TSTP Solution File: SEU295+2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU295+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:09:44 EDT 2022
% Result : Theorem 1.56s 1.98s
% Output : CNFRefutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 307
% Syntax : Number of formulae : 3123 (1247 unt; 145 typ; 0 def)
% Number of atoms : 26920 (9483 equ; 0 cnn)
% Maximal formula atoms : 20 ( 9 avg)
% Number of connectives : 58210 (10153 ~;9678 |; 525 &;37521 @)
% ( 96 <=>; 237 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 228 ( 228 >; 0 *; 0 +; 0 <<)
% Number of symbols : 148 ( 145 usr; 17 con; 0-5 aty)
% Number of variables : 8977 ( 0 ^8921 !; 56 ?;8977 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $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_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_connected,type,
connected: $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_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_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $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_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_SY386,type,
sK10_SY386: $i ).
thf(tp_sK11_SY388,type,
sK11_SY388: $i ).
thf(tp_sK12_REN,type,
sK12_REN: $o ).
thf(tp_sK13_B,type,
sK13_B: $i > $i ).
thf(tp_sK14_D,type,
sK14_D: $i > $i > $i ).
thf(tp_sK15_B,type,
sK15_B: $i > $i ).
thf(tp_sK16_SY393,type,
sK16_SY393: $i > $i ).
thf(tp_sK17_SY395,type,
sK17_SY395: $i > $i ).
thf(tp_sK18_C,type,
sK18_C: $i > $i > $i ).
thf(tp_sK19_E,type,
sK19_E: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY404,type,
sK20_SY404: $i > $i > $i > $i ).
thf(tp_sK21_K,type,
sK21_K: $i > $i > $i > $i > $i > $i ).
thf(tp_sK22_C,type,
sK22_C: $i > $i > $i ).
thf(tp_sK23_SY407,type,
sK23_SY407: $i > $i > $i ).
thf(tp_sK24_SY413,type,
sK24_SY413: $i > $i > $i ).
thf(tp_sK25_SY420,type,
sK25_SY420: $i > $i > $i ).
thf(tp_sK26_SY414,type,
sK26_SY414: $i > $i > $i ).
thf(tp_sK27_A,type,
sK27_A: $i ).
thf(tp_sK28_B,type,
sK28_B: $i > $i ).
thf(tp_sK29_A,type,
sK29_A: $i ).
thf(tp_sK2_SY373,type,
sK2_SY373: $i ).
thf(tp_sK30_B,type,
sK30_B: $i > $i ).
thf(tp_sK31_A,type,
sK31_A: $i ).
thf(tp_sK32_A,type,
sK32_A: $i ).
thf(tp_sK33_A,type,
sK33_A: $i ).
thf(tp_sK34_B,type,
sK34_B: $i > $i ).
thf(tp_sK35_A,type,
sK35_A: $i ).
thf(tp_sK36_A,type,
sK36_A: $i ).
thf(tp_sK37_B,type,
sK37_B: $i > $i ).
thf(tp_sK38_D,type,
sK38_D: $i > $i > $i > $i ).
thf(tp_sK39_D,type,
sK39_D: $i > $i > $i > $i ).
thf(tp_sK3_B,type,
sK3_B: $i > $i ).
thf(tp_sK40_C,type,
sK40_C: $i > $i > $i ).
thf(tp_sK41_SY425,type,
sK41_SY425: $i > $i > $i ).
thf(tp_sK42_C,type,
sK42_C: $i > $i > $i ).
thf(tp_sK43_C,type,
sK43_C: $i > $i > $i ).
thf(tp_sK44_SY426,type,
sK44_SY426: $i > $i > $i ).
thf(tp_sK45_B,type,
sK45_B: $i > $i ).
thf(tp_sK46_SY427,type,
sK46_SY427: $i > $i ).
thf(tp_sK47_D,type,
sK47_D: $i > $i > $i > $i ).
thf(tp_sK48_D,type,
sK48_D: $i > $i > $i > $i ).
thf(tp_sK49_C,type,
sK49_C: $i > $i > $i ).
thf(tp_sK4_SY376,type,
sK4_SY376: $i > $i > $i ).
thf(tp_sK50_SY428,type,
sK50_SY428: $i > $i > $i ).
thf(tp_sK51_B,type,
sK51_B: $i > $i ).
thf(tp_sK52_C,type,
sK52_C: $i > $i > $i ).
thf(tp_sK53_B,type,
sK53_B: $i > $i ).
thf(tp_sK54_C,type,
sK54_C: $i > $i > $i ).
thf(tp_sK55_D,type,
sK55_D: $i > $i > $i > $i ).
thf(tp_sK56_C,type,
sK56_C: $i > $i > $i ).
thf(tp_sK57_SY429,type,
sK57_SY429: $i > $i > $i ).
thf(tp_sK58_C,type,
sK58_C: $i > $i > $i ).
thf(tp_sK59_SY431,type,
sK59_SY431: $i > $i > $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK60_B,type,
sK60_B: $i > $i ).
thf(tp_sK61_E,type,
sK61_E: $i > $i > $i > $i > $i ).
thf(tp_sK62_B,type,
sK62_B: $i > $i ).
thf(tp_sK63_SY434,type,
sK63_SY434: $i > $i ).
thf(tp_sK64_C,type,
sK64_C: $i > $i > $i ).
thf(tp_sK65_B,type,
sK65_B: $i > $i ).
thf(tp_sK66_B,type,
sK66_B: $i > $i ).
thf(tp_sK67_B,type,
sK67_B: $i > $i ).
thf(tp_sK68_B,type,
sK68_B: $i > $i ).
thf(tp_sK69_C,type,
sK69_C: $i > $i > $i ).
thf(tp_sK6_C,type,
sK6_C: $i > $i > $i ).
thf(tp_sK70_A,type,
sK70_A: $i ).
thf(tp_sK71_D,type,
sK71_D: $i > $i > $i > $i ).
thf(tp_sK72_C,type,
sK72_C: $i > $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK8_D,type,
sK8_D: $i > $i > $i ).
thf(tp_sK9_B,type,
sK9_B: $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_succ,type,
succ: $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_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(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
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/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(8,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(10,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(13,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(15,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ( in @ C @ A )
& ? [H: $i] :
( ( C = H )
& ( in @ E @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ E @ I ) @ B ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ A )
& ( in @ E @ A )
& ? [J: $i] :
( ( E = J )
& ( in @ D @ J )
& ! [K: $i] :
( ( in @ K @ J )
=> ( in @ ( ordered_pair @ D @ K ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__1) ).
thf(26,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(37,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(40,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(41,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(42,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(43,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(46,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(48,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(49,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(50,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(54,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(55,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(59,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(64,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(65,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(66,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(67,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(70,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(74,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(79,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(83,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(84,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(85,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(87,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(90,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(91,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(96,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(107,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(114,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(123,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(129,axiom,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(170,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(177,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(178,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(181,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(188,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',d1_enumset1) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(212,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(215,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(217,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(218,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(224,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(236,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(253,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(258,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(264,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(283,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(294,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(303,axiom,
! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(305,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(310,axiom,
! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_wellord2) ).
thf(315,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(330,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(335,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(354,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(365,axiom,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(371,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(394,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(396,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(398,conjecture,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(399,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[398]) ).
thf(400,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[399]) ).
thf(401,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(402,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(403,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(404,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(405,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(406,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(407,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(408,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(409,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(410,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(411,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(412,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(413,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(414,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(416,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)],[19]) ).
thf(417,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)],[22]) ).
thf(418,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ( in @ C @ A )
& ? [H: $i] :
( ( C = H )
& ( in @ E @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ E @ I ) @ B ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ A )
& ( in @ E @ A )
& ? [J: $i] :
( ( E = J )
& ( in @ D @ J )
& ! [K: $i] :
( ( in @ K @ J )
=> ( in @ ( ordered_pair @ D @ K ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(419,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(420,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(421,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(422,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(423,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(424,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(425,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(426,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(427,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(428,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(429,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(430,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(431,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)],[58]) ).
thf(432,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(433,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(435,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(436,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(437,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(438,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(439,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(440,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(442,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(443,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(445,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(446,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(448,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(449,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(450,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(451,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(452,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(454,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(456,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)],[103]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(458,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)],[105]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(460,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(462,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(463,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(466,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(467,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(468,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(469,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(470,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)],[158]) ).
thf(471,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)],[161]) ).
thf(472,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(473,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(474,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)],[171]) ).
thf(475,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)],[173]) ).
thf(476,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)],[175]) ).
thf(477,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)],[176]) ).
thf(478,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(479,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(481,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(482,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(484,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(485,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)],[193]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(487,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(488,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(489,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(491,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(493,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(494,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(498,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(499,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(500,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(501,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(502,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)],[261]) ).
thf(503,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)],[264]) ).
thf(504,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(505,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(506,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(507,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(508,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(509,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)],[284]) ).
thf(510,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(511,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(513,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(514,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(515,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(517,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(518,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(519,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(520,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(521,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(522,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(523,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(524,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(525,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(526,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(527,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(528,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(529,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(530,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(532,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(533,plain,
( ( ! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(534,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(535,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(536,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(537,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(542,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(543,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(544,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(545,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(546,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(547,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(549,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(551,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)],[167]) ).
thf(552,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(553,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(554,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(555,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(556,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(557,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(558,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(559,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(560,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(561,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(562,plain,
( ( ! [SY373: $i] :
( ( finite @ sK1_A )
=> ( finite @ ( set_intersection2 @ sK1_A @ SY373 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[400]) ).
thf(563,plain,
( ( ( finite @ sK1_A )
=> ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY373 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[562]) ).
thf(564,plain,
( ( finite @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[563]) ).
thf(565,plain,
( ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY373 ) )
= $false ),
inference(standard_cnf,[status(thm)],[563]) ).
thf(566,plain,
( ( ~ ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY373 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[565]) ).
thf(567,plain,
( ( ! [A: $i] :
( ! [SY374: $i] :
( ~ ( subset @ SY374 @ ( sK3_B @ A ) )
| ( are_equipotent @ SY374 @ ( sK3_B @ A ) )
| ( in @ SY374 @ ( sK3_B @ A ) ) )
& ! [SY375: $i] :
( ( ! [SY380: $i] :
( ~ ( subset @ SY380 @ SY375 )
| ( in @ SY380 @ ( sK4_SY376 @ SY375 @ A ) ) )
& ( in @ ( sK4_SY376 @ SY375 @ A ) @ ( sK3_B @ A ) ) )
| ~ ( in @ SY375 @ ( sK3_B @ A ) ) )
& ! [SY378: $i,SY379: $i] :
( ~ ( in @ SY378 @ ( sK3_B @ A ) )
| ~ ( subset @ SY379 @ SY378 )
| ( in @ SY379 @ ( sK3_B @ A ) ) )
& ( in @ A @ ( sK3_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(568,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[402]) ).
thf(569,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY381: $i] :
( ~ ( in @ SY381 @ B )
| ~ ( in @ SY381 @ ( sK5_C @ B @ A ) ) )
& ( in @ ( sK5_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(570,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(571,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[405]) ).
thf(572,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(573,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(574,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(575,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_C @ B @ A ) @ A )
| ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
& ( ( in @ ( sK6_C @ B @ A ) @ A )
| ( in @ ( sK6_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[411]) ).
thf(576,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[412]) ).
thf(577,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[413]) ).
thf(578,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[415]) ).
thf(579,plain,
( ( ( sK12_REN
| ! [A: $i] :
( ! [SY382: $i] :
( ! [D: $i] :
( ( D != SY382 )
| ~ ( in @ D @ A ) )
| ~ ( ordinal @ SY382 )
| ( in @ SY382 @ ( sK7_B @ A ) ) )
& ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK7_B @ A ) )
| ( ( ( sK8_D @ SY384 @ A )
= SY384 )
& ( in @ ( sK8_D @ SY384 @ A ) @ A )
& ( ordinal @ SY384 ) ) ) ) )
& ( sK12_REN
=> ( ( sK9_B = sK10_SY386 )
& ( ordinal @ sK10_SY386 )
& ( sK9_B = sK11_SY388 )
& ( ordinal @ sK11_SY388 )
& ( sK10_SY386 != sK11_SY388 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[416]) ).
thf(580,plain,
( ( ! [A: $i] :
( ( ( ( sK16_SY393 @ A )
= ( singleton @ ( sK15_B @ A ) ) )
& ( in @ ( sK15_B @ A ) @ A )
& ( in @ ( sK15_B @ A ) @ A )
& ( ( sK17_SY395 @ A )
= ( singleton @ ( sK15_B @ A ) ) )
& ( ( sK16_SY393 @ A )
!= ( sK17_SY395 @ A ) ) )
| ( ! [SY389: $i] :
( ! [D: $i] :
( ~ ( in @ D @ A )
| ( SY389
!= ( singleton @ D ) ) )
| ( in @ SY389 @ ( sK13_B @ A ) ) )
& ! [SY391: $i] :
( ~ ( in @ SY391 @ ( sK13_B @ A ) )
| ( ( in @ ( sK14_D @ SY391 @ A ) @ A )
& ( SY391
= ( singleton @ ( sK14_D @ SY391 @ A ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[417]) ).
thf(581,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation @ B )
| ( ! [SY423: $i] :
( ~ ( in @ SY423 @ ( sK26_SY414 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ B @ A ) @ SY423 ) @ B ) )
& ( ( sK22_C @ B @ A )
= ( sK26_SY414 @ B @ A ) )
& ( in @ ( sK23_SY407 @ B @ A ) @ ( sK26_SY414 @ B @ A ) )
& ( in @ ( sK22_C @ B @ A ) @ A )
& ( in @ ( sK22_C @ B @ A ) @ A )
& ! [SY422: $i] :
( ~ ( in @ SY422 @ ( sK25_SY420 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ B @ A ) @ SY422 ) @ B ) )
& ( ( sK22_C @ B @ A )
= ( sK25_SY420 @ B @ A ) )
& ( in @ ( sK24_SY413 @ B @ A ) @ ( sK25_SY420 @ B @ A ) )
& ( ( sK23_SY407 @ B @ A )
!= ( sK24_SY413 @ B @ A ) ) )
| ( ! [SY396: $i] :
( ! [E: $i] :
( ~ ( in @ E @ A )
| ! [J: $i] :
( ( ( in @ ( sK21_K @ J @ E @ SY396 @ B @ A ) @ J )
& ~ ( in @ ( ordered_pair @ SY396 @ ( sK21_K @ J @ E @ SY396 @ B @ A ) ) @ B ) )
| ( E != J )
| ~ ( in @ SY396 @ J ) ) )
| ( in @ SY396 @ ( sK18_C @ B @ A ) ) )
& ! [SY400: $i] :
( ~ ( in @ SY400 @ ( sK18_C @ B @ A ) )
| ( ( in @ ( sK19_E @ SY400 @ B @ A ) @ A )
& ! [SY406: $i] :
( ~ ( in @ SY406 @ ( sK20_SY404 @ SY400 @ B @ A ) )
| ( in @ ( ordered_pair @ SY400 @ SY406 ) @ B ) )
& ( ( sK19_E @ SY400 @ B @ A )
= ( sK20_SY404 @ SY400 @ B @ A ) )
& ( in @ SY400 @ ( sK20_SY404 @ SY400 @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[418]) ).
thf(582,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[419]) ).
thf(583,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[420]) ).
thf(584,plain,
( ( ( relation @ sK27_A )
& ( relation_empty_yielding @ sK27_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[421]) ).
thf(585,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK28_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK28_B @ A ) )
& ( finite @ ( sK28_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[422]) ).
thf(586,plain,
( ( ~ ( empty @ sK29_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[423]) ).
thf(587,plain,
( ( ! [A: $i] :
( ( element @ ( sK30_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK30_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[424]) ).
thf(588,plain,
( ( ~ ( empty @ sK31_A )
& ( relation @ sK31_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[425]) ).
thf(589,plain,
( ( ( empty @ sK32_A )
& ( relation @ sK32_A )
& ( function @ sK32_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[426]) ).
thf(590,plain,
( ( empty @ sK33_A )
= $true ),
inference(extcnf_combined,[status(esa)],[427]) ).
thf(591,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK34_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK34_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[428]) ).
thf(592,plain,
( ( ( empty @ sK35_A )
& ( relation @ sK35_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[429]) ).
thf(593,plain,
( ( ( function @ sK36_A )
& ( relation @ sK36_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[430]) ).
thf(594,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[431]) ).
thf(595,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[432]) ).
thf(596,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[433]) ).
thf(597,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[434]) ).
thf(598,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[435]) ).
thf(599,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[436]) ).
thf(600,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[437]) ).
thf(601,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[438]) ).
thf(602,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[439]) ).
thf(603,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[441]) ).
thf(604,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[443]) ).
thf(605,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[444]) ).
thf(606,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[446]) ).
thf(607,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[452]) ).
thf(608,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[453]) ).
thf(609,plain,
( ( ! [A: $i] : ( element @ ( sK37_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[454]) ).
thf(610,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[455]) ).
thf(611,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[456]) ).
thf(612,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[457]) ).
thf(613,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(extcnf_combined,[status(esa)],[458]) ).
thf(614,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[459]) ).
thf(615,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[461]) ).
thf(616,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[462]) ).
thf(617,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[463]) ).
thf(618,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[464]) ).
thf(619,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[465]) ).
thf(620,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[468]) ).
thf(621,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[469]) ).
thf(622,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ A )
| ( in @ ( sK38_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK38_D @ C @ B @ A ) @ A )
| ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ B )
| ( in @ ( sK38_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[470]) ).
thf(623,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY424: $i] :
( ~ ( in @ ( sK40_C @ B @ A ) @ SY424 )
| ~ ( in @ SY424 @ A ) )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK40_C @ B @ A ) @ ( sK41_SY425 @ B @ A ) )
& ( in @ ( sK41_SY425 @ B @ A ) @ A ) )
| ( in @ ( sK40_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK39_D @ C @ B @ A ) )
& ( in @ ( sK39_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[471]) ).
thf(624,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK42_C @ B @ A ) @ A )
& ~ ( in @ ( sK42_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[472]) ).
thf(625,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK43_C @ B @ A ) @ ( sK44_SY426 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK43_C @ B @ A ) @ ( sK44_SY426 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[473]) ).
thf(626,plain,
( ( ! [A: $i] :
( ( ( ( sK45_B @ A )
!= ( sK46_SY427 @ A ) )
& ( in @ ( sK45_B @ A ) @ A )
& ( in @ ( sK46_SY427 @ A ) @ A )
& ~ ( in @ ( sK45_B @ A ) @ ( sK46_SY427 @ A ) )
& ~ ( in @ ( sK46_SY427 @ A ) @ ( sK45_B @ A ) ) )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[474]) ).
thf(627,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK47_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK47_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ( in @ ( sK47_D @ C @ B @ A ) @ A )
| ( in @ ( sK47_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[475]) ).
thf(628,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK48_D @ C @ B @ A ) @ C )
| ( ( sK48_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK48_D @ C @ B @ A ) @ C )
| ( ( sK48_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK48_D @ C @ B @ A ) @ C )
| ( ( sK48_D @ C @ B @ A )
= A )
| ( ( sK48_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[476]) ).
thf(629,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[477]) ).
thf(630,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK49_C @ B @ A ) @ ( sK50_SY428 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ B @ A ) @ ( sK50_SY428 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK49_C @ B @ A ) @ ( sK50_SY428 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK49_C @ B @ A ) @ ( sK50_SY428 @ B @ A ) ) @ B ) ) )
| ( A = B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( A != B )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[478]) ).
thf(631,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK51_B @ A ) @ A )
& ~ ( subset @ ( sK51_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[479]) ).
thf(632,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK52_C @ B @ A ) @ B )
| ~ ( subset @ ( sK52_C @ B @ A ) @ A ) )
& ( ( in @ ( sK52_C @ B @ A ) @ B )
| ( subset @ ( sK52_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[480]) ).
thf(633,plain,
( ( ! [A: $i] :
( ( in @ ( sK53_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[481]) ).
thf(634,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK54_C @ B @ A )
!= A )
| ~ ( in @ ( sK54_C @ B @ A ) @ B ) )
& ( ( ( sK54_C @ B @ A )
= A )
| ( in @ ( sK54_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[482]) ).
thf(635,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK57_SY429 @ B @ A ) @ A )
& ~ ( in @ ( sK56_C @ B @ A ) @ ( sK57_SY429 @ B @ A ) ) )
| ~ ( in @ ( sK56_C @ B @ A ) @ B ) )
& ( ! [SY430: $i] :
( ~ ( in @ SY430 @ A )
| ( in @ ( sK56_C @ B @ A ) @ SY430 ) )
| ( in @ ( sK56_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK55_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK55_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[483]) ).
thf(636,plain,
( ( ! [A: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ( sK60_B @ A )
!= ( ordered_pair @ SY432 @ SY433 ) )
& ( in @ ( sK60_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY431 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[484]) ).
thf(637,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK61_E @ D @ C @ B @ A ) @ D )
| ( ( sK61_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK61_E @ D @ C @ B @ A ) @ D )
| ( ( sK61_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK61_E @ D @ C @ B @ A ) @ D )
| ( ( sK61_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK61_E @ D @ C @ B @ A ) @ D )
| ( ( sK61_E @ D @ C @ B @ A )
= C )
| ( ( sK61_E @ D @ C @ B @ A )
= A )
| ( ( sK61_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[485]) ).
thf(638,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[486]) ).
thf(639,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[487]) ).
thf(640,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[488]) ).
thf(641,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[489]) ).
thf(642,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[490]) ).
thf(643,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[492]) ).
thf(644,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[493]) ).
thf(645,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[494]) ).
thf(646,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[495]) ).
thf(647,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[497]) ).
thf(648,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[498]) ).
thf(649,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[499]) ).
thf(650,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[500]) ).
thf(651,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK62_B @ A ) @ ( sK63_SY434 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[501]) ).
thf(652,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[502]) ).
thf(653,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(extcnf_combined,[status(esa)],[503]) ).
thf(654,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[504]) ).
thf(655,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[505]) ).
thf(656,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[506]) ).
thf(657,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[508]) ).
thf(658,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK64_C @ B @ A ) @ A )
& ( in @ ( sK64_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[509]) ).
thf(659,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[510]) ).
thf(660,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[511]) ).
thf(661,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[513]) ).
thf(662,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[514]) ).
thf(663,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[515]) ).
thf(664,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[517]) ).
thf(665,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK65_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK65_B @ A ) )
| ~ ( subset @ ( sK65_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[518]) ).
thf(666,plain,
( ( ! [A: $i] :
( ( relation @ ( sK66_B @ A ) )
& ( well_orders @ ( sK66_B @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[520]) ).
thf(667,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ( in @ A @ B )
| ( A = B )
| ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[521]) ).
thf(668,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[522]) ).
thf(669,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[524]) ).
thf(670,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[525]) ).
thf(671,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[526]) ).
thf(672,plain,
( ( ! [A: $i] :
( ! [SY435: $i] :
( ~ ( subset @ SY435 @ ( sK67_B @ A ) )
| ( are_equipotent @ SY435 @ ( sK67_B @ A ) )
| ( in @ SY435 @ ( sK67_B @ A ) ) )
& ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK67_B @ A ) )
| ( in @ ( powerset @ SY436 ) @ ( sK67_B @ A ) ) )
& ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK67_B @ A ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK67_B @ A ) ) )
& ( in @ A @ ( sK67_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[527]) ).
thf(673,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[528]) ).
thf(674,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[529]) ).
thf(675,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[530]) ).
thf(676,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[531]) ).
thf(677,plain,
( ( ! [A: $i] :
( ! [SY439: $i] :
( ~ ( in @ SY439 @ A )
| ~ ( ordinal @ SY439 )
| ( in @ SY439 @ ( sK68_B @ A ) ) )
& ! [SY440: $i] :
( ~ ( in @ SY440 @ ( sK68_B @ A ) )
| ( in @ SY440 @ A ) )
& ! [SY441: $i] :
( ~ ( in @ SY441 @ ( sK68_B @ A ) )
| ( ordinal @ SY441 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[533]) ).
thf(678,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK69_C @ B @ A ) @ A )
& ~ ( in @ ( sK69_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[534]) ).
thf(679,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[535]) ).
thf(680,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[536]) ).
thf(681,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[537]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[538]) ).
thf(683,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[539]) ).
thf(684,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[540]) ).
thf(685,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[541]) ).
thf(686,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[542]) ).
thf(687,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[543]) ).
thf(688,plain,
( ( ~ ( empty @ sK70_A )
& ( finite @ sK70_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[545]) ).
thf(689,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[546]) ).
thf(690,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[547]) ).
thf(691,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[548]) ).
thf(692,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ B )
| ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[549]) ).
thf(693,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[550]) ).
thf(694,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK71_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK71_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK71_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK71_D @ C @ B @ A ) @ A )
| ( in @ ( sK71_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK71_D @ C @ B @ A ) @ B )
| ( in @ ( sK71_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[551]) ).
thf(695,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[553]) ).
thf(696,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[554]) ).
thf(697,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK72_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[555]) ).
thf(698,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[557]) ).
thf(699,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[558]) ).
thf(700,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[559]) ).
thf(701,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( finite @ B )
| ~ ( subset @ A @ B ) )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[561]) ).
thf(702,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( finite @ B )
| ~ ( subset @ A @ B ) )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(703,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(704,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(705,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(706,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(707,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(708,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK72_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(709,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(710,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(711,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(712,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK71_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK71_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK71_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK71_D @ C @ B @ A ) @ A )
| ( in @ ( sK71_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK71_D @ C @ B @ A ) @ B )
| ( in @ ( sK71_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(713,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(714,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ B )
| ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(715,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(716,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(717,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(718,plain,
( ( ~ ( empty @ sK70_A )
& ( finite @ sK70_A ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(719,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(720,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(721,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(722,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(723,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(724,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(725,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(726,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(727,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(728,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(729,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK69_C @ B @ A ) @ A )
& ~ ( in @ ( sK69_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(730,plain,
( ( ! [A: $i] :
( ! [SY439: $i] :
( ~ ( in @ SY439 @ A )
| ~ ( ordinal @ SY439 )
| ( in @ SY439 @ ( sK68_B @ A ) ) )
& ! [SY440: $i] :
( ~ ( in @ SY440 @ ( sK68_B @ A ) )
| ( in @ SY440 @ A ) )
& ! [SY441: $i] :
( ~ ( in @ SY441 @ ( sK68_B @ A ) )
| ( ordinal @ SY441 ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(731,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(732,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(733,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(734,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(735,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(736,plain,
( ( ! [A: $i] :
( ! [SY435: $i] :
( ~ ( subset @ SY435 @ ( sK67_B @ A ) )
| ( are_equipotent @ SY435 @ ( sK67_B @ A ) )
| ( in @ SY435 @ ( sK67_B @ A ) ) )
& ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK67_B @ A ) )
| ( in @ ( powerset @ SY436 ) @ ( sK67_B @ A ) ) )
& ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK67_B @ A ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK67_B @ A ) ) )
& ( in @ A @ ( sK67_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(737,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(738,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(739,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(740,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(741,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(742,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ( in @ A @ B )
| ( A = B )
| ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(743,plain,
( ( ! [A: $i] :
( ( relation @ ( sK66_B @ A ) )
& ( well_orders @ ( sK66_B @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(744,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(745,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK65_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK65_B @ A ) )
| ~ ( subset @ ( sK65_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(746,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(747,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(748,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(749,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(750,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(751,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(752,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(753,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(754,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK64_C @ B @ A ) @ A )
& ( in @ ( sK64_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(755,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(756,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(757,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(758,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(759,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(760,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)],[653]) ).
thf(761,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)],[652]) ).
