plain,
! [SV46: $i,SV149: $i] :
( ( ( in @ ( sK55_SY402 @ SV149 @ SV46 ) @ SV46 )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2263,plain,
! [SV46: $i,SV149: $i] :
( ( ( ( sK55_SY402 @ SV149 @ SV46 )
= SV149 )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $false )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2264,plain,
! [SV149: $i,SV46: $i,SV157: $i] :
( ( ( in @ SV157 @ SV46 )
= $false )
| ( ( SV157 != SV149 )
= $true )
| ( ( ~ ( ordinal @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2265,plain,
! [SV46: $i,SV150: $i] :
( ( ( in @ ( sK56_SY404 @ SV150 @ SV46 ) @ SV46 )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2266,plain,
! [SV46: $i,SV150: $i] :
( ( ( ( sK56_SY404 @ SV150 @ SV46 )
= SV150 )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $false )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2267,plain,
! [SV150: $i,SV46: $i,SV158: $i] :
( ( ( in @ SV158 @ SV46 )
= $false )
| ( ( SV158 != SV150 )
= $true )
| ( ( ~ ( ordinal @ SV150 ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2268,plain,
! [SV147: $i,SV18: $i,SV155: $i] :
( ( ( in @ SV155 @ SV18 )
= $false )
| ( ( in @ SV155 @ SV18 )
= $false )
| ( ( SV147
!= ( singleton @ SV155 ) )
= $true )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2269,plain,
! [SV148: $i,SV18: $i,SV156: $i] :
( ( ( in @ SV156 @ SV18 )
= $false )
| ( ( in @ SV156 @ SV18 )
= $false )
| ( ( SV148
!= ( singleton @ SV156 ) )
= $true )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2270,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2271,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
!= SV106 )
= $false )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2272,plain,
! [SV46: $i,SV149: $i,SV157: $i] :
( ( ( SV157 = SV149 )
= $false )
| ( ( in @ SV157 @ SV46 )
= $false )
| ( ( ~ ( ordinal @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2273,plain,
! [SV46: $i,SV150: $i,SV158: $i] :
( ( ( SV158 = SV150 )
= $false )
| ( ( in @ SV158 @ SV46 )
= $false )
| ( ( ~ ( ordinal @ SV150 ) )
= $true )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2274,plain,
! [SV18: $i,SV155: $i,SV147: $i] :
( ( ( SV147
= ( singleton @ SV155 ) )
= $false )
| ( ( in @ SV155 @ SV18 )
= $false )
| ( ( in @ SV155 @ SV18 )
= $false )
| ( ( in @ SV147 @ ( sK44_SY193 @ SV18 ) )
= $true )
| ( ( in @ ( sK8_SY190 @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2275,plain,
! [SV18: $i,SV156: $i,SV148: $i] :
( ( ( SV148
= ( singleton @ SV156 ) )
= $false )
| ( ( in @ SV156 @ SV18 )
= $false )
| ( ( in @ SV156 @ SV18 )
= $false )
| ( ( in @ SV148 @ ( sK45_SY193 @ SV18 ) )
= $true )
| ( ( ( sK12_SY338 @ SV18 )
= ( singleton @ ( sK8_SY190 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2276,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2270]) ).
thf(2277,plain,
! [SV115: $i,SV34: $i,SV84: $i,SV106: $i] :
( ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV106 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV34 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $true )
| ( ( ( sK33_SY341 @ SV106 @ SV84 @ SV34 @ SV115 )
= SV84 )
= $false )
| ( ( SV115
= ( unordered_triple @ SV34 @ SV84 @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2278,plain,
! [SV46: $i,SV157: $i,SV149: $i] :
( ( ( ordinal @ SV149 )
= $false )
| ( ( in @ SV157 @ SV46 )
= $false )
| ( ( SV157 = SV149 )
= $false )
| ( ( in @ SV149 @ ( sK46_SY245 @ SV46 ) )
= $true )
| ( ( ( sK9_SX1 @ SV46 )
= ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2279,plain,
! [SV46: $i,SV158: $i,SV150: $i] :
( ( ( ordinal @ SV150 )
= $false )
| ( ( in @ SV158 @ SV46 )
= $false )
| ( ( SV158 = SV150 )
= $false )
| ( ( in @ SV150 @ ( sK47_SY245 @ SV46 ) )
= $true )
| ( ( ordinal @ ( sK14_SY342 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2280,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[654,2279,2278,2277,2276,2275,2274,2266,2265,2263,2262,2258,2257,2255,2254,2253,2246,2243,2222,2221,2219,2216,2210,2209,2207,2204,2202,2189,2169,2160,2159,2157,2146,2145,2143,2123,2122,2111,2110,2097,2094,2082,2066,2057,2055,2054,2037,2036,2024,2011,2009,1990,1989,1974,1973,1955,1947,1938,1937,1935,1925,1914,1913,1911,1903,1890,1889,1887,1884,1882,1881,1872,1869,1868,1863,1858,1843,1842,1818,1817,1809,1806,1805,1804,1800,1797,1796,1795,1794,1786,1760,1752,1748,1747,1730,1722,1710,1709,1707,1705,1702,1697,1695,1690,1688,1686,1666,1665,1658,1654,1653,1648,1647,1646,1641,1640,1631,1630,1629,1621,1614,1602,1597,1585,1578,1577,1565,1545,1538,1537,1526,1525,1507,1506,1489,1486,1483,1482,1481,1462,1460,1439,1428,1427,1426,1424,1423,1419,1394,1372,1342,1326,1320,1319,1297,1287,1286,1278,1277,1268,1267,1235,1234,1203,1191,1190,1181,1176,1175,1174,1172,1140,1125,1121,1116,1114,1111,1083,1047,1028,1025,1024,1020,998,997,995,988,985,974,970,969,958,957,946,943,928,925,845,783,781,780,779,715,693,692,691,689,686,680,679,678,677,676,674,673,672,671,669,667,666,665,664,663,662,661,659,658,657,656,655]) ).
thf(2281,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU321+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:09:30 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.81/3.52 ....
% 19.81/3.52
% 19.81/3.52 No.of.Axioms: 92
% 19.81/3.52
% 19.81/3.52 Length.of.Defs: 0
% 19.81/3.52
% 19.81/3.52 Contains.Choice.Funs: false
% 19.81/3.52 ...........................................................
% 19.81/3.52
% 19.81/3.52 ********************************
% 19.81/3.52 * All subproblems solved! *
% 19.81/3.52 ********************************
% 19.81/3.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:94,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:2280,loop_count:0,foatp_calls:1,translation:fof_full)
% 19.81/3.52
% 19.81/3.52 %**** Beginning of derivation protocol ****
% 19.81/3.52 % SZS output start CNFRefutation
% See solution above
% 19.81/3.55
% 19.81/3.55 %**** End of derivation protocol ****
% 19.81/3.55 %**** no. of clauses in derivation: 1851 ****
% 19.81/3.55 %**** clause counter: 2280 ****
% 19.81/3.55
% 19.81/3.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:94,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:2280,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------