thf(762,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK62_B @ A ) @ ( sK63_SY434 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(763,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(764,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(765,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(766,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(767,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(768,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(769,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(770,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(771,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(772,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(773,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(774,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(775,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(776,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(777,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(778,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK61_E @ D @ C @ B @ A ) @ D )
| ( ( sK61_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK61_E @ D @ C @ B @ A ) @ D )
| ( ( sK61_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK61_E @ D @ C @ B @ A ) @ D )
| ( ( sK61_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK61_E @ D @ C @ B @ A ) @ D )
| ( ( sK61_E @ D @ C @ B @ A )
= C )
| ( ( sK61_E @ D @ C @ B @ A )
= A )
| ( ( sK61_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(779,plain,
( ( ! [A: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ( sK60_B @ A )
!= ( ordered_pair @ SY432 @ SY433 ) )
& ( in @ ( sK60_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY431 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(780,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK57_SY429 @ B @ A ) @ A )
& ~ ( in @ ( sK56_C @ B @ A ) @ ( sK57_SY429 @ B @ A ) ) )
| ~ ( in @ ( sK56_C @ B @ A ) @ B ) )
& ( ! [SY430: $i] :
( ~ ( in @ SY430 @ A )
| ( in @ ( sK56_C @ B @ A ) @ SY430 ) )
| ( in @ ( sK56_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK55_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK55_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(781,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK54_C @ B @ A )
!= A )
| ~ ( in @ ( sK54_C @ B @ A ) @ B ) )
& ( ( ( sK54_C @ B @ A )
= A )
| ( in @ ( sK54_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(782,plain,
( ( ! [A: $i] :
( ( in @ ( sK53_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(783,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK52_C @ B @ A ) @ B )
| ~ ( subset @ ( sK52_C @ B @ A ) @ A ) )
& ( ( in @ ( sK52_C @ B @ A ) @ B )
| ( subset @ ( sK52_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(784,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK51_B @ A ) @ A )
& ~ ( subset @ ( sK51_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(785,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK49_C @ B @ A ) @ ( sK50_SY428 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ B @ A ) @ ( sK50_SY428 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK49_C @ B @ A ) @ ( sK50_SY428 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK49_C @ B @ A ) @ ( sK50_SY428 @ B @ A ) ) @ B ) ) )
| ( A = B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( A != B )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(786,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(787,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK48_D @ C @ B @ A ) @ C )
| ( ( sK48_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK48_D @ C @ B @ A ) @ C )
| ( ( sK48_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK48_D @ C @ B @ A ) @ C )
| ( ( sK48_D @ C @ B @ A )
= A )
| ( ( sK48_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(788,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK47_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK47_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ( in @ ( sK47_D @ C @ B @ A ) @ A )
| ( in @ ( sK47_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(789,plain,
( ( ! [A: $i] :
( ( ( ( sK45_B @ A )
!= ( sK46_SY427 @ A ) )
& ( in @ ( sK45_B @ A ) @ A )
& ( in @ ( sK46_SY427 @ A ) @ A )
& ~ ( in @ ( sK45_B @ A ) @ ( sK46_SY427 @ A ) )
& ~ ( in @ ( sK46_SY427 @ A ) @ ( sK45_B @ A ) ) )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(790,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK43_C @ B @ A ) @ ( sK44_SY426 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK43_C @ B @ A ) @ ( sK44_SY426 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(791,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK42_C @ B @ A ) @ A )
& ~ ( in @ ( sK42_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(792,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY424: $i] :
( ~ ( in @ ( sK40_C @ B @ A ) @ SY424 )
| ~ ( in @ SY424 @ A ) )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK40_C @ B @ A ) @ ( sK41_SY425 @ B @ A ) )
& ( in @ ( sK41_SY425 @ B @ A ) @ A ) )
| ( in @ ( sK40_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK39_D @ C @ B @ A ) )
& ( in @ ( sK39_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(793,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ A )
| ( in @ ( sK38_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK38_D @ C @ B @ A ) @ A )
| ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ B )
| ( in @ ( sK38_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(794,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(795,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(796,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(797,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(798,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(799,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(800,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(801,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(802,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(803,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(804,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(805,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)],[613]) ).
thf(806,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(807,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(808,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(809,plain,
( ( ! [A: $i] : ( element @ ( sK37_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(810,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(811,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(812,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(813,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(814,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(815,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(816,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(817,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(818,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(819,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(820,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(821,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(822,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(823,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(824,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(825,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(826,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(827,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(828,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(829,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(830,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(831,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(832,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)],[594]) ).
thf(833,plain,
( ( ( function @ sK36_A )
& ( relation @ sK36_A ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(834,plain,
( ( ( empty @ sK35_A )
& ( relation @ sK35_A ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(835,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK34_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK34_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(836,plain,
( ( empty @ sK33_A )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(837,plain,
( ( ( empty @ sK32_A )
& ( relation @ sK32_A )
& ( function @ sK32_A ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(838,plain,
( ( ~ ( empty @ sK31_A )
& ( relation @ sK31_A ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(839,plain,
( ( ! [A: $i] :
( ( element @ ( sK30_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK30_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(840,plain,
( ( ~ ( empty @ sK29_A ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(841,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK28_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK28_B @ A ) )
& ( finite @ ( sK28_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(842,plain,
( ( ( relation @ sK27_A )
& ( relation_empty_yielding @ sK27_A ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(843,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(844,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(845,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation @ B )
| ( ! [SY423: $i] :
( ~ ( in @ SY423 @ ( sK26_SY414 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ B @ A ) @ SY423 ) @ B ) )
& ( ( sK22_C @ B @ A )
= ( sK26_SY414 @ B @ A ) )
& ( in @ ( sK23_SY407 @ B @ A ) @ ( sK26_SY414 @ B @ A ) )
& ( in @ ( sK22_C @ B @ A ) @ A )
& ( in @ ( sK22_C @ B @ A ) @ A )
& ! [SY422: $i] :
( ~ ( in @ SY422 @ ( sK25_SY420 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ B @ A ) @ SY422 ) @ B ) )
& ( ( sK22_C @ B @ A )
= ( sK25_SY420 @ B @ A ) )
& ( in @ ( sK24_SY413 @ B @ A ) @ ( sK25_SY420 @ B @ A ) )
& ( ( sK23_SY407 @ B @ A )
!= ( sK24_SY413 @ B @ A ) ) )
| ( ! [SY396: $i] :
( ! [E: $i] :
( ~ ( in @ E @ A )
| ! [J: $i] :
( ( ( in @ ( sK21_K @ J @ E @ SY396 @ B @ A ) @ J )
& ~ ( in @ ( ordered_pair @ SY396 @ ( sK21_K @ J @ E @ SY396 @ B @ A ) ) @ B ) )
| ( E != J )
| ~ ( in @ SY396 @ J ) ) )
| ( in @ SY396 @ ( sK18_C @ B @ A ) ) )
& ! [SY400: $i] :
( ~ ( in @ SY400 @ ( sK18_C @ B @ A ) )
| ( ( in @ ( sK19_E @ SY400 @ B @ A ) @ A )
& ! [SY406: $i] :
( ~ ( in @ SY406 @ ( sK20_SY404 @ SY400 @ B @ A ) )
| ( in @ ( ordered_pair @ SY400 @ SY406 ) @ B ) )
& ( ( sK19_E @ SY400 @ B @ A )
= ( sK20_SY404 @ SY400 @ B @ A ) )
& ( in @ SY400 @ ( sK20_SY404 @ SY400 @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(846,plain,
( ( ! [A: $i] :
( ( ( ( sK16_SY393 @ A )
= ( singleton @ ( sK15_B @ A ) ) )
& ( in @ ( sK15_B @ A ) @ A )
& ( in @ ( sK15_B @ A ) @ A )
& ( ( sK17_SY395 @ A )
= ( singleton @ ( sK15_B @ A ) ) )
& ( ( sK16_SY393 @ A )
!= ( sK17_SY395 @ A ) ) )
| ( ! [SY389: $i] :
( ! [D: $i] :
( ~ ( in @ D @ A )
| ( SY389
!= ( singleton @ D ) ) )
| ( in @ SY389 @ ( sK13_B @ A ) ) )
& ! [SY391: $i] :
( ~ ( in @ SY391 @ ( sK13_B @ A ) )
| ( ( in @ ( sK14_D @ SY391 @ A ) @ A )
& ( SY391
= ( singleton @ ( sK14_D @ SY391 @ A ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(847,plain,
( ( ( sK12_REN
| ! [A: $i] :
( ! [SY382: $i] :
( ! [D: $i] :
( ( D != SY382 )
| ~ ( in @ D @ A ) )
| ~ ( ordinal @ SY382 )
| ( in @ SY382 @ ( sK7_B @ A ) ) )
& ! [SY384: $i] :
( ~ ( in @ SY384 @ ( sK7_B @ A ) )
| ( ( ( sK8_D @ SY384 @ A )
= SY384 )
& ( in @ ( sK8_D @ SY384 @ A ) @ A )
& ( ordinal @ SY384 ) ) ) ) )
& ( sK12_REN
=> ( ( sK9_B = sK10_SY386 )
& ( ordinal @ sK10_SY386 )
& ( sK9_B = sK11_SY388 )
& ( ordinal @ sK11_SY388 )
& ( sK10_SY386 != sK11_SY388 ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(848,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(849,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(850,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(851,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(852,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_C @ B @ A ) @ A )
| ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
& ( ( in @ ( sK6_C @ B @ A ) @ A )
| ( in @ ( sK6_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(853,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(854,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(855,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(856,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(857,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(858,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(859,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(860,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY381: $i] :
( ~ ( in @ SY381 @ B )
| ~ ( in @ SY381 @ ( sK5_C @ B @ A ) ) )
& ( in @ ( sK5_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(861,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(862,plain,
( ( ! [A: $i] :
( ! [SY374: $i] :
( ~ ( subset @ SY374 @ ( sK3_B @ A ) )
| ( are_equipotent @ SY374 @ ( sK3_B @ A ) )
| ( in @ SY374 @ ( sK3_B @ A ) ) )
& ! [SY375: $i] :
( ( ! [SY380: $i] :
( ~ ( subset @ SY380 @ SY375 )
| ( in @ SY380 @ ( sK4_SY376 @ SY375 @ A ) ) )
& ( in @ ( sK4_SY376 @ SY375 @ A ) @ ( sK3_B @ A ) ) )
| ~ ( in @ SY375 @ ( sK3_B @ A ) ) )
& ! [SY378: $i,SY379: $i] :
( ~ ( in @ SY378 @ ( sK3_B @ A ) )
| ~ ( subset @ SY379 @ SY378 )
| ( in @ SY379 @ ( sK3_B @ A ) ) )
& ( in @ A @ ( sK3_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(863,plain,
( ( finite @ sK1_A )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(864,plain,
( ( ~ ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY373 ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(865,plain,
( ( ~ ( ~ ( sK12_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
| ~ ( ~ sK12_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) )
| ~ ( ( sK10_SY386 != sK11_SY388 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[847]) ).
thf(866,plain,
( ( ~ ( ~ ~ ( empty @ sK70_A )
| ~ ( finite @ sK70_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[718]) ).
thf(867,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[788]) ).
thf(868,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(869,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( sK5_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[860]) ).
thf(870,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(871,plain,
( ( ! [SX0: $i] :
~ ( ~ ( relation @ ( sK66_B @ SX0 ) )
| ~ ( well_orders @ ( sK66_B @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[743]) ).
thf(872,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[795]) ).
thf(873,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[811]) ).
thf(874,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK65_B @ SX0 ) @ SX0 )
| ~ ( ~ ( ordinal @ ( sK65_B @ SX0 ) )
| ~ ( subset @ ( sK65_B @ SX0 ) @ SX0 ) ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[745]) ).
thf(875,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK67_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK67_B @ SX0 ) )
| ( in @ SX1 @ ( sK67_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK67_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK67_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK67_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK67_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK67_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(876,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK53_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[782]) ).
thf(877,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[723]) ).
thf(878,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[713]) ).
thf(879,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[724]) ).
thf(880,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK60_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK60_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK58_C @ SX1 @ SX0 ) @ ( sK59_SY431 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(881,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[750]) ).
thf(882,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK71_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK71_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK71_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK71_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK71_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK71_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[712]) ).
thf(883,plain,
( ( ~ ( ~ ( function @ sK36_A )
| ~ ( relation @ sK36_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[833]) ).
thf(884,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK52_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK52_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(885,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SX1 @ SX0 ) @ ( sK50_SY428 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SX1 @ SX0 ) @ ( sK50_SY428 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SX1 @ SX0 ) @ ( sK50_SY428 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK49_C @ SX1 @ SX0 ) @ ( sK50_SY428 @ SX1 @ SX0 ) ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[785]) ).
thf(886,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK28_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK28_B @ SX0 ) ) )
| ~ ( finite @ ( sK28_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[841]) ).
thf(887,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK26_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SX1 @ SX0 ) @ SX2 ) @ SX1 ) )
| ~ ~ ( ( ( sK22_C @ SX1 @ SX0 )
!= ( sK26_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK23_SY407 @ SX1 @ SX0 ) @ ( sK26_SY414 @ SX1 @ SX0 ) ) ) )
| ~ ( in @ ( sK22_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( in @ ( sK22_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK25_SY420 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SX1 @ SX0 ) @ SX2 ) @ SX1 ) )
| ~ ~ ( ( ( sK22_C @ SX1 @ SX0 )
!= ( sK25_SY420 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK24_SY413 @ SX1 @ SX0 ) @ ( sK25_SY420 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( ( sK23_SY407 @ SX1 @ SX0 )
!= ( sK24_SY413 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 )
| ~ ~ ( in @ ( ordered_pair @ SX2 @ ( sK21_K @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( SX3 != SX4 )
| ~ ( in @ SX2 @ SX4 ) ) )
| ( in @ SX2 @ ( sK18_C @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK18_C @ SX1 @ SX0 ) )
| ~ ( ~ ( in @ ( sK19_E @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( sK20_SY404 @ SX2 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ( ( sK19_E @ SX2 @ SX1 @ SX0 )
!= ( sK20_SY404 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK20_SY404 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[845]) ).
thf(888,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK32_A )
| ~ ( relation @ sK32_A ) )
| ~ ( function @ sK32_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[837]) ).
thf(889,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK68_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK68_B @ SX0 ) )
| ( in @ SX1 @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK68_B @ SX0 ) )
| ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[730]) ).
thf(890,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[754]) ).
thf(891,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY425 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK41_SY425 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK39_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[792]) ).
thf(892,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[786]) ).
thf(893,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[812]) ).
thf(894,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK45_B @ SX0 )
!= ( sK46_SY427 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK46_SY427 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK45_B @ SX0 ) @ ( sK46_SY427 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK46_SY427 @ SX0 ) @ ( sK45_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[789]) ).
thf(895,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[777]) ).
thf(896,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX2 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX2 )
| ( ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK61_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX3
= ( unordered_triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( unordered_triple @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( SX4 = SX2 )
| ( SX4 = SX0 )
| ( SX4 = SX1 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX2 )
| ( in @ SX4 @ SX3 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX0 )
| ( in @ SX4 @ SX3 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SX1 )
| ( in @ SX4 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[778]) ).
thf(897,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[854]) ).
thf(898,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[852]) ).
thf(899,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK30_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK30_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[839]) ).
thf(900,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[828]) ).
thf(901,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[748]) ).
thf(902,plain,
( ( ~ ( ~ ~ ( empty @ sK31_A )
| ~ ( relation @ sK31_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[838]) ).
thf(903,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[793]) ).
thf(904,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX2 )
| ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ( disjoint @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[757]) ).
thf(905,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[733]) ).
thf(906,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK3_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK3_B @ SX0 ) )
| ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK4_SY376 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK4_SY376 @ SX1 @ SX0 ) @ ( sK3_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK3_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK3_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[862]) ).
thf(907,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[749]) ).
thf(908,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[823]) ).
thf(909,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK51_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK51_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[784]) ).
thf(910,plain,
( ( ~ ( ~ ( relation @ sK27_A )
| ~ ( relation_empty_yielding @ sK27_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[842]) ).
thf(911,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[765]) ).
thf(912,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[752]) ).
thf(913,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[827]) ).
thf(914,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK34_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK34_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[835]) ).
thf(915,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[810]) ).
thf(916,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[729]) ).
thf(917,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[727]) ).
thf(918,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK16_SY393 @ SX0 )
!= ( singleton @ ( sK15_B @ SX0 ) ) )
| ~ ( in @ ( sK15_B @ SX0 ) @ SX0 ) )
| ~ ( in @ ( sK15_B @ SX0 ) @ SX0 ) )
| ( ( sK17_SY395 @ SX0 )
!= ( singleton @ ( sK15_B @ SX0 ) ) ) )
| ~ ( ( ( sK16_SY393 @ SX0 )
!= ( sK17_SY395 @ SX0 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1
!= ( singleton @ SX2 ) ) )
| ( in @ SX1 @ ( sK13_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK13_B @ SX0 ) )
| ~ ( ~ ( in @ ( sK14_D @ SX1 @ SX0 ) @ SX0 )
| ( SX1
!= ( singleton @ ( sK14_D @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[846]) ).
thf(919,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY426 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY426 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[790]) ).
thf(920,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[829]) ).
thf(921,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK48_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK48_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK48_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK48_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(922,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK54_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK54_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK54_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK54_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(923,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[791]) ).
thf(924,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ ( sK57_SY429 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(925,plain,
( ( ~ ( ~ ( empty @ sK35_A )
| ~ ( relation @ sK35_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[834]) ).
thf(926,plain,
! [SV1: $i] :
( ( ! [SY442: $i] :
( ~ ( finite @ SY442 )
| ~ ( subset @ SV1 @ SY442 ) )
| ( finite @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(927,plain,
! [SV2: $i] :
( ( ! [SY443: $i] : ( subset @ ( set_intersection2 @ SV2 @ SY443 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(928,plain,
! [SV3: $i] :
( ( ! [SY444: $i,SY445: $i] :
( ~ ( subset @ SV3 @ SY444 )
| ~ ( subset @ SV3 @ SY445 )
| ( subset @ SV3 @ ( set_intersection2 @ SY444 @ SY445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(929,plain,
! [SV4: $i] :
( ( ! [SY446: $i] :
( ~ ( subset @ SV4 @ SY446 )
| ! [SY447: $i] : ( subset @ ( set_intersection2 @ SV4 @ SY447 ) @ ( set_intersection2 @ SY446 @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(930,plain,
! [SV5: $i] :
( ( ! [SY448: $i] :
( ~ ( subset @ SV5 @ SY448 )
| ( ( set_intersection2 @ SV5 @ SY448 )
= SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(931,plain,
! [SV6: $i] :
( ( ! [SY449: $i] :
( ( set_difference @ SV6 @ ( set_difference @ SV6 @ SY449 ) )
= ( set_intersection2 @ SV6 @ SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(932,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ( finite @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(933,plain,
! [SV8: $i] :
( ( ~ ( finite @ SV8 )
| ! [SY450: $i] :
( ~ ( element @ SY450 @ ( powerset @ SV8 ) )
| ( finite @ SY450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(934,plain,
! [SV9: $i] :
( ( ! [SY451: $i] :
( ( set_intersection2 @ SV9 @ SY451 )
= ( set_intersection2 @ SY451 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(935,plain,
! [SV10: $i] :
( ( ! [SY452: $i] :
( ~ ( finite @ SY452 )
| ( finite @ ( set_intersection2 @ SV10 @ SY452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(936,plain,
! [SV11: $i] :
( ( ~ ( finite @ SV11 )
| ! [SY453: $i] : ( finite @ ( set_intersection2 @ SV11 @ SY453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(937,plain,
! [SV12: $i] :
( ( ! [SY454: $i] :
( ~ ( relation @ SV12 )
| ~ ( relation @ SY454 )
| ( relation @ ( set_intersection2 @ SV12 @ SY454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(938,plain,
! [SV13: $i] :
( ( ( set_intersection2 @ SV13 @ SV13 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(939,plain,
! [SV14: $i] :
( ( ( set_intersection2 @ SV14 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(940,plain,
! [SV15: $i] :
( ( ( ( singleton @ SV15 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(941,plain,
! [SV16: $i] :
( ( ! [SY455: $i] :
( ~ ( disjoint @ ( singleton @ SV16 ) @ SY455 )
| ~ ( in @ SV16 @ SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(942,plain,
! [SV17: $i] :
( ( ! [SY456: $i] :
( ( in @ SV17 @ SY456 )
| ( disjoint @ ( singleton @ SV17 ) @ SY456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(943,plain,
! [SV18: $i] :
( ( ! [SY457: $i] :
( ~ ( element @ SY457 @ ( powerset @ SV18 ) )
| ! [SY458: $i] :
( ~ ( in @ SY458 @ SY457 )
| ( in @ SY458 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(944,plain,
! [SV19: $i] :
( ( ! [SY459: $i] :
( ~ ( subset @ SV19 @ SY459 )
| ! [SY460: $i] :
( ( in @ SY460 @ SV19 )
| ( subset @ SV19 @ ( set_difference @ SY459 @ ( singleton @ SY460 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(945,plain,
! [SV20: $i] :
( ( ! [SY461: $i] :
( ~ ( in @ SV20 @ SY461 )
| ( subset @ SV20 @ ( union @ SY461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(946,plain,
! [SV21: $i] :
( ( in @ SV21 @ ( succ @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(947,plain,
! [SV22: $i] :
( ( ! [SY462: $i] :
( ~ ( relation @ SY462 )
| ( subset @ ( relation_rng_restriction @ SV22 @ SY462 ) @ SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(948,plain,
! [SV23: $i] :
( ( ! [SY463: $i,SY464: $i,SY465: $i] :
( ~ ( subset @ SV23 @ SY463 )
| ~ ( subset @ SY464 @ SY465 )
| ( subset @ ( cartesian_product2 @ SV23 @ SY464 ) @ ( cartesian_product2 @ SY463 @ SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(949,plain,
! [SV24: $i] :
( ( ! [SY466: $i] :
( ~ ( subset @ SV24 @ SY466 )
| ( ( set_union2 @ SV24 @ SY466 )
= SY466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(950,plain,
! [SV25: $i] :
( ( ! [SY467: $i,SY468: $i,SY469: $i] :
( ~ ( relation_of2_as_subset @ SY469 @ SY468 @ SV25 )
| ~ ( subset @ SV25 @ SY467 )
| ( relation_of2_as_subset @ SY469 @ SY468 @ SY467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(951,plain,
! [SV26: $i] :
( ( ! [SY470: $i,SY471: $i] :
( ~ ( relation @ SY471 )
| ~ ( subset @ SV26 @ SY470 )
| ( subset @ ( relation_inverse_image @ SY471 @ SV26 ) @ ( relation_inverse_image @ SY471 @ SY470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(952,plain,
! [SV27: $i] :
( ( ! [SY472: $i,SY473: $i] :
( ~ ( subset @ SV27 @ SY472 )
| ~ ( subset @ SY472 @ SY473 )
| ( subset @ SV27 @ SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(953,plain,
! [SV28: $i] :
( ( ! [SY474: $i] :
( ~ ( ordinal @ SY474 )
| ~ ( in @ SV28 @ SY474 )
| ( ordinal @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(954,plain,
! [SV29: $i] :
( ( ~ ( ordinal @ SV29 )
| ! [SY475: $i] :
( ~ ( ordinal @ SY475 )
| ( in @ SV29 @ SY475 )
| ( SV29 = SY475 )
| ( in @ SY475 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(955,plain,
! [SV30: $i] :
( ( subset @ empty_set @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(956,plain,
! [SV31: $i] :
( ( ! [SY476: $i] :
( ~ ( subset @ SV31 @ SY476 )
| ! [SY477: $i] : ( subset @ ( set_difference @ SV31 @ SY477 ) @ ( set_difference @ SY476 @ SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(957,plain,
! [SV32: $i] :
( ( ! [SY478: $i] : ( subset @ ( set_difference @ SV32 @ SY478 ) @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(958,plain,
! [SV33: $i] :
( ( ! [SY479: $i] :
( ( set_union2 @ SV33 @ ( set_difference @ SY479 @ SV33 ) )
= ( set_union2 @ SV33 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(959,plain,
! [SV34: $i] :
( ( ! [SY480: $i,SY481: $i] :
( ~ ( in @ SV34 @ SY480 )
| ~ ( in @ SY480 @ SY481 )
| ~ ( in @ SY481 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(960,plain,
! [SV35: $i] :
( ( ~ ( subset @ SV35 @ empty_set )
| ( SV35 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(961,plain,
! [SV36: $i] :
( ( ! [SY482: $i] :
( ( set_difference @ ( set_union2 @ SV36 @ SY482 ) @ SY482 )
= ( set_difference @ SV36 @ SY482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(962,plain,
! [SV37: $i] :
( ( ! [SY483: $i] :
( ~ ( subset @ SV37 @ SY483 )
| ( SY483
= ( set_union2 @ SV37 @ ( set_difference @ SY483 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(963,plain,
! [SV38: $i] :
( ( ! [SY484: $i] :
( ~ ( element @ SY484 @ ( powerset @ ( powerset @ SV38 ) ) )
| ( SY484 = empty_set )
| ( ( complements_of_subsets @ SV38 @ SY484 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(964,plain,
! [SV39: $i] :
( ( ( SV39 = empty_set )
| ! [SY485: $i] :
( ~ ( element @ SY485 @ ( powerset @ SV39 ) )
| ! [SY486: $i] :
( ~ ( element @ SY486 @ SV39 )
| ( in @ SY486 @ SY485 )
| ( in @ SY486 @ ( subset_complement @ SV39 @ SY485 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(965,plain,
! [SV40: $i] :
( ( ! [SY487: $i,SY488: $i] :
( ~ ( element @ SY488 @ ( powerset @ SV40 ) )
| ~ ( in @ SY487 @ ( subset_complement @ SV40 @ SY488 ) )
| ~ ( in @ SY487 @ SY488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(966,plain,
! [SV41: $i] :
( ( ~ ( relation @ SV41 )
| ( in @ ( ordered_pair @ ( sK62_B @ SV41 ) @ ( sK63_SY434 @ SV41 ) ) @ SV41 )
| ( SV41 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(967,plain,
! [SV42: $i] :
( ( ! [SY489: $i] :
( ~ ( proper_subset @ SY489 @ SV42 )
| ~ ( subset @ SV42 @ SY489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(968,plain,
! [SV43: $i] :
( ( ! [SY490: $i,SY491: $i] :
( ~ ( disjoint @ SY490 @ SY491 )
| ~ ( subset @ SV43 @ SY490 )
| ( disjoint @ SV43 @ SY491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(969,plain,
! [SV44: $i] :
( ( ! [SY492: $i] :
( ~ ( subset @ ( singleton @ SV44 ) @ ( singleton @ SY492 ) )
| ( SV44 = SY492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(970,plain,
! [SV45: $i] :
( ( ! [SY493: $i] : ( subset @ SV45 @ ( set_union2 @ SV45 @ SY493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(971,plain,
! [SV46: $i] :
( ( ! [SY494: $i] :
( ~ ( relation @ SY494 )
| ( subset @ ( relation_dom_restriction @ SY494 @ SV46 ) @ SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(972,plain,
! [SV47: $i] :
( ( ! [SY495: $i,SY496: $i] :
( ~ ( subset @ SV47 @ SY495 )
| ~ ( subset @ SY496 @ SY495 )
| ( subset @ ( set_union2 @ SV47 @ SY496 ) @ SY495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(973,plain,
! [SV48: $i] :
( ( ! [SY497: $i] :
( ~ ( in @ SV48 @ SY497 )
| ( subset @ SV48 @ ( union @ SY497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(974,plain,
! [SV49: $i] :
( ( ( union @ ( powerset @ SV49 ) )
= SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(975,plain,
! [SV50: $i] :
( ( ! [SY498: $i] :
( ~ ( in @ SV50 @ SY498 )
| ~ ( in @ SY498 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(976,plain,
! [SV51: $i] :
( ( ~ ( empty @ SV51 )
| ( function @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(977,plain,
! [SV52: $i] :
( ( ~ ( empty @ SV52 )
| ( relation @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(978,plain,
! [SV53: $i] :
( ( ! [SY499: $i,SY500: $i] :
( ~ ( element @ SY500 @ ( powerset @ ( cartesian_product2 @ SV53 @ SY499 ) ) )
| ( relation @ SY500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(979,plain,
! [SV54: $i] :
( ( ! [SY501: $i] :
( ~ ( element @ SY501 @ ( powerset @ SV54 ) )
| ( ( subset_complement @ SV54 @ SY501 )
= ( set_difference @ SV54 @ SY501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(980,plain,
! [SV55: $i] :
( ( relation @ ( inclusion_relation @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(981,plain,
! [SV56: $i] :
( ( element @ ( cast_to_subset @ SV56 ) @ ( powerset @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(982,plain,
! [SV57: $i] :
( ( ~ ( relation @ SV57 )
| ! [SY502: $i] : ( relation @ ( relation_restriction @ SV57 @ SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(983,plain,
! [SV58: $i] :
( ( ! [SY503: $i] :
( ~ ( element @ SY503 @ ( powerset @ SV58 ) )
| ( element @ ( subset_complement @ SV58 @ SY503 ) @ ( powerset @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(984,plain,
! [SV59: $i] :
( ( ~ ( relation @ SV59 )
| ( relation @ ( relation_inverse @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(985,plain,
! [SV60: $i] :
( ( ! [SY504: $i] :
( ~ ( relation @ SV60 )
| ~ ( relation @ SY504 )
| ( relation @ ( relation_composition @ SV60 @ SY504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(986,plain,
! [SV61: $i] :
( ( ! [SY505: $i] :
( ~ ( element @ SY505 @ ( powerset @ ( powerset @ SV61 ) ) )
| ( element @ ( union_of_subsets @ SV61 @ SY505 ) @ ( powerset @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(987,plain,
! [SV62: $i] :
( ( relation @ ( identity_relation @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(988,plain,
! [SV63: $i] :
( ( ! [SY506: $i] :
( ~ ( element @ SY506 @ ( powerset @ ( powerset @ SV63 ) ) )
| ( element @ ( meet_of_subsets @ SV63 @ SY506 ) @ ( powerset @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(989,plain,
! [SV64: $i] :
( ( ! [SY507: $i,SY508: $i] :
( ~ ( element @ SY507 @ ( powerset @ SV64 ) )
| ~ ( element @ SY508 @ ( powerset @ SV64 ) )
| ( element @ ( subset_difference @ SV64 @ SY507 @ SY508 ) @ ( powerset @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(990,plain,
! [SV65: $i] :
( ( ~ ( relation @ SV65 )
| ! [SY509: $i] : ( relation @ ( relation_dom_restriction @ SV65 @ SY509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(991,plain,
! [SV66: $i] :
( ( ! [SY510: $i] :
( ~ ( element @ SY510 @ ( powerset @ ( powerset @ SV66 ) ) )
| ( element @ ( complements_of_subsets @ SV66 @ SY510 ) @ ( powerset @ ( powerset @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(992,plain,
! [SV67: $i] :
( ( ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ( relation @ ( relation_rng_restriction @ SV67 @ SY511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(993,plain,
! [SV68: $i] :
( ( element @ ( sK37_B @ SV68 ) @ SV68 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(994,plain,
! [SV69: $i] :
( ( ~ ( empty @ ( succ @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(995,plain,
! [SV70: $i] :
( ( ~ ( empty @ ( powerset @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(996,plain,
! [SV71: $i] :
( ( ! [SY512: $i] :
~ ( empty @ ( ordered_pair @ SV71 @ SY512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(997,plain,
! [SV72: $i] :
( ( ! [SY513: $i] :
( ~ ( relation @ SV72 )
| ~ ( relation @ SY513 )
| ( relation @ ( set_union2 @ SV72 @ SY513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(998,plain,
! [SV73: $i] :
( ( ~ ( empty @ ( singleton @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(999,plain,
! [SV74: $i] :
( ( ( empty @ SV74 )
| ! [SY514: $i] :
~ ( empty @ ( set_union2 @ SV74 @ SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1000,plain,
! [SV75: $i] :
( ( ! [SY515: $i] :
( ~ ( relation @ SV75 )
| ~ ( relation @ SY515 )
| ( relation @ ( set_difference @ SV75 @ SY515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1001,plain,
! [SV76: $i] :
( ( ! [SY516: $i] :
~ ( empty @ ( unordered_pair @ SV76 @ SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1002,plain,
! [SV77: $i] :
( ( ( empty @ SV77 )
| ! [SY517: $i] :
~ ( empty @ ( set_union2 @ SY517 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1003,plain,
! [SV78: $i] :
( ( ! [SY518: $i] :
( ( empty @ SV78 )
| ( empty @ SY518 )
| ~ ( empty @ ( cartesian_product2 @ SV78 @ SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1004,plain,
! [SV79: $i] :
( ( ( empty @ SV79 )
| ~ ( relation @ SV79 )
| ~ ( empty @ ( relation_dom @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1005,plain,
! [SV80: $i] :
( ( ( empty @ SV80 )
| ~ ( relation @ SV80 )
| ~ ( empty @ ( relation_rng @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1006,plain,
! [SV81: $i] :
( ( ! [SY519: $i] :
( ~ ( element @ SY519 @ ( powerset @ SV81 ) )
| ( ( subset_complement @ SV81 @ ( subset_complement @ SV81 @ SY519 ) )
= SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1007,plain,
! [SV82: $i] :
( ( ~ ( relation @ SV82 )
| ( ( relation_inverse @ ( relation_inverse @ SV82 ) )
= SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1008,plain,
! [SV83: $i] :
( ( ! [SY520: $i] :
( ~ ( element @ SY520 @ ( powerset @ ( powerset @ SV83 ) ) )
| ( ( complements_of_subsets @ SV83 @ ( complements_of_subsets @ SV83 @ SY520 ) )
= SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1009,plain,
( ( empty @ sK29_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(1010,plain,
! [SV84: $i] :
( ( ! [SY521: $i,SY522: $i] :
( ~ ( element @ SY521 @ ( powerset @ SV84 ) )
| ~ ( element @ SY522 @ ( powerset @ SV84 ) )
| ( ( subset_difference @ SV84 @ SY521 @ SY522 )
= ( set_difference @ SY521 @ SY522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1011,plain,
! [SV85: $i] :
( ( subset @ SV85 @ SV85 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1012,plain,
! [SV86: $i] :
( ( ! [SY523: $i] :
( ~ ( disjoint @ SV86 @ SY523 )
| ( disjoint @ SY523 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1013,plain,
! [SV87: $i] :
( ( ( set_union2 @ SV87 @ empty_set )
= SV87 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1014,plain,
! [SV88: $i] :
( ( ! [SY524: $i] :
( ~ ( in @ SV88 @ SY524 )
| ( element @ SV88 @ SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1015,plain,
! [SV89: $i] :
( ( ! [SY525: $i] :
( ~ ( element @ SV89 @ SY525 )
| ( empty @ SY525 )
| ( in @ SV89 @ SY525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1016,plain,
! [SV90: $i] :
( ( ( set_difference @ SV90 @ empty_set )
= SV90 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1017,plain,
! [SV91: $i] :
( ( ( set_difference @ empty_set @ SV91 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1018,plain,
! [SV92: $i] :
( ( ! [SY526: $i,SY527: $i] :
( ~ ( element @ SY526 @ ( powerset @ SY527 ) )
| ~ ( in @ SV92 @ SY526 )
| ( element @ SV92 @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1019,plain,
! [SV93: $i] :
( ( ! [SY528: $i,SY529: $i] :
( ~ ( element @ SY528 @ ( powerset @ SY529 ) )
| ~ ( in @ SV93 @ SY528 )
| ~ ( empty @ SY529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1020,plain,
! [SV94: $i] :
( ( ~ ( empty @ SV94 )
| ( SV94 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1021,plain,
! [SV95: $i] :
( ( ! [SY530: $i] :
( ~ ( empty @ SY530 )
| ~ ( in @ SV95 @ SY530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1022,plain,
! [SV96: $i] :
( ( ! [SY531: $i] :
( ( SV96 = SY531 )
| ~ ( empty @ SV96 )
| ~ ( empty @ SY531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1023,plain,
( ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY373 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(1024,plain,
( ( ~ ( sK12_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
| ~ ( ~ sK12_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) )
| ~ ( ( sK10_SY386 != sK11_SY388 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(1025,plain,
( ( ~ ~ ( empty @ sK70_A )
| ~ ( finite @ sK70_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(1026,plain,
! [SV97: $i] :
( ( ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY532 ) ) )
| ~ ( ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY532 ) ) )
| ( SY533
= ( set_union2 @ SV97 @ SY532 ) ) )
| ~ ! [SY534: $i,SY535: $i] :
( ( SY535
!= ( set_union2 @ SV97 @ SY534 ) )
| ~ ( ~ ! [SY536: $i] :
( ~ ( in @ SY536 @ SY535 )
| ( in @ SY536 @ SV97 )
| ( in @ SY536 @ SY534 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SV97 )
| ( in @ SY537 @ SY535 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY534 )
| ( in @ SX3 @ SY535 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1027,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(1028,plain,
! [SV98: $i] :
( ( ! [SY539: $i] :
( ~ ( ~ ! [SY540: $i] :
( ~ ( in @ SY540 @ SY539 )
| ~ ( in @ SY540 @ ( sK5_C @ SY539 @ SV98 ) ) )
| ~ ( in @ ( sK5_C @ SY539 @ SV98 ) @ SY539 ) )
| ~ ( in @ SV98 @ SY539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1029,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(1030,plain,
! [SV99: $i] :
( ( ~ ( ~ ( relation @ ( sK66_B @ SV99 ) )
| ~ ( well_orders @ ( sK66_B @ SV99 ) @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1031,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(1032,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(1033,plain,
! [SV100: $i] :
( ( ~ ( ~ ( in @ ( sK65_B @ SV100 ) @ SV100 )
| ~ ( ~ ( ordinal @ ( sK65_B @ SV100 ) )
| ~ ( subset @ ( sK65_B @ SV100 ) @ SV100 ) ) )
| ( ordinal @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1034,plain,
! [SV101: $i] :
( ( ~ ( ~ ! [SY541: $i] :
( ~ ( subset @ SY541 @ ( sK67_B @ SV101 ) )
| ( are_equipotent @ SY541 @ ( sK67_B @ SV101 ) )
| ( in @ SY541 @ ( sK67_B @ SV101 ) ) )
| ~ ~ ( ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ ( sK67_B @ SV101 ) )
| ( in @ ( powerset @ SY542 ) @ ( sK67_B @ SV101 ) ) )
| ~ ~ ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) )
| ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1035,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK53_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(1036,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(1037,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(1038,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(1039,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK60_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK60_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK58_C @ SX1 @ SX0 ) @ ( sK59_SY431 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(1040,plain,
! [SV102: $i] :
( ( ~ ( ~ ! [SY545: $i,SY546: $i] :
( ~ ( in @ SV102 @ SY546 )
| ~ ( in @ SY545 @ SY546 )
| ( subset @ ( unordered_pair @ SV102 @ SY545 ) @ SY546 ) )
| ~ ~ ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY547 ) @ SY548 )
| ( in @ SV102 @ SY548 ) )
| ~ ! [SY549: $i,SY550: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY549 ) @ SY550 )
| ( in @ SY549 @ SY550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1041,plain,
! [SV103: $i] :
( ( ~ ( ~ ! [SY551: $i,SY552: $i] :
( ~ ( ~ ( ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY551 )
| ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) )
| ~ ( ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY551 )
| ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) ) ) )
| ( SY552
= ( set_intersection2 @ SV103 @ SY551 ) ) )
| ~ ! [SY553: $i,SY554: $i] :
( ( SY554
!= ( set_intersection2 @ SV103 @ SY553 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SV103 )
| ~ ( in @ SY555 @ SY553 )
| ( in @ SY555 @ SY554 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ~ ( in @ SY556 @ SY554 )
| ( in @ SY556 @ SV103 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY554 )
| ( in @ SX3 @ SY553 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1042,plain,
( ( ~ ( function @ sK36_A )
| ~ ( relation @ sK36_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(1043,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK52_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK52_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(1044,plain,
! [SV104: $i] :
( ( ~ ( relation @ SV104 )
| ~ ( ~ ! [SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) ) )
| ( SV104 = SY558 ) )
| ~ ! [SY559: $i] :
( ~ ( relation @ SY559 )
| ( SV104 != SY559 )
| ~ ( ~ ! [SY560: $i,SY561: $i] :
( ~ ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SV104 )
| ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SY559 ) )
| ~ ! [SY562: $i,SY563: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SY559 )
| ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SV104 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1045,plain,
! [SV105: $i] :
( ( ( empty @ SV105 )
| ~ ( ~ ~ ( ~ ( element @ ( sK28_B @ SV105 ) @ ( powerset @ SV105 ) )
| ~ ~ ( empty @ ( sK28_B @ SV105 ) ) )
| ~ ( finite @ ( sK28_B @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1046,plain,
! [SV106: $i] :
( ( ! [SY564: $i] :
( ( empty @ SV106 )
| ~ ( relation @ SY564 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY565: $i] :
( ~ ( in @ SY565 @ ( sK26_SY414 @ SY564 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SY564 @ SV106 ) @ SY565 ) @ SY564 ) )
| ~ ~ ( ( ( sK22_C @ SY564 @ SV106 )
!= ( sK26_SY414 @ SY564 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SY564 @ SV106 ) @ ( sK26_SY414 @ SY564 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SY564 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SY564 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY566: $i] :
( ~ ( in @ SY566 @ ( sK25_SY420 @ SY564 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SY564 @ SV106 ) @ SY566 ) @ SY564 ) )
| ~ ~ ( ( ( sK22_C @ SY564 @ SV106 )
!= ( sK25_SY420 @ SY564 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SY564 @ SV106 ) @ ( sK25_SY420 @ SY564 @ SV106 ) ) ) ) )
| ~ ( ( ( sK23_SY407 @ SY564 @ SV106 )
!= ( sK24_SY413 @ SY564 @ SV106 ) ) ) )
| ~ ( ~ ! [SY567: $i] :
( ! [SY568: $i] :
( ~ ( in @ SY568 @ SV106 )
| ! [SY569: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY569 @ SY568 @ SY567 @ SY564 @ SV106 ) @ SY569 )
| ~ ~ ( in @ ( ordered_pair @ SY567 @ ( sK21_K @ SY569 @ SY568 @ SY567 @ SY564 @ SV106 ) ) @ SY564 ) )
| ( SY568 != SY569 )
| ~ ( in @ SY567 @ SY569 ) ) )
| ( in @ SY567 @ ( sK18_C @ SY564 @ SV106 ) ) )
| ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ ( sK18_C @ SY564 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY570 @ SY564 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ ( sK20_SY404 @ SY570 @ SY564 @ SV106 ) )
| ( in @ ( ordered_pair @ SY570 @ SY571 ) @ SY564 ) )
| ~ ~ ( ( ( sK19_E @ SY570 @ SY564 @ SV106 )
!= ( sK20_SY404 @ SY570 @ SY564 @ SV106 ) )
| ~ ( in @ SY570 @ ( sK20_SY404 @ SY570 @ SY564 @ SV106 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1047,plain,
( ( ~ ~ ( ~ ( empty @ sK32_A )
| ~ ( relation @ sK32_A ) )
| ~ ( function @ sK32_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(1048,plain,
! [SV107: $i] :
( ( ~ ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV107 )
| ~ ( ordinal @ SY572 )
| ( in @ SY572 @ ( sK68_B @ SV107 ) ) )
| ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK68_B @ SV107 ) )
| ( in @ SY573 @ SV107 ) )
| ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ ( sK68_B @ SV107 ) )
| ( ordinal @ SY574 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1049,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(1050,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY425 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK41_SY425 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK39_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(1051,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(1052,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(1053,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK45_B @ SX0 )
!= ( sK46_SY427 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK46_SY427 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK45_B @ SX0 ) @ ( sK46_SY427 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK46_SY427 @ SX0 ) @ ( sK45_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(1054,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(1055,plain,
! [SV108: $i] :
( ( ! [SY575: $i] :
~ ( ~ ! [SY576: $i,SY577: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 ) @ SY577 )
| ( ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 )
!= SY576 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 ) @ SY577 )
| ( ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 ) @ SY577 )
| ( ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 )
!= SY575 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 ) @ SY577 )
| ( ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 )
= SY576 )
| ( ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 )
= SV108 )
| ( ( sK61_E @ SY577 @ SY576 @ SY575 @ SV108 )
= SY575 ) ) )
| ( SY577
= ( unordered_triple @ SV108 @ SY575 @ SY576 ) ) )
| ~ ! [SY578: $i,SY579: $i] :
( ( SY579
!= ( unordered_triple @ SV108 @ SY575 @ SY578 ) )
| ~ ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SY579 )
| ( SY580 = SY578 )
| ( SY580 = SV108 )
| ( SY580 = SY575 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY578 )
| ( in @ SX4 @ SY579 ) )
| ~ ~ ( ~ ! [SY582: $i] :
( ( SY582 != SV108 )
| ( in @ SY582 @ SY579 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SY575 )
| ( in @ SX4 @ SY579 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1056,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(1057,plain,
! [SV109: $i] :
( ( ! [SY584: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SY584 @ SV109 ) @ SV109 )
| ~ ( in @ ( sK6_C @ SY584 @ SV109 ) @ SY584 ) )
| ~ ( ( in @ ( sK6_C @ SY584 @ SV109 ) @ SV109 )
| ( in @ ( sK6_C @ SY584 @ SV109 ) @ SY584 ) ) )
| ( SV109 = SY584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1058,plain,
! [SV110: $i] :
( ( ~ ( ~ ( element @ ( sK30_B @ SV110 ) @ ( powerset @ SV110 ) )
| ~ ( empty @ ( sK30_B @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1059,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(1060,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(1061,plain,
( ( ~ ~ ( empty @ sK31_A )
| ~ ( relation @ sK31_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(1062,plain,
! [SV111: $i] :
( ( ~ ( ~ ! [SY585: $i,SY586: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY585 )
| ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY585 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) ) ) )
| ( SY586
= ( set_difference @ SV111 @ SY585 ) ) )
| ~ ! [SY587: $i,SY588: $i] :
( ( SY588
!= ( set_difference @ SV111 @ SY587 ) )
| ~ ( ~ ! [SY589: $i] :
( ~ ( in @ SY589 @ SV111 )
| ( in @ SY589 @ SY587 )
| ( in @ SY589 @ SY588 ) )
| ~ ~ ( ~ ! [SY590: $i] :
( ~ ( in @ SY590 @ SY588 )
| ( in @ SY590 @ SV111 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY588 )
| ~ ( in @ SX3 @ SY587 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1063,plain,
! [SV112: $i] :
( ( ! [SY592: $i] :
( ~ ( element @ SY592 @ ( powerset @ SV112 ) )
| ~ ( ~ ! [SY593: $i] :
( ~ ( element @ SY593 @ ( powerset @ SV112 ) )
| ~ ( disjoint @ SY592 @ SY593 )
| ( subset @ SY592 @ ( subset_complement @ SV112 @ SY593 ) ) )
| ~ ! [SY594: $i] :
( ~ ( element @ SY594 @ ( powerset @ SV112 ) )
| ~ ( subset @ SY592 @ ( subset_complement @ SV112 @ SY594 ) )
| ( disjoint @ SY592 @ SY594 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1064,plain,
! [SV113: $i] :
( ( ~ ( ~ ! [SY595: $i] :
( ~ ( subset @ SV113 @ SY595 )
| ! [SY596: $i] : ( subset @ ( cartesian_product2 @ SV113 @ SY596 ) @ ( cartesian_product2 @ SY595 @ SY596 ) ) )
| ~ ! [SY597: $i] :
( ~ ( subset @ SV113 @ SY597 )
| ! [SY598: $i] : ( subset @ ( cartesian_product2 @ SY598 @ SV113 ) @ ( cartesian_product2 @ SY598 @ SY597 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1065,plain,
! [SV114: $i] :
( ( ~ ( ~ ! [SY599: $i] :
( ~ ( subset @ SY599 @ ( sK3_B @ SV114 ) )
| ( are_equipotent @ SY599 @ ( sK3_B @ SV114 ) )
| ( in @ SY599 @ ( sK3_B @ SV114 ) ) )
| ~ ~ ( ~ ! [SY600: $i] :
( ~ ( ~ ! [SY601: $i] :
( ~ ( subset @ SY601 @ SY600 )
| ( in @ SY601 @ ( sK4_SY376 @ SY600 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SY600 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SY600 @ ( sK3_B @ SV114 ) ) )
| ~ ~ ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1066,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(1067,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1068,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK51_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK51_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(1069,plain,
( ( ~ ( relation @ sK27_A )
| ~ ( relation_empty_yielding @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(1070,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1071,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1072,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(1073,plain,
! [SV115: $i] :
( ( ( empty @ SV115 )
| ~ ( ~ ( element @ ( sK34_B @ SV115 ) @ ( powerset @ SV115 ) )
| ~ ~ ( empty @ ( sK34_B @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1074,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(1075,plain,
! [SV116: $i] :
( ( ! [SY604: $i] :
( ~ ( ~ ( in @ ( sK69_C @ SY604 @ SV116 ) @ SV116 )
| ~ ~ ( in @ ( sK69_C @ SY604 @ SV116 ) @ SY604 ) )
| ( element @ SV116 @ ( powerset @ SY604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1076,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1077,plain,
! [SV117: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ( ( sK17_SY395 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) ) )
| ~ ( ( ( sK16_SY393 @ SV117 )
!= ( sK17_SY395 @ SV117 ) ) ) )
| ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1078,plain,
! [SV118: $i] :
( ( ~ ( relation @ SV118 )
| ~ ( ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SY608 ) )
| ( subset @ SV118 @ SY608 ) )
| ~ ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ~ ( subset @ SV118 @ SY609 )
| ! [SY610: $i,SY611: $i] :
( ~ ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SV118 )
| ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SY609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1079,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1080,plain,
! [SV119: $i] :
( ( ~ ( ~ ! [SY612: $i,SY613: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
!= SY612 ) ) )
| ~ ( ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
= SV119 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
= SY612 ) ) )
| ( SY613
= ( unordered_pair @ SV119 @ SY612 ) ) )
| ~ ! [SY614: $i,SY615: $i] :
( ( SY615
!= ( unordered_pair @ SV119 @ SY614 ) )
| ~ ( ~ ! [SY616: $i] :
( ~ ( in @ SY616 @ SY615 )
| ( SY616 = SV119 )
| ( SY616 = SY614 ) )
| ~ ~ ( ~ ! [SY617: $i] :
( ( SY617 != SV119 )
| ( in @ SY617 @ SY615 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY614 )
| ( in @ SX3 @ SY615 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1081,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK54_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK54_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK54_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK54_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1082,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1083,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ ( sK57_SY429 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(1084,plain,
( ( ~ ( empty @ sK35_A )
| ~ ( relation @ sK35_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1085,plain,
! [SV1: $i] :
( ( ( ! [SY442: $i] :
( ~ ( finite @ SY442 )
| ~ ( subset @ SV1 @ SY442 ) ) )
= $true )
| ( ( finite @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1086,plain,
! [SV120: $i,SV2: $i] :
( ( subset @ ( set_intersection2 @ SV2 @ SV120 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1087,plain,
! [SV121: $i,SV3: $i] :
( ( ! [SY619: $i] :
( ~ ( subset @ SV3 @ SV121 )
| ~ ( subset @ SV3 @ SY619 )
| ( subset @ SV3 @ ( set_intersection2 @ SV121 @ SY619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1088,plain,
! [SV122: $i,SV4: $i] :
( ( ~ ( subset @ SV4 @ SV122 )
| ! [SY620: $i] : ( subset @ ( set_intersection2 @ SV4 @ SY620 ) @ ( set_intersection2 @ SV122 @ SY620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1089,plain,
! [SV123: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV123 )
| ( ( set_intersection2 @ SV5 @ SV123 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1090,plain,
! [SV124: $i,SV6: $i] :
( ( ( set_difference @ SV6 @ ( set_difference @ SV6 @ SV124 ) )
= ( set_intersection2 @ SV6 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1091,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( finite @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(1092,plain,
! [SV8: $i] :
( ( ( ~ ( finite @ SV8 ) )
= $true )
| ( ( ! [SY450: $i] :
( ~ ( element @ SY450 @ ( powerset @ SV8 ) )
| ( finite @ SY450 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1093,plain,
! [SV125: $i,SV9: $i] :
( ( ( set_intersection2 @ SV9 @ SV125 )
= ( set_intersection2 @ SV125 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1094,plain,
! [SV10: $i,SV126: $i] :
( ( ~ ( finite @ SV126 )
| ( finite @ ( set_intersection2 @ SV10 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1095,plain,
! [SV11: $i] :
( ( ( ~ ( finite @ SV11 ) )
= $true )
| ( ( ! [SY453: $i] : ( finite @ ( set_intersection2 @ SV11 @ SY453 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1096,plain,
! [SV127: $i,SV12: $i] :
( ( ~ ( relation @ SV12 )
| ~ ( relation @ SV127 )
| ( relation @ ( set_intersection2 @ SV12 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1097,plain,
! [SV15: $i] :
( ( ( singleton @ SV15 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1098,plain,
! [SV128: $i,SV16: $i] :
( ( ~ ( disjoint @ ( singleton @ SV16 ) @ SV128 )
| ~ ( in @ SV16 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1099,plain,
! [SV129: $i,SV17: $i] :
( ( ( in @ SV17 @ SV129 )
| ( disjoint @ ( singleton @ SV17 ) @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1100,plain,
! [SV18: $i,SV130: $i] :
( ( ~ ( element @ SV130 @ ( powerset @ SV18 ) )
| ! [SY621: $i] :
( ~ ( in @ SY621 @ SV130 )
| ( in @ SY621 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1101,plain,
! [SV131: $i,SV19: $i] :
( ( ~ ( subset @ SV19 @ SV131 )
| ! [SY622: $i] :
( ( in @ SY622 @ SV19 )
| ( subset @ SV19 @ ( set_difference @ SV131 @ ( singleton @ SY622 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1102,plain,
! [SV132: $i,SV20: $i] :
( ( ~ ( in @ SV20 @ SV132 )
| ( subset @ SV20 @ ( union @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1103,plain,
! [SV22: $i,SV133: $i] :
( ( ~ ( relation @ SV133 )
| ( subset @ ( relation_rng_restriction @ SV22 @ SV133 ) @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1104,plain,
! [SV134: $i,SV23: $i] :
( ( ! [SY623: $i,SY624: $i] :
( ~ ( subset @ SV23 @ SV134 )
| ~ ( subset @ SY623 @ SY624 )
| ( subset @ ( cartesian_product2 @ SV23 @ SY623 ) @ ( cartesian_product2 @ SV134 @ SY624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1105,plain,
! [SV135: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV135 )
| ( ( set_union2 @ SV24 @ SV135 )
= SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1106,plain,
! [SV136: $i,SV25: $i] :
( ( ! [SY625: $i,SY626: $i] :
( ~ ( relation_of2_as_subset @ SY626 @ SY625 @ SV25 )
| ~ ( subset @ SV25 @ SV136 )
| ( relation_of2_as_subset @ SY626 @ SY625 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1107,plain,
! [SV137: $i,SV26: $i] :
( ( ! [SY627: $i] :
( ~ ( relation @ SY627 )
| ~ ( subset @ SV26 @ SV137 )
| ( subset @ ( relation_inverse_image @ SY627 @ SV26 ) @ ( relation_inverse_image @ SY627 @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1108,plain,
! [SV138: $i,SV27: $i] :
( ( ! [SY628: $i] :
( ~ ( subset @ SV27 @ SV138 )
| ~ ( subset @ SV138 @ SY628 )
| ( subset @ SV27 @ SY628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1109,plain,
! [SV28: $i,SV139: $i] :
( ( ~ ( ordinal @ SV139 )
| ~ ( in @ SV28 @ SV139 )
| ( ordinal @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1110,plain,
! [SV29: $i] :
( ( ( ~ ( ordinal @ SV29 ) )
= $true )
| ( ( ! [SY475: $i] :
( ~ ( ordinal @ SY475 )
| ( in @ SV29 @ SY475 )
| ( SV29 = SY475 )
| ( in @ SY475 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1111,plain,
! [SV140: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV140 )
| ! [SY629: $i] : ( subset @ ( set_difference @ SV31 @ SY629 ) @ ( set_difference @ SV140 @ SY629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1112,plain,
! [SV141: $i,SV32: $i] :
( ( subset @ ( set_difference @ SV32 @ SV141 ) @ SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1113,plain,
! [SV142: $i,SV33: $i] :
( ( ( set_union2 @ SV33 @ ( set_difference @ SV142 @ SV33 ) )
= ( set_union2 @ SV33 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1114,plain,
! [SV143: $i,SV34: $i] :
( ( ! [SY630: $i] :
( ~ ( in @ SV34 @ SV143 )
| ~ ( in @ SV143 @ SY630 )
| ~ ( in @ SY630 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1115,plain,
! [SV35: $i] :
( ( ( ~ ( subset @ SV35 @ empty_set ) )
= $true )
| ( ( SV35 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1116,plain,
! [SV144: $i,SV36: $i] :
( ( ( set_difference @ ( set_union2 @ SV36 @ SV144 ) @ SV144 )
= ( set_difference @ SV36 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1117,plain,
! [SV145: $i,SV37: $i] :
( ( ~ ( subset @ SV37 @ SV145 )
| ( SV145
= ( set_union2 @ SV37 @ ( set_difference @ SV145 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1118,plain,
! [SV38: $i,SV146: $i] :
( ( ~ ( element @ SV146 @ ( powerset @ ( powerset @ SV38 ) ) )
| ( SV146 = empty_set )
| ( ( complements_of_subsets @ SV38 @ SV146 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1119,plain,
! [SV39: $i] :
( ( ( SV39 = empty_set )
= $true )
| ( ( ! [SY485: $i] :
( ~ ( element @ SY485 @ ( powerset @ SV39 ) )
| ! [SY486: $i] :
( ~ ( element @ SY486 @ SV39 )
| ( in @ SY486 @ SY485 )
| ( in @ SY486 @ ( subset_complement @ SV39 @ SY485 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1120,plain,
! [SV147: $i,SV40: $i] :
( ( ! [SY631: $i] :
( ~ ( element @ SY631 @ ( powerset @ SV40 ) )
| ~ ( in @ SV147 @ ( subset_complement @ SV40 @ SY631 ) )
| ~ ( in @ SV147 @ SY631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1121,plain,
! [SV41: $i] :
( ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK62_B @ SV41 ) @ ( sK63_SY434 @ SV41 ) ) @ SV41 )
| ( SV41 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1122,plain,
! [SV42: $i,SV148: $i] :
( ( ~ ( proper_subset @ SV148 @ SV42 )
| ~ ( subset @ SV42 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1123,plain,
! [SV43: $i,SV149: $i] :
( ( ! [SY632: $i] :
( ~ ( disjoint @ SV149 @ SY632 )
| ~ ( subset @ SV43 @ SV149 )
| ( disjoint @ SV43 @ SY632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1124,plain,
! [SV150: $i,SV44: $i] :
( ( ~ ( subset @ ( singleton @ SV44 ) @ ( singleton @ SV150 ) )
| ( SV44 = SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1125,plain,
! [SV151: $i,SV45: $i] :
( ( subset @ SV45 @ ( set_union2 @ SV45 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1126,plain,
! [SV46: $i,SV152: $i] :
( ( ~ ( relation @ SV152 )
| ( subset @ ( relation_dom_restriction @ SV152 @ SV46 ) @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1127,plain,
! [SV153: $i,SV47: $i] :
( ( ! [SY633: $i] :
( ~ ( subset @ SV47 @ SV153 )
| ~ ( subset @ SY633 @ SV153 )
| ( subset @ ( set_union2 @ SV47 @ SY633 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1128,plain,
! [SV154: $i,SV48: $i] :
( ( ~ ( in @ SV48 @ SV154 )
| ( subset @ SV48 @ ( union @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1129,plain,
! [SV155: $i,SV50: $i] :
( ( ~ ( in @ SV50 @ SV155 )
| ~ ( in @ SV155 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1130,plain,
! [SV51: $i] :
( ( ( ~ ( empty @ SV51 ) )
= $true )
| ( ( function @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1131,plain,
! [SV52: $i] :
( ( ( ~ ( empty @ SV52 ) )
= $true )
| ( ( relation @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1132,plain,
! [SV156: $i,SV53: $i] :
( ( ! [SY634: $i] :
( ~ ( element @ SY634 @ ( powerset @ ( cartesian_product2 @ SV53 @ SV156 ) ) )
| ( relation @ SY634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1133,plain,
! [SV54: $i,SV157: $i] :
( ( ~ ( element @ SV157 @ ( powerset @ SV54 ) )
| ( ( subset_complement @ SV54 @ SV157 )
= ( set_difference @ SV54 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1134,plain,
! [SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( ! [SY502: $i] : ( relation @ ( relation_restriction @ SV57 @ SY502 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1135,plain,
! [SV58: $i,SV158: $i] :
( ( ~ ( element @ SV158 @ ( powerset @ SV58 ) )
| ( element @ ( subset_complement @ SV58 @ SV158 ) @ ( powerset @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1136,plain,
! [SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1137,plain,
! [SV159: $i,SV60: $i] :
( ( ~ ( relation @ SV60 )
| ~ ( relation @ SV159 )
| ( relation @ ( relation_composition @ SV60 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1138,plain,
! [SV61: $i,SV160: $i] :
( ( ~ ( element @ SV160 @ ( powerset @ ( powerset @ SV61 ) ) )
| ( element @ ( union_of_subsets @ SV61 @ SV160 ) @ ( powerset @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1139,plain,
! [SV63: $i,SV161: $i] :
( ( ~ ( element @ SV161 @ ( powerset @ ( powerset @ SV63 ) ) )
| ( element @ ( meet_of_subsets @ SV63 @ SV161 ) @ ( powerset @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1140,plain,
! [SV64: $i,SV162: $i] :
( ( ! [SY635: $i] :
( ~ ( element @ SV162 @ ( powerset @ SV64 ) )
| ~ ( element @ SY635 @ ( powerset @ SV64 ) )
| ( element @ ( subset_difference @ SV64 @ SV162 @ SY635 ) @ ( powerset @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1141,plain,
! [SV65: $i] :
( ( ( ~ ( relation @ SV65 ) )
= $true )
| ( ( ! [SY509: $i] : ( relation @ ( relation_dom_restriction @ SV65 @ SY509 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1142,plain,
! [SV66: $i,SV163: $i] :
( ( ~ ( element @ SV163 @ ( powerset @ ( powerset @ SV66 ) ) )
| ( element @ ( complements_of_subsets @ SV66 @ SV163 ) @ ( powerset @ ( powerset @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1143,plain,
! [SV67: $i,SV164: $i] :
( ( ~ ( relation @ SV164 )
| ( relation @ ( relation_rng_restriction @ SV67 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1144,plain,
! [SV69: $i] :
( ( empty @ ( succ @ SV69 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1145,plain,
! [SV70: $i] :
( ( empty @ ( powerset @ SV70 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1146,plain,
! [SV165: $i,SV71: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV71 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1147,plain,
! [SV166: $i,SV72: $i] :
( ( ~ ( relation @ SV72 )
| ~ ( relation @ SV166 )
| ( relation @ ( set_union2 @ SV72 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1148,plain,
! [SV73: $i] :
( ( empty @ ( singleton @ SV73 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1149,plain,
! [SV74: $i] :
( ( ( empty @ SV74 )
= $true )
| ( ( ! [SY514: $i] :
~ ( empty @ ( set_union2 @ SV74 @ SY514 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1150,plain,
! [SV167: $i,SV75: $i] :
( ( ~ ( relation @ SV75 )
| ~ ( relation @ SV167 )
| ( relation @ ( set_difference @ SV75 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1151,plain,
! [SV168: $i,SV76: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV76 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1152,plain,
! [SV77: $i] :
( ( ( empty @ SV77 )
= $true )
| ( ( ! [SY517: $i] :
~ ( empty @ ( set_union2 @ SY517 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1153,plain,
! [SV169: $i,SV78: $i] :
( ( ( empty @ SV78 )
| ( empty @ SV169 )
| ~ ( empty @ ( cartesian_product2 @ SV78 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1154,plain,
! [SV79: $i] :
( ( ( ( empty @ SV79 )
| ~ ( relation @ SV79 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1155,plain,
! [SV80: $i] :
( ( ( ( empty @ SV80 )
| ~ ( relation @ SV80 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1156,plain,
! [SV81: $i,SV170: $i] :
( ( ~ ( element @ SV170 @ ( powerset @ SV81 ) )
| ( ( subset_complement @ SV81 @ ( subset_complement @ SV81 @ SV170 ) )
= SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1157,plain,
! [SV82: $i] :
( ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV82 ) )
= SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1158,plain,
! [SV83: $i,SV171: $i] :
( ( ~ ( element @ SV171 @ ( powerset @ ( powerset @ SV83 ) ) )
| ( ( complements_of_subsets @ SV83 @ ( complements_of_subsets @ SV83 @ SV171 ) )
= SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1159,plain,
! [SV84: $i,SV172: $i] :
( ( ! [SY636: $i] :
( ~ ( element @ SV172 @ ( powerset @ SV84 ) )
| ~ ( element @ SY636 @ ( powerset @ SV84 ) )
| ( ( subset_difference @ SV84 @ SV172 @ SY636 )
= ( set_difference @ SV172 @ SY636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1160,plain,
! [SV173: $i,SV86: $i] :
( ( ~ ( disjoint @ SV86 @ SV173 )
| ( disjoint @ SV173 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1161,plain,
! [SV174: $i,SV88: $i] :
( ( ~ ( in @ SV88 @ SV174 )
| ( element @ SV88 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1162,plain,
! [SV175: $i,SV89: $i] :
( ( ~ ( element @ SV89 @ SV175 )
| ( empty @ SV175 )
| ( in @ SV89 @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1163,plain,
! [SV92: $i,SV176: $i] :
( ( ! [SY637: $i] :
( ~ ( element @ SV176 @ ( powerset @ SY637 ) )
| ~ ( in @ SV92 @ SV176 )
| ( element @ SV92 @ SY637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1164,plain,
! [SV93: $i,SV177: $i] :
( ( ! [SY638: $i] :
( ~ ( element @ SV177 @ ( powerset @ SY638 ) )
| ~ ( in @ SV93 @ SV177 )
| ~ ( empty @ SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1165,plain,
! [SV94: $i] :
( ( ( ~ ( empty @ SV94 ) )
= $true )
| ( ( SV94 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1166,plain,
! [SV95: $i,SV178: $i] :
( ( ~ ( empty @ SV178 )
| ~ ( in @ SV95 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1167,plain,
! [SV179: $i,SV96: $i] :
( ( ( SV96 = SV179 )
| ~ ( empty @ SV96 )
| ~ ( empty @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1168,plain,
( ( ~ ( sK12_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1169,plain,
( ( ~ ( ~ sK12_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) )
| ~ ( ( sK10_SY386 != sK11_SY388 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1170,plain,
( ( ~ ~ ( empty @ sK70_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1025]) ).
thf(1171,plain,
( ( ~ ( finite @ sK70_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1025]) ).
thf(1172,plain,
! [SV97: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY532 ) ) )
| ~ ( ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY532 ) ) )
| ( SY533
= ( set_union2 @ SV97 @ SY532 ) ) )
| ~ ! [SY534: $i,SY535: $i] :
( ( SY535
!= ( set_union2 @ SV97 @ SY534 ) )
| ~ ( ~ ! [SY536: $i] :
( ~ ( in @ SY536 @ SY535 )
| ( in @ SY536 @ SV97 )
| ( in @ SY536 @ SY534 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SV97 )
| ( in @ SY537 @ SY535 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY534 )
| ( in @ SX3 @ SY535 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1173,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1027]) ).
thf(1174,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1027]) ).
thf(1175,plain,
! [SV98: $i,SV180: $i] :
( ( ~ ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV180 )
| ~ ( in @ SY639 @ ( sK5_C @ SV180 @ SV98 ) ) )
| ~ ( in @ ( sK5_C @ SV180 @ SV98 ) @ SV180 ) )
| ~ ( in @ SV98 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1176,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1177,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1178,plain,
! [SV99: $i] :
( ( ~ ( relation @ ( sK66_B @ SV99 ) )
| ~ ( well_orders @ ( sK66_B @ SV99 ) @ SV99 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1179,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1180,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1181,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1182,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1183,plain,
! [SV100: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_B @ SV100 ) @ SV100 )
| ~ ( ~ ( ordinal @ ( sK65_B @ SV100 ) )
| ~ ( subset @ ( sK65_B @ SV100 ) @ SV100 ) ) ) )
= $true )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1184,plain,
! [SV101: $i] :
( ( ~ ! [SY541: $i] :
( ~ ( subset @ SY541 @ ( sK67_B @ SV101 ) )
| ( are_equipotent @ SY541 @ ( sK67_B @ SV101 ) )
| ( in @ SY541 @ ( sK67_B @ SV101 ) ) )
| ~ ~ ( ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ ( sK67_B @ SV101 ) )
| ( in @ ( powerset @ SY542 ) @ ( sK67_B @ SV101 ) ) )
| ~ ~ ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) )
| ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1185,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK53_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1186,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1187,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1188,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1189,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1190,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1191,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1192,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1193,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK60_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK60_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1039]) ).
thf(1194,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK58_C @ SX1 @ SX0 ) @ ( sK59_SY431 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1039]) ).
thf(1195,plain,
! [SV102: $i] :
( ( ~ ! [SY545: $i,SY546: $i] :
( ~ ( in @ SV102 @ SY546 )
| ~ ( in @ SY545 @ SY546 )
| ( subset @ ( unordered_pair @ SV102 @ SY545 ) @ SY546 ) )
| ~ ~ ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY547 ) @ SY548 )
| ( in @ SV102 @ SY548 ) )
| ~ ! [SY549: $i,SY550: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY549 ) @ SY550 )
| ( in @ SY549 @ SY550 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1196,plain,
! [SV103: $i] :
( ( ~ ! [SY551: $i,SY552: $i] :
( ~ ( ~ ( ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY551 )
| ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) )
| ~ ( ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY551 )
| ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) ) ) )
| ( SY552
= ( set_intersection2 @ SV103 @ SY551 ) ) )
| ~ ! [SY553: $i,SY554: $i] :
( ( SY554
!= ( set_intersection2 @ SV103 @ SY553 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SV103 )
| ~ ( in @ SY555 @ SY553 )
| ( in @ SY555 @ SY554 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ~ ( in @ SY556 @ SY554 )
| ( in @ SY556 @ SV103 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY554 )
| ( in @ SX3 @ SY553 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1197,plain,
( ( ~ ( function @ sK36_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1198,plain,
( ( ~ ( relation @ sK36_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1199,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK52_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK52_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1200,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1201,plain,
! [SV104: $i] :
( ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( ~ ( ~ ! [SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) ) )
| ( SV104 = SY558 ) )
| ~ ! [SY559: $i] :
( ~ ( relation @ SY559 )
| ( SV104 != SY559 )
| ~ ( ~ ! [SY560: $i,SY561: $i] :
( ~ ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SV104 )
| ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SY559 ) )
| ~ ! [SY562: $i,SY563: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SY559 )
| ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SV104 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1202,plain,
! [SV105: $i] :
( ( ( empty @ SV105 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK28_B @ SV105 ) @ ( powerset @ SV105 ) )
| ~ ~ ( empty @ ( sK28_B @ SV105 ) ) )
| ~ ( finite @ ( sK28_B @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1203,plain,
! [SV181: $i,SV106: $i] :
( ( ( empty @ SV106 )
| ~ ( relation @ SV181 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
| ~ ( ( ( sK23_SY407 @ SV181 @ SV106 )
!= ( sK24_SY413 @ SV181 @ SV106 ) ) ) )
| ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1204,plain,
( ( ~ ~ ( ~ ( empty @ sK32_A )
| ~ ( relation @ sK32_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1205,plain,
( ( ~ ( function @ sK32_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1206,plain,
! [SV107: $i] :
( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV107 )
| ~ ( ordinal @ SY572 )
| ( in @ SY572 @ ( sK68_B @ SV107 ) ) )
| ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK68_B @ SV107 ) )
| ( in @ SY573 @ SV107 ) )
| ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ ( sK68_B @ SV107 ) )
| ( ordinal @ SY574 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1207,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1049]) ).
thf(1208,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1049]) ).
thf(1209,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY425 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK41_SY425 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1210,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK39_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1211,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1212,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1213,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1214,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1215,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK45_B @ SX0 )
!= ( sK46_SY427 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK46_SY427 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK45_B @ SX0 ) @ ( sK46_SY427 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK46_SY427 @ SX0 ) @ ( sK45_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1216,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1217,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1218,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1219,plain,
! [SV108: $i,SV182: $i] :
( ( ~ ( ~ ! [SY647: $i,SY648: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SY647 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SV182 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SY647 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SV182 ) ) )
| ( SY648
= ( unordered_triple @ SV108 @ SV182 @ SY647 ) ) )
| ~ ! [SY649: $i,SY650: $i] :
( ( SY650
!= ( unordered_triple @ SV108 @ SV182 @ SY649 ) )
| ~ ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SY650 )
| ( SY651 = SY649 )
| ( SY651 = SV108 )
| ( SY651 = SV182 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY649 )
| ( in @ SX4 @ SY650 ) )
| ~ ~ ( ~ ! [SY582: $i] :
( ( SY582 != SV108 )
| ( in @ SY582 @ SY650 ) )
| ~ ! [SY654: $i] :
( ( SY654 != SV182 )
| ( in @ SY654 @ SY650 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1220,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1221,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1222,plain,
! [SV109: $i,SV183: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) )
| ~ ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) ) )
| ( SV109 = SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1223,plain,
! [SV110: $i] :
( ( ~ ( element @ ( sK30_B @ SV110 ) @ ( powerset @ SV110 ) )
| ~ ( empty @ ( sK30_B @ SV110 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1224,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1225,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1227,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1228,plain,
( ( ~ ~ ( empty @ sK31_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1229,plain,
( ( ~ ( relation @ sK31_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1230,plain,
! [SV111: $i] :
( ( ~ ! [SY585: $i,SY586: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY585 )
| ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY585 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) ) ) )
| ( SY586
= ( set_difference @ SV111 @ SY585 ) ) )
| ~ ! [SY587: $i,SY588: $i] :
( ( SY588
!= ( set_difference @ SV111 @ SY587 ) )
| ~ ( ~ ! [SY589: $i] :
( ~ ( in @ SY589 @ SV111 )
| ( in @ SY589 @ SY587 )
| ( in @ SY589 @ SY588 ) )
| ~ ~ ( ~ ! [SY590: $i] :
( ~ ( in @ SY590 @ SY588 )
| ( in @ SY590 @ SV111 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY588 )
| ~ ( in @ SX3 @ SY587 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1231,plain,
! [SV112: $i,SV184: $i] :
( ( ~ ( element @ SV184 @ ( powerset @ SV112 ) )
| ~ ( ~ ! [SY655: $i] :
( ~ ( element @ SY655 @ ( powerset @ SV112 ) )
| ~ ( disjoint @ SV184 @ SY655 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SY655 ) ) )
| ~ ! [SY656: $i] :
( ~ ( element @ SY656 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SY656 ) )
| ( disjoint @ SV184 @ SY656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1232,plain,
! [SV113: $i] :
( ( ~ ! [SY595: $i] :
( ~ ( subset @ SV113 @ SY595 )
| ! [SY596: $i] : ( subset @ ( cartesian_product2 @ SV113 @ SY596 ) @ ( cartesian_product2 @ SY595 @ SY596 ) ) )
| ~ ! [SY597: $i] :
( ~ ( subset @ SV113 @ SY597 )
| ! [SY598: $i] : ( subset @ ( cartesian_product2 @ SY598 @ SV113 ) @ ( cartesian_product2 @ SY598 @ SY597 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1233,plain,
! [SV114: $i] :
( ( ~ ! [SY599: $i] :
( ~ ( subset @ SY599 @ ( sK3_B @ SV114 ) )
| ( are_equipotent @ SY599 @ ( sK3_B @ SV114 ) )
| ( in @ SY599 @ ( sK3_B @ SV114 ) ) )
| ~ ~ ( ~ ! [SY600: $i] :
( ~ ( ~ ! [SY601: $i] :
( ~ ( subset @ SY601 @ SY600 )
| ( in @ SY601 @ ( sK4_SY376 @ SY600 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SY600 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SY600 @ ( sK3_B @ SV114 ) ) )
| ~ ~ ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1234,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1235,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1236,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1237,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1238,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK51_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK51_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1239,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1240,plain,
( ( ~ ( relation @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1241,plain,
( ( ~ ( relation_empty_yielding @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1242,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1243,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1244,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1245,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1246,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1247,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1248,plain,
! [SV115: $i] :
( ( ( empty @ SV115 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK34_B @ SV115 ) @ ( powerset @ SV115 ) )
| ~ ~ ( empty @ ( sK34_B @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1249,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1074]) ).
thf(1250,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1074]) ).
thf(1251,plain,
! [SV116: $i,SV185: $i] :
( ( ~ ( ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV116 )
| ~ ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV185 ) )
| ( element @ SV116 @ ( powerset @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1252,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1253,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1254,plain,
! [SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ( ( sK17_SY395 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) ) )
| ~ ( ( ( sK16_SY393 @ SV117 )
!= ( sK17_SY395 @ SV117 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1255,plain,
! [SV118: $i] :
( ( ( ~ ( relation @ SV118 ) )
= $true )
| ( ( ~ ( ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SY608 ) )
| ( subset @ SV118 @ SY608 ) )
| ~ ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ~ ( subset @ SV118 @ SY609 )
| ! [SY610: $i,SY611: $i] :
( ~ ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SV118 )
| ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SY609 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1256,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1257,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1258,plain,
! [SV119: $i] :
( ( ~ ! [SY612: $i,SY613: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
!= SY612 ) ) )
| ~ ( ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
= SV119 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
= SY612 ) ) )
| ( SY613
= ( unordered_pair @ SV119 @ SY612 ) ) )
| ~ ! [SY614: $i,SY615: $i] :
( ( SY615
!= ( unordered_pair @ SV119 @ SY614 ) )
| ~ ( ~ ! [SY616: $i] :
( ~ ( in @ SY616 @ SY615 )
| ( SY616 = SV119 )
| ( SY616 = SY614 ) )
| ~ ~ ( ~ ! [SY617: $i] :
( ( SY617 != SV119 )
| ( in @ SY617 @ SY615 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY614 )
| ( in @ SX3 @ SY615 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1259,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK54_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK54_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK54_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK54_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1260,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1261,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1262,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1263,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ ( sK57_SY429 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1264,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1265,plain,
( ( ~ ( empty @ sK35_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1084]) ).
thf(1266,plain,
( ( ~ ( relation @ sK35_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1084]) ).
thf(1267,plain,
! [SV1: $i,SV186: $i] :
( ( ( ~ ( finite @ SV186 )
| ~ ( subset @ SV1 @ SV186 ) )
= $true )
| ( ( finite @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1268,plain,
! [SV187: $i,SV121: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV121 )
| ~ ( subset @ SV3 @ SV187 )
| ( subset @ SV3 @ ( set_intersection2 @ SV121 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1269,plain,
! [SV122: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV122 ) )
= $true )
| ( ( ! [SY620: $i] : ( subset @ ( set_intersection2 @ SV4 @ SY620 ) @ ( set_intersection2 @ SV122 @ SY620 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1270,plain,
! [SV123: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV123 ) )
= $true )
| ( ( ( set_intersection2 @ SV5 @ SV123 )
= SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1271,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( finite @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1272,plain,
! [SV8: $i] :
( ( ( finite @ SV8 )
= $false )
| ( ( ! [SY450: $i] :
( ~ ( element @ SY450 @ ( powerset @ SV8 ) )
| ( finite @ SY450 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1273,plain,
! [SV10: $i,SV126: $i] :
( ( ( ~ ( finite @ SV126 ) )
= $true )
| ( ( finite @ ( set_intersection2 @ SV10 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1274,plain,
! [SV11: $i] :
( ( ( finite @ SV11 )
= $false )
| ( ( ! [SY453: $i] : ( finite @ ( set_intersection2 @ SV11 @ SY453 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1275,plain,
! [SV127: $i,SV12: $i] :
( ( ( ~ ( relation @ SV12 )
| ~ ( relation @ SV127 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV12 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1276,plain,
! [SV128: $i,SV16: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV16 ) @ SV128 ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1277,plain,
! [SV129: $i,SV17: $i] :
( ( ( in @ SV17 @ SV129 )
= $true )
| ( ( disjoint @ ( singleton @ SV17 ) @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1278,plain,
! [SV18: $i,SV130: $i] :
( ( ( ~ ( element @ SV130 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( ! [SY621: $i] :
( ~ ( in @ SY621 @ SV130 )
| ( in @ SY621 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1279,plain,
! [SV131: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV131 ) )
= $true )
| ( ( ! [SY622: $i] :
( ( in @ SY622 @ SV19 )
| ( subset @ SV19 @ ( set_difference @ SV131 @ ( singleton @ SY622 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1280,plain,
! [SV132: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV132 ) )
= $true )
| ( ( subset @ SV20 @ ( union @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1281,plain,
! [SV22: $i,SV133: $i] :
( ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV22 @ SV133 ) @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1282,plain,
! [SV188: $i,SV134: $i,SV23: $i] :
( ( ! [SY657: $i] :
( ~ ( subset @ SV23 @ SV134 )
| ~ ( subset @ SV188 @ SY657 )
| ( subset @ ( cartesian_product2 @ SV23 @ SV188 ) @ ( cartesian_product2 @ SV134 @ SY657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1283,plain,
! [SV135: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV135 ) )
= $true )
| ( ( ( set_union2 @ SV24 @ SV135 )
= SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1284,plain,
! [SV136: $i,SV25: $i,SV189: $i] :
( ( ! [SY658: $i] :
( ~ ( relation_of2_as_subset @ SY658 @ SV189 @ SV25 )
| ~ ( subset @ SV25 @ SV136 )
| ( relation_of2_as_subset @ SY658 @ SV189 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1285,plain,
! [SV137: $i,SV26: $i,SV190: $i] :
( ( ~ ( relation @ SV190 )
| ~ ( subset @ SV26 @ SV137 )
| ( subset @ ( relation_inverse_image @ SV190 @ SV26 ) @ ( relation_inverse_image @ SV190 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1286,plain,
! [SV191: $i,SV138: $i,SV27: $i] :
( ( ~ ( subset @ SV27 @ SV138 )
| ~ ( subset @ SV138 @ SV191 )
| ( subset @ SV27 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1287,plain,
! [SV28: $i,SV139: $i] :
( ( ( ~ ( ordinal @ SV139 ) )
= $true )
| ( ( ~ ( in @ SV28 @ SV139 )
| ( ordinal @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1288,plain,
! [SV29: $i] :
( ( ( ordinal @ SV29 )
= $false )
| ( ( ! [SY475: $i] :
( ~ ( ordinal @ SY475 )
| ( in @ SV29 @ SY475 )
| ( SV29 = SY475 )
| ( in @ SY475 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1289,plain,
! [SV140: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV140 ) )
= $true )
| ( ( ! [SY629: $i] : ( subset @ ( set_difference @ SV31 @ SY629 ) @ ( set_difference @ SV140 @ SY629 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1290,plain,
! [SV192: $i,SV143: $i,SV34: $i] :
( ( ~ ( in @ SV34 @ SV143 )
| ~ ( in @ SV143 @ SV192 )
| ~ ( in @ SV192 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1291,plain,
! [SV35: $i] :
( ( ( subset @ SV35 @ empty_set )
= $false )
| ( ( SV35 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1292,plain,
! [SV145: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV145 ) )
= $true )
| ( ( SV145
= ( set_union2 @ SV37 @ ( set_difference @ SV145 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1293,plain,
! [SV38: $i,SV146: $i] :
( ( ( ~ ( element @ SV146 @ ( powerset @ ( powerset @ SV38 ) ) ) )
= $true )
| ( ( ( SV146 = empty_set )
| ( ( complements_of_subsets @ SV38 @ SV146 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1294,plain,
! [SV39: $i,SV193: $i] :
( ( ( ~ ( element @ SV193 @ ( powerset @ SV39 ) )
| ! [SY659: $i] :
( ~ ( element @ SY659 @ SV39 )
| ( in @ SY659 @ SV193 )
| ( in @ SY659 @ ( subset_complement @ SV39 @ SV193 ) ) ) )
= $true )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1295,plain,
! [SV147: $i,SV40: $i,SV194: $i] :
( ( ~ ( element @ SV194 @ ( powerset @ SV40 ) )
| ~ ( in @ SV147 @ ( subset_complement @ SV40 @ SV194 ) )
| ~ ( in @ SV147 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1296,plain,
! [SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK62_B @ SV41 ) @ ( sK63_SY434 @ SV41 ) ) @ SV41 )
| ( SV41 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1297,plain,
! [SV42: $i,SV148: $i] :
( ( ( ~ ( proper_subset @ SV148 @ SV42 ) )
= $true )
| ( ( ~ ( subset @ SV42 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1298,plain,
! [SV43: $i,SV195: $i,SV149: $i] :
( ( ~ ( disjoint @ SV149 @ SV195 )
| ~ ( subset @ SV43 @ SV149 )
| ( disjoint @ SV43 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1299,plain,
! [SV150: $i,SV44: $i] :
( ( ( ~ ( subset @ ( singleton @ SV44 ) @ ( singleton @ SV150 ) ) )
= $true )
| ( ( SV44 = SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1300,plain,
! [SV46: $i,SV152: $i] :
( ( ( ~ ( relation @ SV152 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV152 @ SV46 ) @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1301,plain,
! [SV196: $i,SV153: $i,SV47: $i] :
( ( ~ ( subset @ SV47 @ SV153 )
| ~ ( subset @ SV196 @ SV153 )
| ( subset @ ( set_union2 @ SV47 @ SV196 ) @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1302,plain,
! [SV154: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV154 ) )
= $true )
| ( ( subset @ SV48 @ ( union @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1303,plain,
! [SV155: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ SV155 ) )
= $true )
| ( ( ~ ( in @ SV155 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1304,plain,
! [SV51: $i] :
( ( ( empty @ SV51 )
= $false )
| ( ( function @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1305,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
= $false )
| ( ( relation @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1306,plain,
! [SV156: $i,SV53: $i,SV197: $i] :
( ( ~ ( element @ SV197 @ ( powerset @ ( cartesian_product2 @ SV53 @ SV156 ) ) )
| ( relation @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1307,plain,
! [SV54: $i,SV157: $i] :
( ( ( ~ ( element @ SV157 @ ( powerset @ SV54 ) ) )
= $true )
| ( ( ( subset_complement @ SV54 @ SV157 )
= ( set_difference @ SV54 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1308,plain,
! [SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( ! [SY502: $i] : ( relation @ ( relation_restriction @ SV57 @ SY502 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1309,plain,
! [SV58: $i,SV158: $i] :
( ( ( ~ ( element @ SV158 @ ( powerset @ SV58 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV58 @ SV158 ) @ ( powerset @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1310,plain,
! [SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( relation @ ( relation_inverse @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1311,plain,
! [SV159: $i,SV60: $i] :
( ( ( ~ ( relation @ SV60 )
| ~ ( relation @ SV159 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV60 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1312,plain,
! [SV61: $i,SV160: $i] :
( ( ( ~ ( element @ SV160 @ ( powerset @ ( powerset @ SV61 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV61 @ SV160 ) @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1313,plain,
! [SV63: $i,SV161: $i] :
( ( ( ~ ( element @ SV161 @ ( powerset @ ( powerset @ SV63 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV63 @ SV161 ) @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1314,plain,
! [SV198: $i,SV64: $i,SV162: $i] :
( ( ~ ( element @ SV162 @ ( powerset @ SV64 ) )
| ~ ( element @ SV198 @ ( powerset @ SV64 ) )
| ( element @ ( subset_difference @ SV64 @ SV162 @ SV198 ) @ ( powerset @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1315,plain,
! [SV65: $i] :
( ( ( relation @ SV65 )
= $false )
| ( ( ! [SY509: $i] : ( relation @ ( relation_dom_restriction @ SV65 @ SY509 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1316,plain,
! [SV66: $i,SV163: $i] :
( ( ( ~ ( element @ SV163 @ ( powerset @ ( powerset @ SV66 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV66 @ SV163 ) @ ( powerset @ ( powerset @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1317,plain,
! [SV67: $i,SV164: $i] :
( ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV67 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1318,plain,
! [SV165: $i,SV71: $i] :
( ( empty @ ( ordered_pair @ SV71 @ SV165 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1319,plain,
! [SV166: $i,SV72: $i] :
( ( ( ~ ( relation @ SV72 )
| ~ ( relation @ SV166 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV72 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1320,plain,
! [SV199: $i,SV74: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV74 @ SV199 ) ) )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1321,plain,
! [SV167: $i,SV75: $i] :
( ( ( ~ ( relation @ SV75 )
| ~ ( relation @ SV167 ) )
= $true )
| ( ( relation @ ( set_difference @ SV75 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1322,plain,
! [SV168: $i,SV76: $i] :
( ( empty @ ( unordered_pair @ SV76 @ SV168 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1323,plain,
! [SV77: $i,SV200: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV200 @ SV77 ) ) )
= $true )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1324,plain,
! [SV169: $i,SV78: $i] :
( ( ( ( empty @ SV78 )
| ( empty @ SV169 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV78 @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1325,plain,
! [SV79: $i] :
( ( ( empty @ SV79 )
= $true )
| ( ( ~ ( relation @ SV79 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1326,plain,
! [SV80: $i] :
( ( ( empty @ SV80 )
= $true )
| ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1327,plain,
! [SV81: $i,SV170: $i] :
( ( ( ~ ( element @ SV170 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( ( subset_complement @ SV81 @ ( subset_complement @ SV81 @ SV170 ) )
= SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1328,plain,
! [SV82: $i] :
( ( ( relation @ SV82 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV82 ) )
= SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1329,plain,
! [SV83: $i,SV171: $i] :
( ( ( ~ ( element @ SV171 @ ( powerset @ ( powerset @ SV83 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV83 @ ( complements_of_subsets @ SV83 @ SV171 ) )
= SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1330,plain,
! [SV201: $i,SV84: $i,SV172: $i] :
( ( ~ ( element @ SV172 @ ( powerset @ SV84 ) )
| ~ ( element @ SV201 @ ( powerset @ SV84 ) )
| ( ( subset_difference @ SV84 @ SV172 @ SV201 )
= ( set_difference @ SV172 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1331,plain,
! [SV173: $i,SV86: $i] :
( ( ( ~ ( disjoint @ SV86 @ SV173 ) )
= $true )
| ( ( disjoint @ SV173 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1332,plain,
! [SV174: $i,SV88: $i] :
( ( ( ~ ( in @ SV88 @ SV174 ) )
= $true )
| ( ( element @ SV88 @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1333,plain,
! [SV175: $i,SV89: $i] :
( ( ( ~ ( element @ SV89 @ SV175 ) )
= $true )
| ( ( ( empty @ SV175 )
| ( in @ SV89 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1334,plain,
! [SV92: $i,SV202: $i,SV176: $i] :
( ( ~ ( element @ SV176 @ ( powerset @ SV202 ) )
| ~ ( in @ SV92 @ SV176 )
| ( element @ SV92 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1335,plain,
! [SV93: $i,SV203: $i,SV177: $i] :
( ( ~ ( element @ SV177 @ ( powerset @ SV203 ) )
| ~ ( in @ SV93 @ SV177 )
| ~ ( empty @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1336,plain,
! [SV94: $i] :
( ( ( empty @ SV94 )
= $false )
| ( ( SV94 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1337,plain,
! [SV95: $i,SV178: $i] :
( ( ( ~ ( empty @ SV178 ) )
= $true )
| ( ( ~ ( in @ SV95 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1338,plain,
! [SV179: $i,SV96: $i] :
( ( ( ( SV96 = SV179 )
| ~ ( empty @ SV96 ) )
= $true )
| ( ( ~ ( empty @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1339,plain,
( ( sK12_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1340,plain,
( ( ~ sK12_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) )
| ~ ( ( sK10_SY386 != sK11_SY388 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1341,plain,
( ( ~ ( empty @ sK70_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1342,plain,
( ( finite @ sK70_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1343,plain,
! [SV97: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY532 ) ) )
| ~ ( ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY532 ) ) )
| ( SY533
= ( set_union2 @ SV97 @ SY532 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1172]) ).
thf(1344,plain,
! [SV97: $i] :
( ( ~ ! [SY534: $i,SY535: $i] :
( ( SY535
!= ( set_union2 @ SV97 @ SY534 ) )
| ~ ( ~ ! [SY536: $i] :
( ~ ( in @ SY536 @ SY535 )
| ( in @ SY536 @ SV97 )
| ( in @ SY536 @ SY534 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SV97 )
| ( in @ SY537 @ SY535 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY534 )
| ( in @ SX3 @ SY535 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1172]) ).
thf(1345,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1346,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1347,plain,
! [SV98: $i,SV180: $i] :
( ( ( ~ ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV180 )
| ~ ( in @ SY639 @ ( sK5_C @ SV180 @ SV98 ) ) )
| ~ ( in @ ( sK5_C @ SV180 @ SV98 ) @ SV180 ) ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1348,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1349,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1350,plain,
! [SV99: $i] :
( ( ~ ( relation @ ( sK66_B @ SV99 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1351,plain,
! [SV99: $i] :
( ( ~ ( well_orders @ ( sK66_B @ SV99 ) @ SV99 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1352,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1353,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1354,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1355,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1356,plain,
! [SV100: $i] :
( ( ( ~ ( in @ ( sK65_B @ SV100 ) @ SV100 )
| ~ ( ~ ( ordinal @ ( sK65_B @ SV100 ) )
| ~ ( subset @ ( sK65_B @ SV100 ) @ SV100 ) ) )
= $false )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1357,plain,
! [SV101: $i] :
( ( ~ ! [SY541: $i] :
( ~ ( subset @ SY541 @ ( sK67_B @ SV101 ) )
| ( are_equipotent @ SY541 @ ( sK67_B @ SV101 ) )
| ( in @ SY541 @ ( sK67_B @ SV101 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1358,plain,
! [SV101: $i] :
( ( ~ ~ ( ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ ( sK67_B @ SV101 ) )
| ( in @ ( powerset @ SY542 ) @ ( sK67_B @ SV101 ) ) )
| ~ ~ ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) )
| ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1359,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK53_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1360,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1361,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1362,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1363,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1364,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1365,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1366,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1192]) ).
thf(1367,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK60_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK60_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1368,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK58_C @ SX1 @ SX0 ) @ ( sK59_SY431 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1369,plain,
! [SV102: $i] :
( ( ~ ! [SY545: $i,SY546: $i] :
( ~ ( in @ SV102 @ SY546 )
| ~ ( in @ SY545 @ SY546 )
| ( subset @ ( unordered_pair @ SV102 @ SY545 ) @ SY546 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1370,plain,
! [SV102: $i] :
( ( ~ ~ ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY547 ) @ SY548 )
| ( in @ SV102 @ SY548 ) )
| ~ ! [SY549: $i,SY550: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY549 ) @ SY550 )
| ( in @ SY549 @ SY550 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1371,plain,
! [SV103: $i] :
( ( ~ ! [SY551: $i,SY552: $i] :
( ~ ( ~ ( ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY551 )
| ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) )
| ~ ( ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY551 )
| ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) ) ) )
| ( SY552
= ( set_intersection2 @ SV103 @ SY551 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1372,plain,
! [SV103: $i] :
( ( ~ ! [SY553: $i,SY554: $i] :
( ( SY554
!= ( set_intersection2 @ SV103 @ SY553 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SV103 )
| ~ ( in @ SY555 @ SY553 )
| ( in @ SY555 @ SY554 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ~ ( in @ SY556 @ SY554 )
| ( in @ SY556 @ SV103 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY554 )
| ( in @ SX3 @ SY553 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1373,plain,
( ( function @ sK36_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1374,plain,
( ( relation @ sK36_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1375,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK52_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK52_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1376,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1377,plain,
! [SV104: $i] :
( ( ( relation @ SV104 )
= $false )
| ( ( ~ ( ~ ! [SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) ) )
| ( SV104 = SY558 ) )
| ~ ! [SY559: $i] :
( ~ ( relation @ SY559 )
| ( SV104 != SY559 )
| ~ ( ~ ! [SY560: $i,SY561: $i] :
( ~ ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SV104 )
| ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SY559 ) )
| ~ ! [SY562: $i,SY563: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SY559 )
| ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SV104 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1378,plain,
! [SV105: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK28_B @ SV105 ) @ ( powerset @ SV105 ) )
| ~ ~ ( empty @ ( sK28_B @ SV105 ) ) )
| ~ ( finite @ ( sK28_B @ SV105 ) ) )
= $false )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1379,plain,
! [SV181: $i,SV106: $i] :
( ( ( ( empty @ SV106 )
| ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
| ~ ( ( ( sK23_SY407 @ SV181 @ SV106 )
!= ( sK24_SY413 @ SV181 @ SV106 ) ) ) )
| ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1380,plain,
( ( ~ ( ~ ( empty @ sK32_A )
| ~ ( relation @ sK32_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1204]) ).
thf(1381,plain,
( ( function @ sK32_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1382,plain,
! [SV107: $i] :
( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV107 )
| ~ ( ordinal @ SY572 )
| ( in @ SY572 @ ( sK68_B @ SV107 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1383,plain,
! [SV107: $i] :
( ( ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK68_B @ SV107 ) )
| ( in @ SY573 @ SV107 ) )
| ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ ( sK68_B @ SV107 ) )
| ( ordinal @ SY574 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1384,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1385,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1386,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY425 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK41_SY425 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1387,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK39_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1388,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1211]) ).
thf(1389,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1390,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1391,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1392,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK45_B @ SX0 )
!= ( sK46_SY427 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK46_SY427 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK45_B @ SX0 ) @ ( sK46_SY427 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK46_SY427 @ SX0 ) @ ( sK45_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1215]) ).
thf(1393,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1394,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1395,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1396,plain,
! [SV108: $i,SV182: $i] :
( ( ~ ! [SY647: $i,SY648: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SY647 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SV182 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SY647 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SV182 ) ) )
| ( SY648
= ( unordered_triple @ SV108 @ SV182 @ SY647 ) ) )
| ~ ! [SY649: $i,SY650: $i] :
( ( SY650
!= ( unordered_triple @ SV108 @ SV182 @ SY649 ) )
| ~ ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SY650 )
| ( SY651 = SY649 )
| ( SY651 = SV108 )
| ( SY651 = SV182 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY649 )
| ( in @ SX4 @ SY650 ) )
| ~ ~ ( ~ ! [SY582: $i] :
( ( SY582 != SV108 )
| ( in @ SY582 @ SY650 ) )
| ~ ! [SY654: $i] :
( ( SY654 != SV182 )
| ( in @ SY654 @ SY650 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1397,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1398,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1399,plain,
! [SV109: $i,SV183: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) )
| ~ ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) ) ) )
= $true )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1400,plain,
! [SV110: $i] :
( ( ~ ( element @ ( sK30_B @ SV110 ) @ ( powerset @ SV110 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1223]) ).
thf(1401,plain,
! [SV110: $i] :
( ( ~ ( empty @ ( sK30_B @ SV110 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1223]) ).
thf(1402,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1403,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1404,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1405,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1406,plain,
( ( ~ ( empty @ sK31_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1407,plain,
( ( relation @ sK31_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1229]) ).
thf(1408,plain,
! [SV111: $i] :
( ( ~ ! [SY585: $i,SY586: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY585 )
| ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY585 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) ) ) )
| ( SY586
= ( set_difference @ SV111 @ SY585 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1409,plain,
! [SV111: $i] :
( ( ~ ! [SY587: $i,SY588: $i] :
( ( SY588
!= ( set_difference @ SV111 @ SY587 ) )
| ~ ( ~ ! [SY589: $i] :
( ~ ( in @ SY589 @ SV111 )
| ( in @ SY589 @ SY587 )
| ( in @ SY589 @ SY588 ) )
| ~ ~ ( ~ ! [SY590: $i] :
( ~ ( in @ SY590 @ SY588 )
| ( in @ SY590 @ SV111 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY588 )
| ~ ( in @ SX3 @ SY587 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1410,plain,
! [SV112: $i,SV184: $i] :
( ( ( ~ ( element @ SV184 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY655: $i] :
( ~ ( element @ SY655 @ ( powerset @ SV112 ) )
| ~ ( disjoint @ SV184 @ SY655 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SY655 ) ) )
| ~ ! [SY656: $i] :
( ~ ( element @ SY656 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SY656 ) )
| ( disjoint @ SV184 @ SY656 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1411,plain,
! [SV113: $i] :
( ( ~ ! [SY595: $i] :
( ~ ( subset @ SV113 @ SY595 )
| ! [SY596: $i] : ( subset @ ( cartesian_product2 @ SV113 @ SY596 ) @ ( cartesian_product2 @ SY595 @ SY596 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1232]) ).
thf(1412,plain,
! [SV113: $i] :
( ( ~ ! [SY597: $i] :
( ~ ( subset @ SV113 @ SY597 )
| ! [SY598: $i] : ( subset @ ( cartesian_product2 @ SY598 @ SV113 ) @ ( cartesian_product2 @ SY598 @ SY597 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1232]) ).
thf(1413,plain,
! [SV114: $i] :
( ( ~ ! [SY599: $i] :
( ~ ( subset @ SY599 @ ( sK3_B @ SV114 ) )
| ( are_equipotent @ SY599 @ ( sK3_B @ SV114 ) )
| ( in @ SY599 @ ( sK3_B @ SV114 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1414,plain,
! [SV114: $i] :
( ( ~ ~ ( ~ ! [SY600: $i] :
( ~ ( ~ ! [SY601: $i] :
( ~ ( subset @ SY601 @ SY600 )
| ( in @ SY601 @ ( sK4_SY376 @ SY600 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SY600 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SY600 @ ( sK3_B @ SV114 ) ) )
| ~ ~ ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1415,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1416,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1417,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1418,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1419,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK51_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK51_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1238]) ).
thf(1420,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1239]) ).
thf(1421,plain,
( ( relation @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1422,plain,
( ( relation_empty_yielding @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1423,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1424,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1425,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1426,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1427,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1428,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1429,plain,
! [SV115: $i] :
( ( ( ~ ( element @ ( sK34_B @ SV115 ) @ ( powerset @ SV115 ) )
| ~ ~ ( empty @ ( sK34_B @ SV115 ) ) )
= $false )
| ( ( empty @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1430,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1431,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1432,plain,
! [SV116: $i,SV185: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV116 )
| ~ ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV185 ) ) )
= $true )
| ( ( element @ SV116 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1433,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1434,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1253]) ).
thf(1435,plain,
! [SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ( ( sK17_SY395 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) ) )
| ~ ( ( ( sK16_SY393 @ SV117 )
!= ( sK17_SY395 @ SV117 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1436,plain,
! [SV118: $i] :
( ( ( relation @ SV118 )
= $false )
| ( ( ~ ( ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SY608 ) )
| ( subset @ SV118 @ SY608 ) )
| ~ ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ~ ( subset @ SV118 @ SY609 )
| ! [SY610: $i,SY611: $i] :
( ~ ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SV118 )
| ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SY609 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1437,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1256]) ).
thf(1438,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1257]) ).
thf(1439,plain,
! [SV119: $i] :
( ( ~ ! [SY612: $i,SY613: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
!= SY612 ) ) )
| ~ ( ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
= SV119 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
= SY612 ) ) )
| ( SY613
= ( unordered_pair @ SV119 @ SY612 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1258]) ).
thf(1440,plain,
! [SV119: $i] :
( ( ~ ! [SY614: $i,SY615: $i] :
( ( SY615
!= ( unordered_pair @ SV119 @ SY614 ) )
| ~ ( ~ ! [SY616: $i] :
( ~ ( in @ SY616 @ SY615 )
| ( SY616 = SV119 )
| ( SY616 = SY614 ) )
| ~ ~ ( ~ ! [SY617: $i] :
( ( SY617 != SV119 )
| ( in @ SY617 @ SY615 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY614 )
| ( in @ SX3 @ SY615 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1258]) ).
thf(1441,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK54_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK54_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK54_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK54_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1442,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1443,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1444,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1445,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ ( sK57_SY429 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1446,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1447,plain,
( ( empty @ sK35_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1448,plain,
( ( relation @ sK35_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1449,plain,
! [SV1: $i,SV186: $i] :
( ( ( ~ ( finite @ SV186 ) )
= $true )
| ( ( ~ ( subset @ SV1 @ SV186 ) )
= $true )
| ( ( finite @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1450,plain,
! [SV187: $i,SV121: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV121 )
| ~ ( subset @ SV3 @ SV187 ) )
= $true )
| ( ( subset @ SV3 @ ( set_intersection2 @ SV121 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1451,plain,
! [SV122: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV122 )
= $false )
| ( ( ! [SY620: $i] : ( subset @ ( set_intersection2 @ SV4 @ SY620 ) @ ( set_intersection2 @ SV122 @ SY620 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1452,plain,
! [SV123: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV123 )
= $false )
| ( ( ( set_intersection2 @ SV5 @ SV123 )
= SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1453,plain,
! [SV8: $i,SV204: $i] :
( ( ( ~ ( element @ SV204 @ ( powerset @ SV8 ) )
| ( finite @ SV204 ) )
= $true )
| ( ( finite @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1454,plain,
! [SV10: $i,SV126: $i] :
( ( ( finite @ SV126 )
= $false )
| ( ( finite @ ( set_intersection2 @ SV10 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1455,plain,
! [SV205: $i,SV11: $i] :
( ( ( finite @ ( set_intersection2 @ SV11 @ SV205 ) )
= $true )
| ( ( finite @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1456,plain,
! [SV127: $i,SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( ~ ( relation @ SV127 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV12 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1457,plain,
! [SV128: $i,SV16: $i] :
( ( ( disjoint @ ( singleton @ SV16 ) @ SV128 )
= $false )
| ( ( ~ ( in @ SV16 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1458,plain,
! [SV18: $i,SV130: $i] :
( ( ( element @ SV130 @ ( powerset @ SV18 ) )
= $false )
| ( ( ! [SY621: $i] :
( ~ ( in @ SY621 @ SV130 )
| ( in @ SY621 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1459,plain,
! [SV131: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV131 )
= $false )
| ( ( ! [SY622: $i] :
( ( in @ SY622 @ SV19 )
| ( subset @ SV19 @ ( set_difference @ SV131 @ ( singleton @ SY622 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1460,plain,
! [SV132: $i,SV20: $i] :
( ( ( in @ SV20 @ SV132 )
= $false )
| ( ( subset @ SV20 @ ( union @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1461,plain,
! [SV22: $i,SV133: $i] :
( ( ( relation @ SV133 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV22 @ SV133 ) @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1462,plain,
! [SV206: $i,SV188: $i,SV134: $i,SV23: $i] :
( ( ~ ( subset @ SV23 @ SV134 )
| ~ ( subset @ SV188 @ SV206 )
| ( subset @ ( cartesian_product2 @ SV23 @ SV188 ) @ ( cartesian_product2 @ SV134 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1463,plain,
! [SV135: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV135 )
= $false )
| ( ( ( set_union2 @ SV24 @ SV135 )
= SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1464,plain,
! [SV136: $i,SV25: $i,SV189: $i,SV207: $i] :
( ( ~ ( relation_of2_as_subset @ SV207 @ SV189 @ SV25 )
| ~ ( subset @ SV25 @ SV136 )
| ( relation_of2_as_subset @ SV207 @ SV189 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1465,plain,
! [SV137: $i,SV26: $i,SV190: $i] :
( ( ( ~ ( relation @ SV190 ) )
= $true )
| ( ( ~ ( subset @ SV26 @ SV137 )
| ( subset @ ( relation_inverse_image @ SV190 @ SV26 ) @ ( relation_inverse_image @ SV190 @ SV137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1466,plain,
! [SV191: $i,SV138: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV138 )
| ~ ( subset @ SV138 @ SV191 ) )
= $true )
| ( ( subset @ SV27 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1467,plain,
! [SV28: $i,SV139: $i] :
( ( ( ordinal @ SV139 )
= $false )
| ( ( ~ ( in @ SV28 @ SV139 )
| ( ordinal @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1468,plain,
! [SV29: $i,SV208: $i] :
( ( ( ~ ( ordinal @ SV208 )
| ( in @ SV29 @ SV208 )
| ( SV29 = SV208 )
| ( in @ SV208 @ SV29 ) )
= $true )
| ( ( ordinal @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1469,plain,
! [SV140: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV140 )
= $false )
| ( ( ! [SY629: $i] : ( subset @ ( set_difference @ SV31 @ SY629 ) @ ( set_difference @ SV140 @ SY629 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1470,plain,
! [SV192: $i,SV143: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ SV143 )
| ~ ( in @ SV143 @ SV192 ) )
= $true )
| ( ( ~ ( in @ SV192 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1471,plain,
! [SV145: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV145 )
= $false )
| ( ( SV145
= ( set_union2 @ SV37 @ ( set_difference @ SV145 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1472,plain,
! [SV38: $i,SV146: $i] :
( ( ( element @ SV146 @ ( powerset @ ( powerset @ SV38 ) ) )
= $false )
| ( ( ( SV146 = empty_set )
| ( ( complements_of_subsets @ SV38 @ SV146 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1473,plain,
! [SV39: $i,SV193: $i] :
( ( ( ~ ( element @ SV193 @ ( powerset @ SV39 ) ) )
= $true )
| ( ( ! [SY659: $i] :
( ~ ( element @ SY659 @ SV39 )
| ( in @ SY659 @ SV193 )
| ( in @ SY659 @ ( subset_complement @ SV39 @ SV193 ) ) ) )
= $true )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1474,plain,
! [SV147: $i,SV40: $i,SV194: $i] :
( ( ( ~ ( element @ SV194 @ ( powerset @ SV40 ) ) )
= $true )
| ( ( ~ ( in @ SV147 @ ( subset_complement @ SV40 @ SV194 ) )
| ~ ( in @ SV147 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1475,plain,
! [SV41: $i] :
( ( ( in @ ( ordered_pair @ ( sK62_B @ SV41 ) @ ( sK63_SY434 @ SV41 ) ) @ SV41 )
= $true )
| ( ( SV41 = empty_set )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1476,plain,
! [SV42: $i,SV148: $i] :
( ( ( proper_subset @ SV148 @ SV42 )
= $false )
| ( ( ~ ( subset @ SV42 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1477,plain,
! [SV43: $i,SV195: $i,SV149: $i] :
( ( ( ~ ( disjoint @ SV149 @ SV195 )
| ~ ( subset @ SV43 @ SV149 ) )
= $true )
| ( ( disjoint @ SV43 @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1478,plain,
! [SV150: $i,SV44: $i] :
( ( ( subset @ ( singleton @ SV44 ) @ ( singleton @ SV150 ) )
= $false )
| ( ( SV44 = SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1479,plain,
! [SV46: $i,SV152: $i] :
( ( ( relation @ SV152 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV152 @ SV46 ) @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1480,plain,
! [SV196: $i,SV153: $i,SV47: $i] :
( ( ( ~ ( subset @ SV47 @ SV153 )
| ~ ( subset @ SV196 @ SV153 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV47 @ SV196 ) @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1481,plain,
! [SV154: $i,SV48: $i] :
( ( ( in @ SV48 @ SV154 )
= $false )
| ( ( subset @ SV48 @ ( union @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1482,plain,
! [SV155: $i,SV50: $i] :
( ( ( in @ SV50 @ SV155 )
= $false )
| ( ( ~ ( in @ SV155 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1483,plain,
! [SV156: $i,SV53: $i,SV197: $i] :
( ( ( ~ ( element @ SV197 @ ( powerset @ ( cartesian_product2 @ SV53 @ SV156 ) ) ) )
= $true )
| ( ( relation @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1484,plain,
! [SV54: $i,SV157: $i] :
( ( ( element @ SV157 @ ( powerset @ SV54 ) )
= $false )
| ( ( ( subset_complement @ SV54 @ SV157 )
= ( set_difference @ SV54 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1485,plain,
! [SV209: $i,SV57: $i] :
( ( ( relation @ ( relation_restriction @ SV57 @ SV209 ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1486,plain,
! [SV58: $i,SV158: $i] :
( ( ( element @ SV158 @ ( powerset @ SV58 ) )
= $false )
| ( ( element @ ( subset_complement @ SV58 @ SV158 ) @ ( powerset @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1487,plain,
! [SV159: $i,SV60: $i] :
( ( ( ~ ( relation @ SV60 ) )
= $true )
| ( ( ~ ( relation @ SV159 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV60 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1488,plain,
! [SV61: $i,SV160: $i] :
( ( ( element @ SV160 @ ( powerset @ ( powerset @ SV61 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV61 @ SV160 ) @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1489,plain,
! [SV63: $i,SV161: $i] :
( ( ( element @ SV161 @ ( powerset @ ( powerset @ SV63 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV63 @ SV161 ) @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1490,plain,
! [SV198: $i,SV64: $i,SV162: $i] :
( ( ( ~ ( element @ SV162 @ ( powerset @ SV64 ) )
| ~ ( element @ SV198 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV64 @ SV162 @ SV198 ) @ ( powerset @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1491,plain,
! [SV210: $i,SV65: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV65 @ SV210 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1492,plain,
! [SV66: $i,SV163: $i] :
( ( ( element @ SV163 @ ( powerset @ ( powerset @ SV66 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV66 @ SV163 ) @ ( powerset @ ( powerset @ SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1493,plain,
! [SV67: $i,SV164: $i] :
( ( ( relation @ SV164 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV67 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1494,plain,
! [SV166: $i,SV72: $i] :
( ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( ~ ( relation @ SV166 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV72 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1495,plain,
! [SV199: $i,SV74: $i] :
( ( ( empty @ ( set_union2 @ SV74 @ SV199 ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1496,plain,
! [SV167: $i,SV75: $i] :
( ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( ~ ( relation @ SV167 ) )
= $true )
| ( ( relation @ ( set_difference @ SV75 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1497,plain,
! [SV77: $i,SV200: $i] :
( ( ( empty @ ( set_union2 @ SV200 @ SV77 ) )
= $false )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1498,plain,
! [SV169: $i,SV78: $i] :
( ( ( empty @ SV78 )
= $true )
| ( ( empty @ SV169 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV78 @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1499,plain,
! [SV79: $i] :
( ( ( relation @ SV79 )
= $false )
| ( ( empty @ SV79 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1500,plain,
! [SV80: $i] :
( ( ( relation @ SV80 )
= $false )
| ( ( empty @ SV80 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1501,plain,
! [SV81: $i,SV170: $i] :
( ( ( element @ SV170 @ ( powerset @ SV81 ) )
= $false )
| ( ( ( subset_complement @ SV81 @ ( subset_complement @ SV81 @ SV170 ) )
= SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1502,plain,
! [SV83: $i,SV171: $i] :
( ( ( element @ SV171 @ ( powerset @ ( powerset @ SV83 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV83 @ ( complements_of_subsets @ SV83 @ SV171 ) )
= SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1503,plain,
! [SV201: $i,SV84: $i,SV172: $i] :
( ( ( ~ ( element @ SV172 @ ( powerset @ SV84 ) )
| ~ ( element @ SV201 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ( subset_difference @ SV84 @ SV172 @ SV201 )
= ( set_difference @ SV172 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1504,plain,
! [SV173: $i,SV86: $i] :
( ( ( disjoint @ SV86 @ SV173 )
= $false )
| ( ( disjoint @ SV173 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1505,plain,
! [SV174: $i,SV88: $i] :
( ( ( in @ SV88 @ SV174 )
= $false )
| ( ( element @ SV88 @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1506,plain,
! [SV175: $i,SV89: $i] :
( ( ( element @ SV89 @ SV175 )
= $false )
| ( ( ( empty @ SV175 )
| ( in @ SV89 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1507,plain,
! [SV92: $i,SV202: $i,SV176: $i] :
( ( ( ~ ( element @ SV176 @ ( powerset @ SV202 ) )
| ~ ( in @ SV92 @ SV176 ) )
= $true )
| ( ( element @ SV92 @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1508,plain,
! [SV93: $i,SV203: $i,SV177: $i] :
( ( ( ~ ( element @ SV177 @ ( powerset @ SV203 ) )
| ~ ( in @ SV93 @ SV177 ) )
= $true )
| ( ( ~ ( empty @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1509,plain,
! [SV95: $i,SV178: $i] :
( ( ( empty @ SV178 )
= $false )
| ( ( ~ ( in @ SV95 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1510,plain,
! [SV179: $i,SV96: $i] :
( ( ( SV96 = SV179 )
= $true )
| ( ( ~ ( empty @ SV96 ) )
= $true )
| ( ( ~ ( empty @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1511,plain,
( ( sK12_REN = $true )
| ( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1512,plain,
( ( ( ~ sK12_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) )
| ~ ( ( sK10_SY386 != sK11_SY388 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1513,plain,
( ( empty @ sK70_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1514,plain,
! [SV97: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ~ ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY532 ) ) )
| ~ ( ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY533 )
| ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SY533 @ SY532 @ SV97 ) @ SY532 ) ) )
| ( SY533
= ( set_union2 @ SV97 @ SY532 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1515,plain,
! [SV97: $i] :
( ( ! [SY534: $i,SY535: $i] :
( ( SY535
!= ( set_union2 @ SV97 @ SY534 ) )
| ~ ( ~ ! [SY536: $i] :
( ~ ( in @ SY536 @ SY535 )
| ( in @ SY536 @ SV97 )
| ( in @ SY536 @ SY534 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SV97 )
| ( in @ SY537 @ SY535 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY534 )
| ( in @ SX3 @ SY535 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1516,plain,
! [SV211: $i] :
( ( ! [SY660: $i] :
( ( disjoint @ SV211 @ SY660 )
| ( in @ ( sK72_C @ SY660 @ SV211 ) @ ( set_intersection2 @ SV211 @ SY660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1517,plain,
! [SV212: $i] :
( ( ! [SY661: $i] :
( ! [SY662: $i] :
~ ( in @ SY662 @ ( set_intersection2 @ SV212 @ SY661 ) )
| ~ ( disjoint @ SV212 @ SY661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1518,plain,
! [SV98: $i,SV180: $i] :
( ( ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV180 )
| ~ ( in @ SY639 @ ( sK5_C @ SV180 @ SV98 ) ) )
| ~ ( in @ ( sK5_C @ SV180 @ SV98 ) @ SV180 ) )
= $false )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1519,plain,
! [SV213: $i] :
( ( ! [SY663: $i] :
( ( ( set_difference @ SV213 @ SY663 )
!= SV213 )
| ( disjoint @ SV213 @ SY663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1520,plain,
! [SV214: $i] :
( ( ! [SY664: $i] :
( ~ ( disjoint @ SV214 @ SY664 )
| ( ( set_difference @ SV214 @ SY664 )
= SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1521,plain,
! [SV99: $i] :
( ( relation @ ( sK66_B @ SV99 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1522,plain,
! [SV99: $i] :
( ( well_orders @ ( sK66_B @ SV99 ) @ SV99 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1523,plain,
! [SV215: $i] :
( ( ! [SY665: $i] :
( ( SV215 = SY665 )
| ~ ( subset @ SV215 @ SY665 )
| ( proper_subset @ SV215 @ SY665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1524,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1525,plain,
! [SV216: $i] :
( ( ~ ( empty @ SV216 )
| ( empty @ ( relation_inverse @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1526,plain,
! [SV217: $i] :
( ( ~ ( empty @ SV217 )
| ( relation @ ( relation_inverse @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1527,plain,
! [SV100: $i] :
( ( ( ~ ( in @ ( sK65_B @ SV100 ) @ SV100 ) )
= $false )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1528,plain,
! [SV100: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK65_B @ SV100 ) )
| ~ ( subset @ ( sK65_B @ SV100 ) @ SV100 ) ) )
= $false )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1529,plain,
! [SV101: $i] :
( ( ! [SY541: $i] :
( ~ ( subset @ SY541 @ ( sK67_B @ SV101 ) )
| ( are_equipotent @ SY541 @ ( sK67_B @ SV101 ) )
| ( in @ SY541 @ ( sK67_B @ SV101 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1357]) ).
thf(1530,plain,
! [SV101: $i] :
( ( ~ ( ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ ( sK67_B @ SV101 ) )
| ( in @ ( powerset @ SY542 ) @ ( sK67_B @ SV101 ) ) )
| ~ ~ ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) )
| ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1531,plain,
! [SV218: $i] :
( ( ( in @ ( sK53_B @ SV218 ) @ SV218 )
| ( SV218 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1532,plain,
! [SV219: $i] :
( ( ( SV219 != empty_set )
| ! [SY666: $i] :
~ ( in @ SY666 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1533,plain,
! [SV220: $i] :
( ( ! [SY667: $i] :
( ~ ( in @ SV220 @ SY667 )
| ( subset @ ( singleton @ SV220 ) @ SY667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1534,plain,
! [SV221: $i] :
( ( ! [SY668: $i] :
( ~ ( subset @ ( singleton @ SV221 ) @ SY668 )
| ( in @ SV221 @ SY668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1535,plain,
! [SV222: $i] :
( ( ! [SY669: $i] :
( ( ( set_intersection2 @ SV222 @ SY669 )
!= empty_set )
| ( disjoint @ SV222 @ SY669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1536,plain,
! [SV223: $i] :
( ( ! [SY670: $i] :
( ~ ( disjoint @ SV223 @ SY670 )
| ( ( set_intersection2 @ SV223 @ SY670 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1537,plain,
! [SV224: $i] :
( ( ! [SY671: $i] :
( ( ( set_difference @ SV224 @ SY671 )
!= empty_set )
| ( subset @ SV224 @ SY671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1538,plain,
! [SV225: $i] :
( ( ! [SY672: $i] :
( ~ ( subset @ SV225 @ SY672 )
| ( ( set_difference @ SV225 @ SY672 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1539,plain,
! [SV226: $i] :
( ( ~ ( ~ ! [SY673: $i,SY674: $i] :
( ( sK60_B @ SV226 )
!= ( ordered_pair @ SY673 @ SY674 ) )
| ~ ( in @ ( sK60_B @ SV226 ) @ SV226 ) )
| ( relation @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1540,plain,
! [SV227: $i] :
( ( ~ ( relation @ SV227 )
| ! [SY675: $i] :
( ( SY675
= ( ordered_pair @ ( sK58_C @ SY675 @ SV227 ) @ ( sK59_SY431 @ SY675 @ SV227 ) ) )
| ~ ( in @ SY675 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1541,plain,
! [SV102: $i] :
( ( ! [SY545: $i,SY546: $i] :
( ~ ( in @ SV102 @ SY546 )
| ~ ( in @ SY545 @ SY546 )
| ( subset @ ( unordered_pair @ SV102 @ SY545 ) @ SY546 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1542,plain,
! [SV102: $i] :
( ( ~ ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY547 ) @ SY548 )
| ( in @ SV102 @ SY548 ) )
| ~ ! [SY549: $i,SY550: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY549 ) @ SY550 )
| ( in @ SY549 @ SY550 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1370]) ).
thf(1543,plain,
! [SV103: $i] :
( ( ! [SY551: $i,SY552: $i] :
( ~ ( ~ ( ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY551 )
| ~ ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) )
| ~ ( ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY551 )
| ( in @ ( sK71_D @ SY552 @ SY551 @ SV103 ) @ SY552 ) ) ) )
| ( SY552
= ( set_intersection2 @ SV103 @ SY551 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1544,plain,
! [SV103: $i] :
( ( ! [SY553: $i,SY554: $i] :
( ( SY554
!= ( set_intersection2 @ SV103 @ SY553 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SV103 )
| ~ ( in @ SY555 @ SY553 )
| ( in @ SY555 @ SY554 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ~ ( in @ SY556 @ SY554 )
| ( in @ SY556 @ SV103 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY554 )
| ( in @ SX3 @ SY553 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1545,plain,
! [SV228: $i] :
( ( ! [SY676: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_C @ SY676 @ SV228 ) @ SY676 )
| ~ ( subset @ ( sK52_C @ SY676 @ SV228 ) @ SV228 ) )
| ~ ( ( in @ ( sK52_C @ SY676 @ SV228 ) @ SY676 )
| ( subset @ ( sK52_C @ SY676 @ SV228 ) @ SV228 ) ) )
| ( SY676
= ( powerset @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1546,plain,
! [SV229: $i] :
( ( ! [SY677: $i] :
( ( SY677
!= ( powerset @ SV229 ) )
| ~ ( ~ ! [SY678: $i] :
( ~ ( in @ SY678 @ SY677 )
| ( subset @ SY678 @ SV229 ) )
| ~ ! [SY679: $i] :
( ~ ( subset @ SY679 @ SV229 )
| ( in @ SY679 @ SY677 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1547,plain,
! [SV104: $i] :
( ( ( ~ ! [SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) ) )
| ( SV104 = SY558 ) )
| ~ ! [SY559: $i] :
( ~ ( relation @ SY559 )
| ( SV104 != SY559 )
| ~ ( ~ ! [SY560: $i,SY561: $i] :
( ~ ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SV104 )
| ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SY559 ) )
| ~ ! [SY562: $i,SY563: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SY559 )
| ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SV104 ) ) ) ) )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1548,plain,
! [SV105: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK28_B @ SV105 ) @ ( powerset @ SV105 ) )
| ~ ~ ( empty @ ( sK28_B @ SV105 ) ) ) )
= $false )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1549,plain,
! [SV105: $i] :
( ( ( ~ ( finite @ ( sK28_B @ SV105 ) ) )
= $false )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1550,plain,
! [SV181: $i,SV106: $i] :
( ( ( empty @ SV106 )
= $true )
| ( ( ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
| ~ ( ( ( sK23_SY407 @ SV181 @ SV106 )
!= ( sK24_SY413 @ SV181 @ SV106 ) ) ) )
| ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1551,plain,
( ( ~ ( empty @ sK32_A )
| ~ ( relation @ sK32_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1552,plain,
! [SV107: $i] :
( ( ! [SY572: $i] :
( ~ ( in @ SY572 @ SV107 )
| ~ ( ordinal @ SY572 )
| ( in @ SY572 @ ( sK68_B @ SV107 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1553,plain,
! [SV107: $i] :
( ( ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK68_B @ SV107 ) )
| ( in @ SY573 @ SV107 ) )
| ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ ( sK68_B @ SV107 ) )
| ( ordinal @ SY574 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1554,plain,
! [SV230: $i] :
( ( ! [SY680: $i] :
( ( disjoint @ SV230 @ SY680 )
| ~ ( ~ ( in @ ( sK64_C @ SY680 @ SV230 ) @ SV230 )
| ~ ( in @ ( sK64_C @ SY680 @ SV230 ) @ SY680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1555,plain,
! [SV231: $i] :
( ( ! [SY681: $i] :
( ! [SY682: $i] :
( ~ ( in @ SY682 @ SV231 )
| ~ ( in @ SY682 @ SY681 ) )
| ~ ( disjoint @ SV231 @ SY681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1556,plain,
! [SV232: $i] :
( ( ! [SY683: $i] :
( ~ ( ~ ( ! [SY684: $i] :
( ~ ( in @ ( sK40_C @ SY683 @ SV232 ) @ SY684 )
| ~ ( in @ SY684 @ SV232 ) )
| ~ ( in @ ( sK40_C @ SY683 @ SV232 ) @ SY683 ) )
| ~ ( ~ ( ~ ( in @ ( sK40_C @ SY683 @ SV232 ) @ ( sK41_SY425 @ SY683 @ SV232 ) )
| ~ ( in @ ( sK41_SY425 @ SY683 @ SV232 ) @ SV232 ) )
| ( in @ ( sK40_C @ SY683 @ SV232 ) @ SY683 ) ) )
| ( SY683
= ( union @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1557,plain,
! [SV233: $i] :
( ( ! [SY685: $i] :
( ( SY685
!= ( union @ SV233 ) )
| ~ ( ~ ! [SY686: $i] :
( ! [SY687: $i] :
( ~ ( in @ SY686 @ SY687 )
| ~ ( in @ SY687 @ SV233 ) )
| ( in @ SY686 @ SY685 ) )
| ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SY685 )
| ~ ( ~ ( in @ SY688 @ ( sK39_D @ SY688 @ SY685 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SY688 @ SY685 @ SV233 ) @ SV233 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1558,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1559,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1560,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1561,plain,
! [SV234: $i] :
( ( ~ ( ~ ~ ( ~ ( ( ( sK45_B @ SV234 )
!= ( sK46_SY427 @ SV234 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) ) )
| ~ ~ ( in @ ( sK46_SY427 @ SV234 ) @ ( sK45_B @ SV234 ) ) )
| ( epsilon_connected @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1562,plain,
! [SV235: $i] :
( ( ~ ( epsilon_connected @ SV235 )
| ! [SY689: $i,SY690: $i] :
( ( SY689 = SY690 )
| ~ ( in @ SY689 @ SV235 )
| ~ ( in @ SY690 @ SV235 )
| ( in @ SY689 @ SY690 )
| ( in @ SY690 @ SY689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1563,plain,
! [SV236: $i] :
( ( ! [SY691: $i] :
( ~ ( subset @ SV236 @ SY691 )
| ~ ( subset @ SY691 @ SV236 )
| ( SV236 = SY691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1564,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1565,plain,
! [SV108: $i,SV182: $i] :
( ( ~ ! [SY647: $i,SY648: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SY647 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SV182 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SY647 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SV182 ) ) )
| ( SY648
= ( unordered_triple @ SV108 @ SV182 @ SY647 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1566,plain,
! [SV182: $i,SV108: $i] :
( ( ~ ! [SY649: $i,SY650: $i] :
( ( SY650
!= ( unordered_triple @ SV108 @ SV182 @ SY649 ) )
| ~ ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SY650 )
| ( SY651 = SY649 )
| ( SY651 = SV108 )
| ( SY651 = SV182 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY649 )
| ( in @ SX4 @ SY650 ) )
| ~ ~ ( ~ ! [SY582: $i] :
( ( SY582 != SV108 )
| ( in @ SY582 @ SY650 ) )
| ~ ! [SY654: $i] :
( ( SY654 != SV182 )
| ( in @ SY654 @ SY650 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1567,plain,
! [SV237: $i] :
( ( ! [SY692: $i] :
( ~ ( element @ SV237 @ ( powerset @ SY692 ) )
| ( subset @ SV237 @ SY692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1568,plain,
! [SV238: $i] :
( ( ! [SY693: $i] :
( ~ ( subset @ SV238 @ SY693 )
| ( element @ SV238 @ ( powerset @ SY693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1569,plain,
! [SV109: $i,SV183: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) )
| ~ ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) ) )
= $false )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1570,plain,
! [SV110: $i] :
( ( element @ ( sK30_B @ SV110 ) @ ( powerset @ SV110 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1571,plain,
! [SV110: $i] :
( ( empty @ ( sK30_B @ SV110 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1572,plain,
! [SV239: $i] :
( ( ~ ( empty @ SV239 )
| ( empty @ ( relation_rng @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1573,plain,
! [SV240: $i] :
( ( ~ ( empty @ SV240 )
| ( relation @ ( relation_rng @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1574,plain,
! [SV241: $i] :
( ( ! [SY694: $i] :
( ( ( set_difference @ SV241 @ SY694 )
!= empty_set )
| ( subset @ SV241 @ SY694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1575,plain,
! [SV242: $i] :
( ( ! [SY695: $i] :
( ~ ( subset @ SV242 @ SY695 )
| ( ( set_difference @ SV242 @ SY695 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1576,plain,
( ( empty @ sK31_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1577,plain,
! [SV111: $i] :
( ( ! [SY585: $i,SY586: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY585 )
| ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY585 )
| ( in @ ( sK38_D @ SY586 @ SY585 @ SV111 ) @ SY586 ) ) ) )
| ( SY586
= ( set_difference @ SV111 @ SY585 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1578,plain,
! [SV111: $i] :
( ( ! [SY587: $i,SY588: $i] :
( ( SY588
!= ( set_difference @ SV111 @ SY587 ) )
| ~ ( ~ ! [SY589: $i] :
( ~ ( in @ SY589 @ SV111 )
| ( in @ SY589 @ SY587 )
| ( in @ SY589 @ SY588 ) )
| ~ ~ ( ~ ! [SY590: $i] :
( ~ ( in @ SY590 @ SY588 )
| ( in @ SY590 @ SV111 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY588 )
| ~ ( in @ SX3 @ SY587 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1579,plain,
! [SV112: $i,SV184: $i] :
( ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false )
| ( ( ~ ( ~ ! [SY655: $i] :
( ~ ( element @ SY655 @ ( powerset @ SV112 ) )
| ~ ( disjoint @ SV184 @ SY655 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SY655 ) ) )
| ~ ! [SY656: $i] :
( ~ ( element @ SY656 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SY656 ) )
| ( disjoint @ SV184 @ SY656 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1580,plain,
! [SV113: $i] :
( ( ! [SY595: $i] :
( ~ ( subset @ SV113 @ SY595 )
| ! [SY596: $i] : ( subset @ ( cartesian_product2 @ SV113 @ SY596 ) @ ( cartesian_product2 @ SY595 @ SY596 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1581,plain,
! [SV113: $i] :
( ( ! [SY597: $i] :
( ~ ( subset @ SV113 @ SY597 )
| ! [SY598: $i] : ( subset @ ( cartesian_product2 @ SY598 @ SV113 ) @ ( cartesian_product2 @ SY598 @ SY597 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1582,plain,
! [SV114: $i] :
( ( ! [SY599: $i] :
( ~ ( subset @ SY599 @ ( sK3_B @ SV114 ) )
| ( are_equipotent @ SY599 @ ( sK3_B @ SV114 ) )
| ( in @ SY599 @ ( sK3_B @ SV114 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1583,plain,
! [SV114: $i] :
( ( ~ ( ~ ! [SY600: $i] :
( ~ ( ~ ! [SY601: $i] :
( ~ ( subset @ SY601 @ SY600 )
| ( in @ SY601 @ ( sK4_SY376 @ SY600 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SY600 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SY600 @ ( sK3_B @ SV114 ) ) )
| ~ ~ ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1584,plain,
! [SV243: $i] :
( ( ! [SY696: $i] :
( ~ ( in @ SV243 @ SY696 )
| ( subset @ ( singleton @ SV243 ) @ SY696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1585,plain,
! [SV244: $i] :
( ( ! [SY697: $i] :
( ~ ( subset @ ( singleton @ SV244 ) @ SY697 )
| ( in @ SV244 @ SY697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1586,plain,
! [SV245: $i] :
( ( ~ ( ~ ( in @ ( sK51_B @ SV245 ) @ SV245 )
| ~ ~ ( subset @ ( sK51_B @ SV245 ) @ SV245 ) )
| ( epsilon_transitive @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1587,plain,
! [SV246: $i] :
( ( ~ ( epsilon_transitive @ SV246 )
| ! [SY698: $i] :
( ~ ( in @ SY698 @ SV246 )
| ( subset @ SY698 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1588,plain,
! [SV247: $i] :
( ( ! [SY699: $i] :
( ( ( set_difference @ SV247 @ ( singleton @ SY699 ) )
!= SV247 )
| ~ ( in @ SY699 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1589,plain,
! [SV248: $i] :
( ( ! [SY700: $i] :
( ( in @ SY700 @ SV248 )
| ( ( set_difference @ SV248 @ ( singleton @ SY700 ) )
= SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1590,plain,
! [SV249: $i] :
( ( ! [SY701: $i] :
( ~ ( subset @ SV249 @ ( singleton @ SY701 ) )
| ( SV249 = empty_set )
| ( SV249
= ( singleton @ SY701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1591,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1592,plain,
! [SV250: $i] :
( ( ~ ( empty @ SV250 )
| ( empty @ ( relation_dom @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1593,plain,
! [SV251: $i] :
( ( ~ ( empty @ SV251 )
| ( relation @ ( relation_dom @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1594,plain,
! [SV115: $i] :
( ( ( ~ ( element @ ( sK34_B @ SV115 ) @ ( powerset @ SV115 ) ) )
= $false )
| ( ( empty @ SV115 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1595,plain,
! [SV115: $i] :
( ( ( ~ ~ ( empty @ ( sK34_B @ SV115 ) ) )
= $false )
| ( ( empty @ SV115 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1596,plain,
! [SV252: $i] :
( ( ! [SY702: $i] :
( ~ ( empty @ SV252 )
| ~ ( relation @ SY702 )
| ( empty @ ( relation_composition @ SY702 @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1597,plain,
! [SV253: $i] :
( ( ! [SY703: $i] :
( ~ ( empty @ SV253 )
| ~ ( relation @ SY703 )
| ( relation @ ( relation_composition @ SY703 @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1598,plain,
! [SV116: $i,SV185: $i] :
( ( ( ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV116 )
| ~ ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV185 ) )
= $false )
| ( ( element @ SV116 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1599,plain,
! [SV254: $i] :
( ( ! [SY704: $i] :
( ~ ( subset @ SV254 @ ( singleton @ SY704 ) )
| ( SV254 = empty_set )
| ( SV254
= ( singleton @ SY704 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1600,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1601,plain,
! [SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ( ( sK17_SY395 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1602,plain,
! [SV117: $i] :
( ( ( ~ ( ( ( sK16_SY393 @ SV117 )
!= ( sK17_SY395 @ SV117 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1603,plain,
! [SV118: $i] :
( ( ( ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SY608 ) )
| ( subset @ SV118 @ SY608 ) )
| ~ ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ~ ( subset @ SV118 @ SY609 )
| ! [SY610: $i,SY611: $i] :
( ~ ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SV118 )
| ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SY609 ) ) ) )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1604,plain,
! [SV255: $i] :
( ( ! [SY705: $i] :
( ~ ( empty @ SV255 )
| ~ ( relation @ SY705 )
| ( empty @ ( relation_composition @ SV255 @ SY705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1605,plain,
! [SV256: $i] :
( ( ! [SY706: $i] :
( ~ ( empty @ SV256 )
| ~ ( relation @ SY706 )
| ( relation @ ( relation_composition @ SV256 @ SY706 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1606,plain,
! [SV119: $i] :
( ( ! [SY612: $i,SY613: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
!= SY612 ) ) )
| ~ ( ( in @ ( sK48_D @ SY613 @ SY612 @ SV119 ) @ SY613 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
= SV119 )
| ( ( sK48_D @ SY613 @ SY612 @ SV119 )
= SY612 ) ) )
| ( SY613
= ( unordered_pair @ SV119 @ SY612 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1607,plain,
! [SV119: $i] :
( ( ! [SY614: $i,SY615: $i] :
( ( SY615
!= ( unordered_pair @ SV119 @ SY614 ) )
| ~ ( ~ ! [SY616: $i] :
( ~ ( in @ SY616 @ SY615 )
| ( SY616 = SV119 )
| ( SY616 = SY614 ) )
| ~ ~ ( ~ ! [SY617: $i] :
( ( SY617 != SV119 )
| ( in @ SY617 @ SY615 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY614 )
| ( in @ SX3 @ SY615 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1608,plain,
! [SV257: $i] :
( ( ! [SY707: $i] :
( ~ ( ~ ( ( ( sK54_C @ SY707 @ SV257 )
!= SV257 )
| ~ ( in @ ( sK54_C @ SY707 @ SV257 ) @ SY707 ) )
| ~ ( ( ( sK54_C @ SY707 @ SV257 )
= SV257 )
| ( in @ ( sK54_C @ SY707 @ SV257 ) @ SY707 ) ) )
| ( SY707
= ( singleton @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1609,plain,
! [SV258: $i] :
( ( ! [SY708: $i] :
( ( SY708
!= ( singleton @ SV258 ) )
| ~ ( ~ ! [SY709: $i] :
( ( SY709 != SV258 )
| ( in @ SY709 @ SY708 ) )
| ~ ! [SY710: $i] :
( ~ ( in @ SY710 @ SY708 )
| ( SY710 = SV258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1610,plain,
! [SV259: $i] :
( ( ! [SY711: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY711 @ SV259 ) @ SV259 )
| ~ ~ ( in @ ( sK42_C @ SY711 @ SV259 ) @ SY711 ) )
| ( subset @ SV259 @ SY711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1611,plain,
! [SV260: $i] :
( ( ! [SY712: $i] :
( ~ ( subset @ SV260 @ SY712 )
| ! [SY713: $i] :
( ~ ( in @ SY713 @ SV260 )
| ( in @ SY713 @ SY712 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1612,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ ( sK57_SY429 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1613,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1614,plain,
! [SV1: $i,SV186: $i] :
( ( ( finite @ SV186 )
= $false )
| ( ( ~ ( subset @ SV1 @ SV186 ) )
= $true )
| ( ( finite @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1615,plain,
! [SV187: $i,SV121: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV121 ) )
= $true )
| ( ( ~ ( subset @ SV3 @ SV187 ) )
= $true )
| ( ( subset @ SV3 @ ( set_intersection2 @ SV121 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1616,plain,
! [SV122: $i,SV261: $i,SV4: $i] :
( ( ( subset @ ( set_intersection2 @ SV4 @ SV261 ) @ ( set_intersection2 @ SV122 @ SV261 ) )
= $true )
| ( ( subset @ SV4 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1617,plain,
! [SV8: $i,SV204: $i] :
( ( ( ~ ( element @ SV204 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( finite @ SV204 )
= $true )
| ( ( finite @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1618,plain,
! [SV127: $i,SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( ~ ( relation @ SV127 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV12 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1619,plain,
! [SV128: $i,SV16: $i] :
( ( ( in @ SV16 @ SV128 )
= $false )
| ( ( disjoint @ ( singleton @ SV16 ) @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1620,plain,
! [SV18: $i,SV130: $i,SV262: $i] :
( ( ( ~ ( in @ SV262 @ SV130 )
| ( in @ SV262 @ SV18 ) )
= $true )
| ( ( element @ SV130 @ ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1621,plain,
! [SV131: $i,SV19: $i,SV263: $i] :
( ( ( ( in @ SV263 @ SV19 )
| ( subset @ SV19 @ ( set_difference @ SV131 @ ( singleton @ SV263 ) ) ) )
= $true )
| ( ( subset @ SV19 @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1622,plain,
! [SV206: $i,SV188: $i,SV134: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV134 )
| ~ ( subset @ SV188 @ SV206 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV23 @ SV188 ) @ ( cartesian_product2 @ SV134 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1623,plain,
! [SV136: $i,SV25: $i,SV189: $i,SV207: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV207 @ SV189 @ SV25 ) )
= $true )
| ( ( ~ ( subset @ SV25 @ SV136 )
| ( relation_of2_as_subset @ SV207 @ SV189 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1624,plain,
! [SV137: $i,SV26: $i,SV190: $i] :
( ( ( relation @ SV190 )
= $false )
| ( ( ~ ( subset @ SV26 @ SV137 )
| ( subset @ ( relation_inverse_image @ SV190 @ SV26 ) @ ( relation_inverse_image @ SV190 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1625,plain,
! [SV191: $i,SV138: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV138 ) )
= $true )
| ( ( ~ ( subset @ SV138 @ SV191 ) )
= $true )
| ( ( subset @ SV27 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1626,plain,
! [SV139: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV139 ) )
= $true )
| ( ( ordinal @ SV28 )
= $true )
| ( ( ordinal @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1627,plain,
! [SV29: $i,SV208: $i] :
( ( ( ~ ( ordinal @ SV208 ) )
= $true )
| ( ( ( in @ SV29 @ SV208 )
| ( SV29 = SV208 )
| ( in @ SV208 @ SV29 ) )
= $true )
| ( ( ordinal @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1628,plain,
! [SV140: $i,SV264: $i,SV31: $i] :
( ( ( subset @ ( set_difference @ SV31 @ SV264 ) @ ( set_difference @ SV140 @ SV264 ) )
= $true )
| ( ( subset @ SV31 @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1629,plain,
! [SV192: $i,SV143: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ SV143 ) )
= $true )
| ( ( ~ ( in @ SV143 @ SV192 ) )
= $true )
| ( ( ~ ( in @ SV192 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1630,plain,
! [SV38: $i,SV146: $i] :
( ( ( SV146 = empty_set )
= $true )
| ( ( ( ( complements_of_subsets @ SV38 @ SV146 )
!= empty_set ) )
= $true )
| ( ( element @ SV146 @ ( powerset @ ( powerset @ SV38 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1631,plain,
! [SV39: $i,SV193: $i] :
( ( ( element @ SV193 @ ( powerset @ SV39 ) )
= $false )
| ( ( ! [SY659: $i] :
( ~ ( element @ SY659 @ SV39 )
| ( in @ SY659 @ SV193 )
| ( in @ SY659 @ ( subset_complement @ SV39 @ SV193 ) ) ) )
= $true )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1632,plain,
! [SV147: $i,SV40: $i,SV194: $i] :
( ( ( element @ SV194 @ ( powerset @ SV40 ) )
= $false )
| ( ( ~ ( in @ SV147 @ ( subset_complement @ SV40 @ SV194 ) )
| ~ ( in @ SV147 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1633,plain,
! [SV148: $i,SV42: $i] :
( ( ( subset @ SV42 @ SV148 )
= $false )
| ( ( proper_subset @ SV148 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1634,plain,
! [SV43: $i,SV195: $i,SV149: $i] :
( ( ( ~ ( disjoint @ SV149 @ SV195 ) )
= $true )
| ( ( ~ ( subset @ SV43 @ SV149 ) )
= $true )
| ( ( disjoint @ SV43 @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1635,plain,
! [SV196: $i,SV153: $i,SV47: $i] :
( ( ( ~ ( subset @ SV47 @ SV153 ) )
= $true )
| ( ( ~ ( subset @ SV196 @ SV153 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV47 @ SV196 ) @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1636,plain,
! [SV50: $i,SV155: $i] :
( ( ( in @ SV155 @ SV50 )
= $false )
| ( ( in @ SV50 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1637,plain,
! [SV156: $i,SV53: $i,SV197: $i] :
( ( ( element @ SV197 @ ( powerset @ ( cartesian_product2 @ SV53 @ SV156 ) ) )
= $false )
| ( ( relation @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1638,plain,
! [SV159: $i,SV60: $i] :
( ( ( relation @ SV60 )
= $false )
| ( ( ~ ( relation @ SV159 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV60 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1639,plain,
! [SV198: $i,SV64: $i,SV162: $i] :
( ( ( ~ ( element @ SV162 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( ~ ( element @ SV198 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV64 @ SV162 @ SV198 ) @ ( powerset @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1640,plain,
! [SV166: $i,SV72: $i] :
( ( ( relation @ SV72 )
= $false )
| ( ( ~ ( relation @ SV166 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV72 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1641,plain,
! [SV167: $i,SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( ~ ( relation @ SV167 ) )
= $true )
| ( ( relation @ ( set_difference @ SV75 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1642,plain,
! [SV169: $i,SV78: $i] :
( ( ( empty @ ( cartesian_product2 @ SV78 @ SV169 ) )
= $false )
| ( ( empty @ SV169 )
= $true )
| ( ( empty @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1643,plain,
! [SV79: $i] :
( ( ( empty @ ( relation_dom @ SV79 ) )
= $false )
| ( ( empty @ SV79 )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1644,plain,
! [SV80: $i] :
( ( ( empty @ ( relation_rng @ SV80 ) )
= $false )
| ( ( empty @ SV80 )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1645,plain,
! [SV201: $i,SV84: $i,SV172: $i] :
( ( ( ~ ( element @ SV172 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ~ ( element @ SV201 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ( subset_difference @ SV84 @ SV172 @ SV201 )
= ( set_difference @ SV172 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1646,plain,
! [SV89: $i,SV175: $i] :
( ( ( empty @ SV175 )
= $true )
| ( ( in @ SV89 @ SV175 )
= $true )
| ( ( element @ SV89 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1647,plain,
! [SV92: $i,SV202: $i,SV176: $i] :
( ( ( ~ ( element @ SV176 @ ( powerset @ SV202 ) ) )
= $true )
| ( ( ~ ( in @ SV92 @ SV176 ) )
= $true )
| ( ( element @ SV92 @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1648,plain,
! [SV93: $i,SV203: $i,SV177: $i] :
( ( ( ~ ( element @ SV177 @ ( powerset @ SV203 ) ) )
= $true )
| ( ( ~ ( in @ SV93 @ SV177 ) )
= $true )
| ( ( ~ ( empty @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1649,plain,
! [SV178: $i,SV95: $i] :
( ( ( in @ SV95 @ SV178 )
= $false )
| ( ( empty @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1650,plain,
! [SV179: $i,SV96: $i] :
( ( ( empty @ SV96 )
= $false )
| ( ( SV96 = SV179 )
= $true )
| ( ( ~ ( empty @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1651,plain,
! [SV265: $i] :
( ( ( ~ ( ~ ! [SY714: $i] :
( ! [SY715: $i] :
( ( SY715 != SY714 )
| ~ ( in @ SY715 @ SV265 ) )
| ~ ( ordinal @ SY714 )
| ( in @ SY714 @ ( sK7_B @ SV265 ) ) )
| ~ ! [SY716: $i] :
( ~ ( in @ SY716 @ ( sK7_B @ SV265 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SY716 @ SV265 )
!= SY716 )
| ~ ( in @ ( sK8_D @ SY716 @ SV265 ) @ SV265 ) )
| ~ ( ordinal @ SY716 ) ) ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1652,plain,
( ( sK12_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) )
| ~ ( ( sK10_SY386 != sK11_SY388 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1653,plain,
! [SV97: $i,SV266: $i] :
( ( ! [SY717: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY717 @ SV266 @ SV97 ) @ SY717 )
| ~ ( in @ ( sK47_D @ SY717 @ SV266 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY717 @ SV266 @ SV97 ) @ SY717 )
| ~ ( in @ ( sK47_D @ SY717 @ SV266 @ SV97 ) @ SV266 ) ) )
| ~ ( ( in @ ( sK47_D @ SY717 @ SV266 @ SV97 ) @ SY717 )
| ( in @ ( sK47_D @ SY717 @ SV266 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SY717 @ SV266 @ SV97 ) @ SV266 ) ) )
| ( SY717
= ( set_union2 @ SV97 @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1654,plain,
! [SV267: $i,SV97: $i] :
( ( ! [SY718: $i] :
( ( SY718
!= ( set_union2 @ SV97 @ SV267 ) )
| ~ ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SY718 )
| ( in @ SY719 @ SV97 )
| ( in @ SY719 @ SV267 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SV97 )
| ( in @ SY537 @ SY718 ) )
| ~ ! [SY721: $i] :
( ~ ( in @ SY721 @ SV267 )
| ( in @ SY721 @ SY718 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1655,plain,
! [SV268: $i,SV211: $i] :
( ( ( disjoint @ SV211 @ SV268 )
| ( in @ ( sK72_C @ SV268 @ SV211 ) @ ( set_intersection2 @ SV211 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1656,plain,
! [SV269: $i,SV212: $i] :
( ( ! [SY722: $i] :
~ ( in @ SY722 @ ( set_intersection2 @ SV212 @ SV269 ) )
| ~ ( disjoint @ SV212 @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1657,plain,
! [SV98: $i,SV180: $i] :
( ( ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV180 )
| ~ ( in @ SY639 @ ( sK5_C @ SV180 @ SV98 ) ) ) )
= $false )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1658,plain,
! [SV98: $i,SV180: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV180 @ SV98 ) @ SV180 ) )
= $false )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1659,plain,
! [SV270: $i,SV213: $i] :
( ( ( ( set_difference @ SV213 @ SV270 )
!= SV213 )
| ( disjoint @ SV213 @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1660,plain,
! [SV271: $i,SV214: $i] :
( ( ~ ( disjoint @ SV214 @ SV271 )
| ( ( set_difference @ SV214 @ SV271 )
= SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1661,plain,
! [SV272: $i,SV215: $i] :
( ( ( SV215 = SV272 )
| ~ ( subset @ SV215 @ SV272 )
| ( proper_subset @ SV215 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1662,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1663,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1664,plain,
! [SV216: $i] :
( ( ( ~ ( empty @ SV216 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1665,plain,
! [SV217: $i] :
( ( ( ~ ( empty @ SV217 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1666,plain,
! [SV100: $i] :
( ( ( in @ ( sK65_B @ SV100 ) @ SV100 )
= $true )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1667,plain,
! [SV100: $i] :
( ( ( ~ ( ordinal @ ( sK65_B @ SV100 ) )
| ~ ( subset @ ( sK65_B @ SV100 ) @ SV100 ) )
= $true )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1668,plain,
! [SV101: $i,SV273: $i] :
( ( ~ ( subset @ SV273 @ ( sK67_B @ SV101 ) )
| ( are_equipotent @ SV273 @ ( sK67_B @ SV101 ) )
| ( in @ SV273 @ ( sK67_B @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1669,plain,
! [SV101: $i] :
( ( ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ ( sK67_B @ SV101 ) )
| ( in @ ( powerset @ SY542 ) @ ( sK67_B @ SV101 ) ) )
| ~ ~ ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) )
| ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1670,plain,
! [SV218: $i] :
( ( ( in @ ( sK53_B @ SV218 ) @ SV218 )
= $true )
| ( ( SV218 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1671,plain,
! [SV219: $i] :
( ( ( ( SV219 != empty_set ) )
= $true )
| ( ( ! [SY666: $i] :
~ ( in @ SY666 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1672,plain,
! [SV274: $i,SV220: $i] :
( ( ~ ( in @ SV220 @ SV274 )
| ( subset @ ( singleton @ SV220 ) @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1673,plain,
! [SV275: $i,SV221: $i] :
( ( ~ ( subset @ ( singleton @ SV221 ) @ SV275 )
| ( in @ SV221 @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1674,plain,
! [SV276: $i,SV222: $i] :
( ( ( ( set_intersection2 @ SV222 @ SV276 )
!= empty_set )
| ( disjoint @ SV222 @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1675,plain,
! [SV277: $i,SV223: $i] :
( ( ~ ( disjoint @ SV223 @ SV277 )
| ( ( set_intersection2 @ SV223 @ SV277 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1676,plain,
! [SV278: $i,SV224: $i] :
( ( ( ( set_difference @ SV224 @ SV278 )
!= empty_set )
| ( subset @ SV224 @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1677,plain,
! [SV279: $i,SV225: $i] :
( ( ~ ( subset @ SV225 @ SV279 )
| ( ( set_difference @ SV225 @ SV279 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1678,plain,
! [SV226: $i] :
( ( ( ~ ( ~ ! [SY673: $i,SY674: $i] :
( ( sK60_B @ SV226 )
!= ( ordered_pair @ SY673 @ SY674 ) )
| ~ ( in @ ( sK60_B @ SV226 ) @ SV226 ) ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1679,plain,
! [SV227: $i] :
( ( ( ~ ( relation @ SV227 ) )
= $true )
| ( ( ! [SY675: $i] :
( ( SY675
= ( ordered_pair @ ( sK58_C @ SY675 @ SV227 ) @ ( sK59_SY431 @ SY675 @ SV227 ) ) )
| ~ ( in @ SY675 @ SV227 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1680,plain,
! [SV280: $i,SV102: $i] :
( ( ! [SY723: $i] :
( ~ ( in @ SV102 @ SY723 )
| ~ ( in @ SV280 @ SY723 )
| ( subset @ ( unordered_pair @ SV102 @ SV280 ) @ SY723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1681,plain,
! [SV102: $i] :
( ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY547 ) @ SY548 )
| ( in @ SV102 @ SY548 ) )
| ~ ! [SY549: $i,SY550: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY549 ) @ SY550 )
| ( in @ SY549 @ SY550 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1682,plain,
! [SV103: $i,SV281: $i] :
( ( ! [SY724: $i] :
( ~ ( ~ ( ~ ( in @ ( sK71_D @ SY724 @ SV281 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SY724 @ SV281 @ SV103 ) @ SV281 )
| ~ ( in @ ( sK71_D @ SY724 @ SV281 @ SV103 ) @ SY724 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SY724 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SY724 @ SV281 @ SV103 ) @ SY724 ) )
| ~ ( ( in @ ( sK71_D @ SY724 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SY724 @ SV281 @ SV103 ) @ SY724 ) ) ) )
| ( SY724
= ( set_intersection2 @ SV103 @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1683,plain,
! [SV282: $i,SV103: $i] :
( ( ! [SY725: $i] :
( ( SY725
!= ( set_intersection2 @ SV103 @ SV282 ) )
| ~ ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV103 )
| ~ ( in @ SY726 @ SV282 )
| ( in @ SY726 @ SY725 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ~ ( in @ SY556 @ SY725 )
| ( in @ SY556 @ SV103 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SY725 )
| ( in @ SY728 @ SV282 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1684,plain,
! [SV228: $i,SV283: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ~ ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) )
| ~ ( ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) ) )
| ( SV283
= ( powerset @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1685,plain,
! [SV229: $i,SV284: $i] :
( ( ( SV284
!= ( powerset @ SV229 ) )
| ~ ( ~ ! [SY729: $i] :
( ~ ( in @ SY729 @ SV284 )
| ( subset @ SY729 @ SV229 ) )
| ~ ! [SY730: $i] :
( ~ ( subset @ SY730 @ SV229 )
| ( in @ SY730 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1686,plain,
! [SV104: $i] :
( ( ( ~ ! [SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) ) )
| ( SV104 = SY558 ) ) )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1687,plain,
! [SV104: $i] :
( ( ( ~ ! [SY559: $i] :
( ~ ( relation @ SY559 )
| ( SV104 != SY559 )
| ~ ( ~ ! [SY560: $i,SY561: $i] :
( ~ ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SV104 )
| ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SY559 ) )
| ~ ! [SY562: $i,SY563: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SY559 )
| ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SV104 ) ) ) ) )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1688,plain,
! [SV105: $i] :
( ( ( ~ ( ~ ( element @ ( sK28_B @ SV105 ) @ ( powerset @ SV105 ) )
| ~ ~ ( empty @ ( sK28_B @ SV105 ) ) ) )
= $true )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1548]) ).
thf(1689,plain,
! [SV105: $i] :
( ( ( finite @ ( sK28_B @ SV105 ) )
= $true )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1690,plain,
! [SV106: $i,SV181: $i] :
( ( ( relation @ SV181 )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
| ~ ( ( ( sK23_SY407 @ SV181 @ SV106 )
!= ( sK24_SY413 @ SV181 @ SV106 ) ) ) )
| ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1691,plain,
( ( ~ ( empty @ sK32_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1551]) ).
thf(1692,plain,
( ( ~ ( relation @ sK32_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1551]) ).
thf(1693,plain,
! [SV107: $i,SV285: $i] :
( ( ~ ( in @ SV285 @ SV107 )
| ~ ( ordinal @ SV285 )
| ( in @ SV285 @ ( sK68_B @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1694,plain,
! [SV107: $i] :
( ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK68_B @ SV107 ) )
| ( in @ SY573 @ SV107 ) )
| ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ ( sK68_B @ SV107 ) )
| ( ordinal @ SY574 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1695,plain,
! [SV286: $i,SV230: $i] :
( ( ( disjoint @ SV230 @ SV286 )
| ~ ( ~ ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV230 )
| ~ ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1696,plain,
! [SV287: $i,SV231: $i] :
( ( ! [SY731: $i] :
( ~ ( in @ SY731 @ SV231 )
| ~ ( in @ SY731 @ SV287 ) )
| ~ ( disjoint @ SV231 @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1697,plain,
! [SV232: $i,SV288: $i] :
( ( ~ ( ~ ( ! [SY732: $i] :
( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SY732 )
| ~ ( in @ SY732 @ SV232 ) )
| ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
| ~ ( ~ ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) )
| ~ ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 ) )
| ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) ) )
| ( SV288
= ( union @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1698,plain,
! [SV233: $i,SV289: $i] :
( ( ( SV289
!= ( union @ SV233 ) )
| ~ ( ~ ! [SY733: $i] :
( ! [SY687: $i] :
( ~ ( in @ SY733 @ SY687 )
| ~ ( in @ SY687 @ SV233 ) )
| ( in @ SY733 @ SV289 ) )
| ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV289 )
| ~ ( ~ ( in @ SY735 @ ( sK39_D @ SY735 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SY735 @ SV289 @ SV233 ) @ SV233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1699,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1700,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1701,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1702,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1703,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1704,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1705,plain,
! [SV234: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK45_B @ SV234 )
!= ( sK46_SY427 @ SV234 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) ) )
| ~ ~ ( in @ ( sK46_SY427 @ SV234 ) @ ( sK45_B @ SV234 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1706,plain,
! [SV235: $i] :
( ( ( ~ ( epsilon_connected @ SV235 ) )
= $true )
| ( ( ! [SY689: $i,SY690: $i] :
( ( SY689 = SY690 )
| ~ ( in @ SY689 @ SV235 )
| ~ ( in @ SY690 @ SV235 )
| ( in @ SY689 @ SY690 )
| ( in @ SY690 @ SY689 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1707,plain,
! [SV290: $i,SV236: $i] :
( ( ~ ( subset @ SV236 @ SV290 )
| ~ ( subset @ SV290 @ SV236 )
| ( SV236 = SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1708,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1709,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1710,plain,
! [SV108: $i,SV182: $i] :
( ( ! [SY647: $i,SY648: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SY647 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
!= SV182 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 ) @ SY648 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SY647 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SY648 @ SY647 @ SV182 @ SV108 )
= SV182 ) ) )
| ( SY648
= ( unordered_triple @ SV108 @ SV182 @ SY647 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1711,plain,
! [SV182: $i,SV108: $i] :
( ( ! [SY649: $i,SY650: $i] :
( ( SY650
!= ( unordered_triple @ SV108 @ SV182 @ SY649 ) )
| ~ ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SY650 )
| ( SY651 = SY649 )
| ( SY651 = SV108 )
| ( SY651 = SV182 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY649 )
| ( in @ SX4 @ SY650 ) )
| ~ ~ ( ~ ! [SY582: $i] :
( ( SY582 != SV108 )
| ( in @ SY582 @ SY650 ) )
| ~ ! [SY654: $i] :
( ( SY654 != SV182 )
| ( in @ SY654 @ SY650 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1712,plain,
! [SV291: $i,SV237: $i] :
( ( ~ ( element @ SV237 @ ( powerset @ SV291 ) )
| ( subset @ SV237 @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1713,plain,
! [SV292: $i,SV238: $i] :
( ( ~ ( subset @ SV238 @ SV292 )
| ( element @ SV238 @ ( powerset @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1714,plain,
! [SV109: $i,SV183: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) ) )
= $false )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1715,plain,
! [SV109: $i,SV183: $i] :
( ( ( ~ ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) ) )
= $false )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1716,plain,
! [SV239: $i] :
( ( ( ~ ( empty @ SV239 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1717,plain,
! [SV240: $i] :
( ( ( ~ ( empty @ SV240 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1718,plain,
! [SV293: $i,SV241: $i] :
( ( ( ( set_difference @ SV241 @ SV293 )
!= empty_set )
| ( subset @ SV241 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1719,plain,
! [SV294: $i,SV242: $i] :
( ( ~ ( subset @ SV242 @ SV294 )
| ( ( set_difference @ SV242 @ SV294 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1720,plain,
! [SV111: $i,SV295: $i] :
( ( ! [SY736: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY736 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY736 @ SV295 @ SV111 ) @ SV295 )
| ~ ( in @ ( sK38_D @ SY736 @ SV295 @ SV111 ) @ SY736 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY736 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SY736 @ SV295 @ SV111 ) @ SY736 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY736 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SY736 @ SV295 @ SV111 ) @ SY736 ) ) ) )
| ( SY736
= ( set_difference @ SV111 @ SV295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1721,plain,
! [SV296: $i,SV111: $i] :
( ( ! [SY737: $i] :
( ( SY737
!= ( set_difference @ SV111 @ SV296 ) )
| ~ ( ~ ! [SY738: $i] :
( ~ ( in @ SY738 @ SV111 )
| ( in @ SY738 @ SV296 )
| ( in @ SY738 @ SY737 ) )
| ~ ~ ( ~ ! [SY590: $i] :
( ~ ( in @ SY590 @ SY737 )
| ( in @ SY590 @ SV111 ) )
| ~ ! [SY740: $i] :
( ~ ( in @ SY740 @ SY737 )
| ~ ( in @ SY740 @ SV296 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1722,plain,
! [SV184: $i,SV112: $i] :
( ( ( ~ ! [SY655: $i] :
( ~ ( element @ SY655 @ ( powerset @ SV112 ) )
| ~ ( disjoint @ SV184 @ SY655 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SY655 ) ) )
| ~ ! [SY656: $i] :
( ~ ( element @ SY656 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SY656 ) )
| ( disjoint @ SV184 @ SY656 ) ) )
= $false )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1723,plain,
! [SV297: $i,SV113: $i] :
( ( ~ ( subset @ SV113 @ SV297 )
| ! [SY741: $i] : ( subset @ ( cartesian_product2 @ SV113 @ SY741 ) @ ( cartesian_product2 @ SV297 @ SY741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1724,plain,
! [SV298: $i,SV113: $i] :
( ( ~ ( subset @ SV113 @ SV298 )
| ! [SY742: $i] : ( subset @ ( cartesian_product2 @ SY742 @ SV113 ) @ ( cartesian_product2 @ SY742 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1725,plain,
! [SV114: $i,SV299: $i] :
( ( ~ ( subset @ SV299 @ ( sK3_B @ SV114 ) )
| ( are_equipotent @ SV299 @ ( sK3_B @ SV114 ) )
| ( in @ SV299 @ ( sK3_B @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1726,plain,
! [SV114: $i] :
( ( ~ ! [SY600: $i] :
( ~ ( ~ ! [SY601: $i] :
( ~ ( subset @ SY601 @ SY600 )
| ( in @ SY601 @ ( sK4_SY376 @ SY600 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SY600 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SY600 @ ( sK3_B @ SV114 ) ) )
| ~ ~ ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1727,plain,
! [SV300: $i,SV243: $i] :
( ( ~ ( in @ SV243 @ SV300 )
| ( subset @ ( singleton @ SV243 ) @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1728,plain,
! [SV301: $i,SV244: $i] :
( ( ~ ( subset @ ( singleton @ SV244 ) @ SV301 )
| ( in @ SV244 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1729,plain,
! [SV245: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_B @ SV245 ) @ SV245 )
| ~ ~ ( subset @ ( sK51_B @ SV245 ) @ SV245 ) ) )
= $true )
| ( ( epsilon_transitive @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1730,plain,
! [SV246: $i] :
( ( ( ~ ( epsilon_transitive @ SV246 ) )
= $true )
| ( ( ! [SY698: $i] :
( ~ ( in @ SY698 @ SV246 )
| ( subset @ SY698 @ SV246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1731,plain,
! [SV302: $i,SV247: $i] :
( ( ( ( set_difference @ SV247 @ ( singleton @ SV302 ) )
!= SV247 )
| ~ ( in @ SV302 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1732,plain,
! [SV248: $i,SV303: $i] :
( ( ( in @ SV303 @ SV248 )
| ( ( set_difference @ SV248 @ ( singleton @ SV303 ) )
= SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1733,plain,
! [SV304: $i,SV249: $i] :
( ( ~ ( subset @ SV249 @ ( singleton @ SV304 ) )
| ( SV249 = empty_set )
| ( SV249
= ( singleton @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1734,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1735,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1736,plain,
! [SV250: $i] :
( ( ( ~ ( empty @ SV250 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1737,plain,
! [SV251: $i] :
( ( ( ~ ( empty @ SV251 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1738,plain,
! [SV115: $i] :
( ( ( element @ ( sK34_B @ SV115 ) @ ( powerset @ SV115 ) )
= $true )
| ( ( empty @ SV115 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1594]) ).
thf(1739,plain,
! [SV115: $i] :
( ( ( ~ ( empty @ ( sK34_B @ SV115 ) ) )
= $true )
| ( ( empty @ SV115 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1740,plain,
! [SV305: $i,SV252: $i] :
( ( ~ ( empty @ SV252 )
| ~ ( relation @ SV305 )
| ( empty @ ( relation_composition @ SV305 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1741,plain,
! [SV306: $i,SV253: $i] :
( ( ~ ( empty @ SV253 )
| ~ ( relation @ SV306 )
| ( relation @ ( relation_composition @ SV306 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1742,plain,
! [SV116: $i,SV185: $i] :
( ( ( ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV116 ) )
= $false )
| ( ( element @ SV116 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1743,plain,
! [SV116: $i,SV185: $i] :
( ( ( ~ ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV185 ) )
= $false )
| ( ( element @ SV116 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1744,plain,
! [SV307: $i,SV254: $i] :
( ( ~ ( subset @ SV254 @ ( singleton @ SV307 ) )
| ( SV254 = empty_set )
| ( SV254
= ( singleton @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1745,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1746,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1747,plain,
! [SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ( ( sK17_SY395 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1601]) ).
thf(1748,plain,
! [SV117: $i] :
( ( ( ( ( sK16_SY393 @ SV117 )
!= ( sK17_SY395 @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1749,plain,
! [SV118: $i] :
( ( ( ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SY608 ) )
| ( subset @ SV118 @ SY608 ) ) )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1750,plain,
! [SV118: $i] :
( ( ( ~ ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ~ ( subset @ SV118 @ SY609 )
| ! [SY610: $i,SY611: $i] :
( ~ ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SV118 )
| ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SY609 ) ) ) )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1751,plain,
! [SV308: $i,SV255: $i] :
( ( ~ ( empty @ SV255 )
| ~ ( relation @ SV308 )
| ( empty @ ( relation_composition @ SV255 @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1752,plain,
! [SV309: $i,SV256: $i] :
( ( ~ ( empty @ SV256 )
| ~ ( relation @ SV309 )
| ( relation @ ( relation_composition @ SV256 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1753,plain,
! [SV119: $i,SV310: $i] :
( ( ! [SY743: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SY743 @ SV310 @ SV119 ) @ SY743 )
| ( ( sK48_D @ SY743 @ SV310 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SY743 @ SV310 @ SV119 ) @ SY743 )
| ( ( sK48_D @ SY743 @ SV310 @ SV119 )
!= SV310 ) ) )
| ~ ( ( in @ ( sK48_D @ SY743 @ SV310 @ SV119 ) @ SY743 )
| ( ( sK48_D @ SY743 @ SV310 @ SV119 )
= SV119 )
| ( ( sK48_D @ SY743 @ SV310 @ SV119 )
= SV310 ) ) )
| ( SY743
= ( unordered_pair @ SV119 @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1754,plain,
! [SV311: $i,SV119: $i] :
( ( ! [SY744: $i] :
( ( SY744
!= ( unordered_pair @ SV119 @ SV311 ) )
| ~ ( ~ ! [SY745: $i] :
( ~ ( in @ SY745 @ SY744 )
| ( SY745 = SV119 )
| ( SY745 = SV311 ) )
| ~ ~ ( ~ ! [SY617: $i] :
( ( SY617 != SV119 )
| ( in @ SY617 @ SY744 ) )
| ~ ! [SY747: $i] :
( ( SY747 != SV311 )
| ( in @ SY747 @ SY744 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1755,plain,
! [SV257: $i,SV312: $i] :
( ( ~ ( ~ ( ( ( sK54_C @ SV312 @ SV257 )
!= SV257 )
| ~ ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) )
| ~ ( ( ( sK54_C @ SV312 @ SV257 )
= SV257 )
| ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) ) )
| ( SV312
= ( singleton @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1756,plain,
! [SV258: $i,SV313: $i] :
( ( ( SV313
!= ( singleton @ SV258 ) )
| ~ ( ~ ! [SY748: $i] :
( ( SY748 != SV258 )
| ( in @ SY748 @ SV313 ) )
| ~ ! [SY749: $i] :
( ~ ( in @ SY749 @ SV313 )
| ( SY749 = SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1757,plain,
! [SV259: $i,SV314: $i] :
( ( ~ ( ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV259 )
| ~ ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV314 ) )
| ( subset @ SV259 @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1758,plain,
! [SV315: $i,SV260: $i] :
( ( ~ ( subset @ SV260 @ SV315 )
| ! [SY750: $i] :
( ~ ( in @ SY750 @ SV260 )
| ( in @ SY750 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1759,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ ( sK57_SY429 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1760,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1761,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1762,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1763,plain,
! [SV186: $i,SV1: $i] :
( ( ( subset @ SV1 @ SV186 )
= $false )
| ( ( finite @ SV186 )
= $false )
| ( ( finite @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1764,plain,
! [SV187: $i,SV121: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV121 )
= $false )
| ( ( ~ ( subset @ SV3 @ SV187 ) )
= $true )
| ( ( subset @ SV3 @ ( set_intersection2 @ SV121 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1765,plain,
! [SV8: $i,SV204: $i] :
( ( ( element @ SV204 @ ( powerset @ SV8 ) )
= $false )
| ( ( finite @ SV204 )
= $true )
| ( ( finite @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1766,plain,
! [SV12: $i,SV127: $i] :
( ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV12 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV12 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1767,plain,
! [SV18: $i,SV130: $i,SV262: $i] :
( ( ( ~ ( in @ SV262 @ SV130 ) )
= $true )
| ( ( in @ SV262 @ SV18 )
= $true )
| ( ( element @ SV130 @ ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1768,plain,
! [SV131: $i,SV19: $i,SV263: $i] :
( ( ( in @ SV263 @ SV19 )
= $true )
| ( ( subset @ SV19 @ ( set_difference @ SV131 @ ( singleton @ SV263 ) ) )
= $true )
| ( ( subset @ SV19 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1769,plain,
! [SV206: $i,SV188: $i,SV134: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV134 ) )
= $true )
| ( ( ~ ( subset @ SV188 @ SV206 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV23 @ SV188 ) @ ( cartesian_product2 @ SV134 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1770,plain,
! [SV136: $i,SV25: $i,SV189: $i,SV207: $i] :
( ( ( relation_of2_as_subset @ SV207 @ SV189 @ SV25 )
= $false )
| ( ( ~ ( subset @ SV25 @ SV136 )
| ( relation_of2_as_subset @ SV207 @ SV189 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1771,plain,
! [SV190: $i,SV137: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV137 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV190 @ SV26 ) @ ( relation_inverse_image @ SV190 @ SV137 ) )
= $true )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1772,plain,
! [SV191: $i,SV138: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV138 )
= $false )
| ( ( ~ ( subset @ SV138 @ SV191 ) )
= $true )
| ( ( subset @ SV27 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1773,plain,
! [SV139: $i,SV28: $i] :
( ( ( in @ SV28 @ SV139 )
= $false )
| ( ( ordinal @ SV28 )
= $true )
| ( ( ordinal @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1774,plain,
! [SV29: $i,SV208: $i] :
( ( ( ordinal @ SV208 )
= $false )
| ( ( ( in @ SV29 @ SV208 )
| ( SV29 = SV208 )
| ( in @ SV208 @ SV29 ) )
= $true )
| ( ( ordinal @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1775,plain,
! [SV192: $i,SV143: $i,SV34: $i] :
( ( ( in @ SV34 @ SV143 )
= $false )
| ( ( ~ ( in @ SV143 @ SV192 ) )
= $true )
| ( ( ~ ( in @ SV192 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1776,plain,
! [SV146: $i,SV38: $i] :
( ( ( ( complements_of_subsets @ SV38 @ SV146 )
= empty_set )
= $false )
| ( ( SV146 = empty_set )
= $true )
| ( ( element @ SV146 @ ( powerset @ ( powerset @ SV38 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1777,plain,
! [SV193: $i,SV39: $i,SV316: $i] :
( ( ( ~ ( element @ SV316 @ SV39 )
| ( in @ SV316 @ SV193 )
| ( in @ SV316 @ ( subset_complement @ SV39 @ SV193 ) ) )
= $true )
| ( ( element @ SV193 @ ( powerset @ SV39 ) )
= $false )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1778,plain,
! [SV194: $i,SV40: $i,SV147: $i] :
( ( ( ~ ( in @ SV147 @ ( subset_complement @ SV40 @ SV194 ) ) )
= $true )
| ( ( ~ ( in @ SV147 @ SV194 ) )
= $true )
| ( ( element @ SV194 @ ( powerset @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1779,plain,
! [SV43: $i,SV195: $i,SV149: $i] :
( ( ( disjoint @ SV149 @ SV195 )
= $false )
| ( ( ~ ( subset @ SV43 @ SV149 ) )
= $true )
| ( ( disjoint @ SV43 @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1780,plain,
! [SV196: $i,SV153: $i,SV47: $i] :
( ( ( subset @ SV47 @ SV153 )
= $false )
| ( ( ~ ( subset @ SV196 @ SV153 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV47 @ SV196 ) @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1781,plain,
! [SV60: $i,SV159: $i] :
( ( ( relation @ SV159 )
= $false )
| ( ( relation @ SV60 )
= $false )
| ( ( relation @ ( relation_composition @ SV60 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1782,plain,
! [SV198: $i,SV64: $i,SV162: $i] :
( ( ( element @ SV162 @ ( powerset @ SV64 ) )
= $false )
| ( ( ~ ( element @ SV198 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV64 @ SV162 @ SV198 ) @ ( powerset @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1783,plain,
! [SV72: $i,SV166: $i] :
( ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV72 )
= $false )
| ( ( relation @ ( set_union2 @ SV72 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1784,plain,
! [SV75: $i,SV167: $i] :
( ( ( relation @ SV167 )
= $false )
| ( ( relation @ SV75 )
= $false )
| ( ( relation @ ( set_difference @ SV75 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1785,plain,
! [SV201: $i,SV84: $i,SV172: $i] :
( ( ( element @ SV172 @ ( powerset @ SV84 ) )
= $false )
| ( ( ~ ( element @ SV201 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ( subset_difference @ SV84 @ SV172 @ SV201 )
= ( set_difference @ SV172 @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1786,plain,
! [SV92: $i,SV202: $i,SV176: $i] :
( ( ( element @ SV176 @ ( powerset @ SV202 ) )
= $false )
| ( ( ~ ( in @ SV92 @ SV176 ) )
= $true )
| ( ( element @ SV92 @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1787,plain,
! [SV93: $i,SV203: $i,SV177: $i] :
( ( ( element @ SV177 @ ( powerset @ SV203 ) )
= $false )
| ( ( ~ ( in @ SV93 @ SV177 ) )
= $true )
| ( ( ~ ( empty @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1788,plain,
! [SV96: $i,SV179: $i] :
( ( ( empty @ SV179 )
= $false )
| ( ( SV96 = SV179 )
= $true )
| ( ( empty @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1650]) ).
thf(1789,plain,
! [SV265: $i] :
( ( ( ~ ! [SY714: $i] :
( ! [SY715: $i] :
( ( SY715 != SY714 )
| ~ ( in @ SY715 @ SV265 ) )
| ~ ( ordinal @ SY714 )
| ( in @ SY714 @ ( sK7_B @ SV265 ) ) )
| ~ ! [SY716: $i] :
( ~ ( in @ SY716 @ ( sK7_B @ SV265 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SY716 @ SV265 )
!= SY716 )
| ~ ( in @ ( sK8_D @ SY716 @ SV265 ) @ SV265 ) )
| ~ ( ordinal @ SY716 ) ) ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1790,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) )
| ~ ( ( sK10_SY386 != sK11_SY388 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1791,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) )
| ~ ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) )
| ( SV317
= ( set_union2 @ SV97 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1792,plain,
! [SV267: $i,SV97: $i,SV318: $i] :
( ( ( SV318
!= ( set_union2 @ SV97 @ SV267 ) )
| ~ ( ~ ! [SY751: $i] :
( ~ ( in @ SY751 @ SV318 )
| ( in @ SY751 @ SV97 )
| ( in @ SY751 @ SV267 ) )
| ~ ~ ( ~ ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) )
| ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1793,plain,
! [SV268: $i,SV211: $i] :
( ( ( disjoint @ SV211 @ SV268 )
= $true )
| ( ( in @ ( sK72_C @ SV268 @ SV211 ) @ ( set_intersection2 @ SV211 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1794,plain,
! [SV269: $i,SV212: $i] :
( ( ( ! [SY722: $i] :
~ ( in @ SY722 @ ( set_intersection2 @ SV212 @ SV269 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV212 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1795,plain,
! [SV98: $i,SV180: $i] :
( ( ( ! [SY639: $i] :
( ~ ( in @ SY639 @ SV180 )
| ~ ( in @ SY639 @ ( sK5_C @ SV180 @ SV98 ) ) ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1796,plain,
! [SV98: $i,SV180: $i] :
( ( ( in @ ( sK5_C @ SV180 @ SV98 ) @ SV180 )
= $true )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1797,plain,
! [SV270: $i,SV213: $i] :
( ( ( ( ( set_difference @ SV213 @ SV270 )
!= SV213 ) )
= $true )
| ( ( disjoint @ SV213 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1798,plain,
! [SV271: $i,SV214: $i] :
( ( ( ~ ( disjoint @ SV214 @ SV271 ) )
= $true )
| ( ( ( set_difference @ SV214 @ SV271 )
= SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1799,plain,
! [SV272: $i,SV215: $i] :
( ( ( ( SV215 = SV272 )
| ~ ( subset @ SV215 @ SV272 ) )
= $true )
| ( ( proper_subset @ SV215 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1800,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1801,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1802,plain,
! [SV216: $i] :
( ( ( empty @ SV216 )
= $false )
| ( ( empty @ ( relation_inverse @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1803,plain,
! [SV217: $i] :
( ( ( empty @ SV217 )
= $false )
| ( ( relation @ ( relation_inverse @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1804,plain,
! [SV100: $i] :
( ( ( ~ ( ordinal @ ( sK65_B @ SV100 ) ) )
= $true )
| ( ( ~ ( subset @ ( sK65_B @ SV100 ) @ SV100 ) )
= $true )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1667]) ).
thf(1805,plain,
! [SV101: $i,SV273: $i] :
( ( ( ~ ( subset @ SV273 @ ( sK67_B @ SV101 ) )
| ( are_equipotent @ SV273 @ ( sK67_B @ SV101 ) ) )
= $true )
| ( ( in @ SV273 @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1806,plain,
! [SV101: $i] :
( ( ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ ( sK67_B @ SV101 ) )
| ( in @ ( powerset @ SY542 ) @ ( sK67_B @ SV101 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1807,plain,
! [SV101: $i] :
( ( ~ ~ ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) )
| ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1808,plain,
! [SV219: $i] :
( ( ( SV219 = empty_set )
= $false )
| ( ( ! [SY666: $i] :
~ ( in @ SY666 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1809,plain,
! [SV274: $i,SV220: $i] :
( ( ( ~ ( in @ SV220 @ SV274 ) )
= $true )
| ( ( subset @ ( singleton @ SV220 ) @ SV274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1810,plain,
! [SV275: $i,SV221: $i] :
( ( ( ~ ( subset @ ( singleton @ SV221 ) @ SV275 ) )
= $true )
| ( ( in @ SV221 @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1811,plain,
! [SV276: $i,SV222: $i] :
( ( ( ( ( set_intersection2 @ SV222 @ SV276 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV222 @ SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1812,plain,
! [SV277: $i,SV223: $i] :
( ( ( ~ ( disjoint @ SV223 @ SV277 ) )
= $true )
| ( ( ( set_intersection2 @ SV223 @ SV277 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1813,plain,
! [SV278: $i,SV224: $i] :
( ( ( ( ( set_difference @ SV224 @ SV278 )
!= empty_set ) )
= $true )
| ( ( subset @ SV224 @ SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1814,plain,
! [SV279: $i,SV225: $i] :
( ( ( ~ ( subset @ SV225 @ SV279 ) )
= $true )
| ( ( ( set_difference @ SV225 @ SV279 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1815,plain,
! [SV226: $i] :
( ( ( ~ ! [SY673: $i,SY674: $i] :
( ( sK60_B @ SV226 )
!= ( ordered_pair @ SY673 @ SY674 ) )
| ~ ( in @ ( sK60_B @ SV226 ) @ SV226 ) )
= $false )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1816,plain,
! [SV227: $i] :
( ( ( relation @ SV227 )
= $false )
| ( ( ! [SY675: $i] :
( ( SY675
= ( ordered_pair @ ( sK58_C @ SY675 @ SV227 ) @ ( sK59_SY431 @ SY675 @ SV227 ) ) )
| ~ ( in @ SY675 @ SV227 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1817,plain,
! [SV280: $i,SV319: $i,SV102: $i] :
( ( ~ ( in @ SV102 @ SV319 )
| ~ ( in @ SV280 @ SV319 )
| ( subset @ ( unordered_pair @ SV102 @ SV280 ) @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1818,plain,
! [SV102: $i] :
( ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY547 ) @ SY548 )
| ( in @ SV102 @ SY548 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1819,plain,
! [SV102: $i] :
( ( ~ ! [SY549: $i,SY550: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY549 ) @ SY550 )
| ( in @ SY549 @ SY550 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1820,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) ) )
| ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1821,plain,
! [SV282: $i,SV103: $i,SV321: $i] :
( ( ( SV321
!= ( set_intersection2 @ SV103 @ SV282 ) )
| ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SV103 )
| ~ ( in @ SY754 @ SV282 )
| ( in @ SY754 @ SV321 ) )
| ~ ~ ( ~ ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) )
| ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1822,plain,
! [SV228: $i,SV283: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ~ ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) )
| ~ ( ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) ) ) )
= $true )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1823,plain,
! [SV229: $i,SV284: $i] :
( ( ( ( SV284
!= ( powerset @ SV229 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY729: $i] :
( ~ ( in @ SY729 @ SV284 )
| ( subset @ SY729 @ SV229 ) )
| ~ ! [SY730: $i] :
( ~ ( subset @ SY730 @ SV229 )
| ( in @ SY730 @ SV284 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1824,plain,
! [SV104: $i] :
( ( ( ! [SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SY558 @ SV104 ) @ ( sK50_SY428 @ SY558 @ SV104 ) ) @ SY558 ) ) )
| ( SV104 = SY558 ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1825,plain,
! [SV104: $i] :
( ( ( ! [SY559: $i] :
( ~ ( relation @ SY559 )
| ( SV104 != SY559 )
| ~ ( ~ ! [SY560: $i,SY561: $i] :
( ~ ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SV104 )
| ( in @ ( ordered_pair @ SY560 @ SY561 ) @ SY559 ) )
| ~ ! [SY562: $i,SY563: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SY559 )
| ( in @ ( ordered_pair @ SY562 @ SY563 ) @ SV104 ) ) ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1826,plain,
! [SV105: $i] :
( ( ( ~ ( element @ ( sK28_B @ SV105 ) @ ( powerset @ SV105 ) )
| ~ ~ ( empty @ ( sK28_B @ SV105 ) ) )
= $false )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1827,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
| ~ ( ( ( sK23_SY407 @ SV181 @ SV106 )
!= ( sK24_SY413 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1828,plain,
( ( empty @ sK32_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1829,plain,
( ( relation @ sK32_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1830,plain,
! [SV107: $i,SV285: $i] :
( ( ( ~ ( in @ SV285 @ SV107 )
| ~ ( ordinal @ SV285 ) )
= $true )
| ( ( in @ SV285 @ ( sK68_B @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1831,plain,
! [SV107: $i] :
( ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK68_B @ SV107 ) )
| ( in @ SY573 @ SV107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1694]) ).
thf(1832,plain,
! [SV107: $i] :
( ( ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ ( sK68_B @ SV107 ) )
| ( ordinal @ SY574 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1694]) ).
thf(1833,plain,
! [SV286: $i,SV230: $i] :
( ( ( disjoint @ SV230 @ SV286 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV230 )
| ~ ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1834,plain,
! [SV287: $i,SV231: $i] :
( ( ( ! [SY731: $i] :
( ~ ( in @ SY731 @ SV231 )
| ~ ( in @ SY731 @ SV287 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV231 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1835,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( ~ ( ! [SY732: $i] :
( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SY732 )
| ~ ( in @ SY732 @ SV232 ) )
| ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
| ~ ( ~ ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) )
| ~ ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 ) )
| ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) ) ) )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1836,plain,
! [SV233: $i,SV289: $i] :
( ( ( ( SV289
!= ( union @ SV233 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY733: $i] :
( ! [SY687: $i] :
( ~ ( in @ SY733 @ SY687 )
| ~ ( in @ SY687 @ SV233 ) )
| ( in @ SY733 @ SV289 ) )
| ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV289 )
| ~ ( ~ ( in @ SY735 @ ( sK39_D @ SY735 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SY735 @ SV289 @ SV233 ) @ SV233 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1837,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1838,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1839,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1840,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1841,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1842,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1843,plain,
! [SV234: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK45_B @ SV234 )
!= ( sK46_SY427 @ SV234 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) ) )
| ~ ~ ( in @ ( sK46_SY427 @ SV234 ) @ ( sK45_B @ SV234 ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1844,plain,
! [SV235: $i] :
( ( ( epsilon_connected @ SV235 )
= $false )
| ( ( ! [SY689: $i,SY690: $i] :
( ( SY689 = SY690 )
| ~ ( in @ SY689 @ SV235 )
| ~ ( in @ SY690 @ SV235 )
| ( in @ SY689 @ SY690 )
| ( in @ SY690 @ SY689 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1845,plain,
! [SV290: $i,SV236: $i] :
( ( ( ~ ( subset @ SV236 @ SV290 )
| ~ ( subset @ SV290 @ SV236 ) )
= $true )
| ( ( SV236 = SV290 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1846,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1847,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1848,plain,
! [SV108: $i,SV182: $i,SV322: $i] :
( ( ! [SY757: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 ) @ SY757 )
| ( ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 ) @ SY757 )
| ( ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 ) @ SY757 )
| ( ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 ) @ SY757 )
| ( ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 )
= SV322 )
| ( ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SY757 @ SV322 @ SV182 @ SV108 )
= SV182 ) ) )
| ( SY757
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1849,plain,
! [SV323: $i,SV182: $i,SV108: $i] :
( ( ! [SY758: $i] :
( ( SY758
!= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
| ~ ( ~ ! [SY759: $i] :
( ~ ( in @ SY759 @ SY758 )
| ( SY759 = SV323 )
| ( SY759 = SV108 )
| ( SY759 = SV182 ) )
| ~ ~ ( ~ ! [SY760: $i] :
( ( SY760 != SV323 )
| ( in @ SY760 @ SY758 ) )
| ~ ~ ( ~ ! [SY582: $i] :
( ( SY582 != SV108 )
| ( in @ SY582 @ SY758 ) )
| ~ ! [SY654: $i] :
( ( SY654 != SV182 )
| ( in @ SY654 @ SY758 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1850,plain,
! [SV291: $i,SV237: $i] :
( ( ( ~ ( element @ SV237 @ ( powerset @ SV291 ) ) )
= $true )
| ( ( subset @ SV237 @ SV291 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(1851,plain,
! [SV292: $i,SV238: $i] :
( ( ( ~ ( subset @ SV238 @ SV292 ) )
= $true )
| ( ( element @ SV238 @ ( powerset @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1852,plain,
! [SV109: $i,SV183: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) )
= $true )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1853,plain,
! [SV109: $i,SV183: $i] :
( ( ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
| ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) )
= $true )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1854,plain,
! [SV239: $i] :
( ( ( empty @ SV239 )
= $false )
| ( ( empty @ ( relation_rng @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1855,plain,
! [SV240: $i] :
( ( ( empty @ SV240 )
= $false )
| ( ( relation @ ( relation_rng @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1856,plain,
! [SV293: $i,SV241: $i] :
( ( ( ( ( set_difference @ SV241 @ SV293 )
!= empty_set ) )
= $true )
| ( ( subset @ SV241 @ SV293 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1857,plain,
! [SV294: $i,SV242: $i] :
( ( ( ~ ( subset @ SV242 @ SV294 ) )
= $true )
| ( ( ( set_difference @ SV242 @ SV294 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1858,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) ) )
| ( SV324
= ( set_difference @ SV111 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(1859,plain,
! [SV296: $i,SV111: $i,SV325: $i] :
( ( ( SV325
!= ( set_difference @ SV111 @ SV296 ) )
| ~ ( ~ ! [SY763: $i] :
( ~ ( in @ SY763 @ SV111 )
| ( in @ SY763 @ SV296 )
| ( in @ SY763 @ SV325 ) )
| ~ ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) )
| ~ ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1860,plain,
! [SV184: $i,SV112: $i] :
( ( ( ~ ! [SY655: $i] :
( ~ ( element @ SY655 @ ( powerset @ SV112 ) )
| ~ ( disjoint @ SV184 @ SY655 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SY655 ) ) ) )
= $false )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1861,plain,
! [SV184: $i,SV112: $i] :
( ( ( ~ ! [SY656: $i] :
( ~ ( element @ SY656 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SY656 ) )
| ( disjoint @ SV184 @ SY656 ) ) )
= $false )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1862,plain,
! [SV297: $i,SV113: $i] :
( ( ( ~ ( subset @ SV113 @ SV297 ) )
= $true )
| ( ( ! [SY741: $i] : ( subset @ ( cartesian_product2 @ SV113 @ SY741 ) @ ( cartesian_product2 @ SV297 @ SY741 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1863,plain,
! [SV298: $i,SV113: $i] :
( ( ( ~ ( subset @ SV113 @ SV298 ) )
= $true )
| ( ( ! [SY742: $i] : ( subset @ ( cartesian_product2 @ SY742 @ SV113 ) @ ( cartesian_product2 @ SY742 @ SV298 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1864,plain,
! [SV114: $i,SV299: $i] :
( ( ( ~ ( subset @ SV299 @ ( sK3_B @ SV114 ) )
| ( are_equipotent @ SV299 @ ( sK3_B @ SV114 ) ) )
= $true )
| ( ( in @ SV299 @ ( sK3_B @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1865,plain,
! [SV114: $i] :
( ( ~ ! [SY600: $i] :
( ~ ( ~ ! [SY601: $i] :
( ~ ( subset @ SY601 @ SY600 )
| ( in @ SY601 @ ( sK4_SY376 @ SY600 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SY600 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SY600 @ ( sK3_B @ SV114 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1726]) ).
thf(1866,plain,
! [SV114: $i] :
( ( ~ ~ ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1726]) ).
thf(1867,plain,
! [SV300: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV300 ) )
= $true )
| ( ( subset @ ( singleton @ SV243 ) @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1868,plain,
! [SV301: $i,SV244: $i] :
( ( ( ~ ( subset @ ( singleton @ SV244 ) @ SV301 ) )
= $true )
| ( ( in @ SV244 @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(1869,plain,
! [SV245: $i] :
( ( ( ~ ( in @ ( sK51_B @ SV245 ) @ SV245 )
| ~ ~ ( subset @ ( sK51_B @ SV245 ) @ SV245 ) )
= $false )
| ( ( epsilon_transitive @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1870,plain,
! [SV246: $i] :
( ( ( epsilon_transitive @ SV246 )
= $false )
| ( ( ! [SY698: $i] :
( ~ ( in @ SY698 @ SV246 )
| ( subset @ SY698 @ SV246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1871,plain,
! [SV302: $i,SV247: $i] :
( ( ( ( ( set_difference @ SV247 @ ( singleton @ SV302 ) )
!= SV247 ) )
= $true )
| ( ( ~ ( in @ SV302 @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1872,plain,
! [SV248: $i,SV303: $i] :
( ( ( in @ SV303 @ SV248 )
= $true )
| ( ( ( set_difference @ SV248 @ ( singleton @ SV303 ) )
= SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1873,plain,
! [SV304: $i,SV249: $i] :
( ( ( ~ ( subset @ SV249 @ ( singleton @ SV304 ) ) )
= $true )
| ( ( ( SV249 = empty_set )
| ( SV249
= ( singleton @ SV304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1874,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1875,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1876,plain,
! [SV250: $i] :
( ( ( empty @ SV250 )
= $false )
| ( ( empty @ ( relation_dom @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1877,plain,
! [SV251: $i] :
( ( ( empty @ SV251 )
= $false )
| ( ( relation @ ( relation_dom @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1878,plain,
! [SV115: $i] :
( ( ( empty @ ( sK34_B @ SV115 ) )
= $false )
| ( ( empty @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1879,plain,
! [SV305: $i,SV252: $i] :
( ( ( ~ ( empty @ SV252 )
| ~ ( relation @ SV305 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV305 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1880,plain,
! [SV306: $i,SV253: $i] :
( ( ( ~ ( empty @ SV253 )
| ~ ( relation @ SV306 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV306 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1881,plain,
! [SV116: $i,SV185: $i] :
( ( ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV116 )
= $true )
| ( ( element @ SV116 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1882,plain,
! [SV116: $i,SV185: $i] :
( ( ( ~ ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV185 ) )
= $true )
| ( ( element @ SV116 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1883,plain,
! [SV307: $i,SV254: $i] :
( ( ( ~ ( subset @ SV254 @ ( singleton @ SV307 ) ) )
= $true )
| ( ( ( SV254 = empty_set )
| ( SV254
= ( singleton @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(1884,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1885,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1886,plain,
! [SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ( ( sK17_SY395 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1887,plain,
! [SV117: $i] :
( ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1888,plain,
! [SV118: $i] :
( ( ( ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SY608 @ SV118 ) @ ( sK44_SY426 @ SY608 @ SV118 ) ) @ SY608 ) )
| ( subset @ SV118 @ SY608 ) ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1889,plain,
! [SV118: $i] :
( ( ( ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ~ ( subset @ SV118 @ SY609 )
| ! [SY610: $i,SY611: $i] :
( ~ ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SV118 )
| ( in @ ( ordered_pair @ SY610 @ SY611 ) @ SY609 ) ) ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1890,plain,
! [SV308: $i,SV255: $i] :
( ( ( ~ ( empty @ SV255 )
| ~ ( relation @ SV308 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV255 @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1891,plain,
! [SV309: $i,SV256: $i] :
( ( ( ~ ( empty @ SV256 )
| ~ ( relation @ SV309 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV256 @ SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1892,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) ) )
| ~ ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV119 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV310 ) ) )
| ( SV326
= ( unordered_pair @ SV119 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1893,plain,
! [SV311: $i,SV119: $i,SV327: $i] :
( ( ( SV327
!= ( unordered_pair @ SV119 @ SV311 ) )
| ~ ( ~ ! [SY766: $i] :
( ~ ( in @ SY766 @ SV327 )
| ( SY766 = SV119 )
| ( SY766 = SV311 ) )
| ~ ~ ( ~ ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) )
| ~ ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1894,plain,
! [SV257: $i,SV312: $i] :
( ( ( ~ ( ~ ( ( ( sK54_C @ SV312 @ SV257 )
!= SV257 )
| ~ ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) )
| ~ ( ( ( sK54_C @ SV312 @ SV257 )
= SV257 )
| ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) ) ) )
= $true )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1895,plain,
! [SV258: $i,SV313: $i] :
( ( ( ( SV313
!= ( singleton @ SV258 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY748: $i] :
( ( SY748 != SV258 )
| ( in @ SY748 @ SV313 ) )
| ~ ! [SY749: $i] :
( ~ ( in @ SY749 @ SV313 )
| ( SY749 = SV258 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1896,plain,
! [SV259: $i,SV314: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV259 )
| ~ ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV314 ) ) )
= $true )
| ( ( subset @ SV259 @ SV314 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(1897,plain,
! [SV315: $i,SV260: $i] :
( ( ( ~ ( subset @ SV260 @ SV315 ) )
= $true )
| ( ( ! [SY750: $i] :
( ~ ( in @ SY750 @ SV260 )
| ( in @ SY750 @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1758]) ).
thf(1898,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ ( sK57_SY429 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK56_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1899,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(1900,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1901,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1902,plain,
! [SV121: $i,SV187: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV187 )
= $false )
| ( ( subset @ SV3 @ SV121 )
= $false )
| ( ( subset @ SV3 @ ( set_intersection2 @ SV121 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1903,plain,
! [SV18: $i,SV130: $i,SV262: $i] :
( ( ( in @ SV262 @ SV130 )
= $false )
| ( ( in @ SV262 @ SV18 )
= $true )
| ( ( element @ SV130 @ ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1904,plain,
! [SV206: $i,SV188: $i,SV134: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV134 )
= $false )
| ( ( ~ ( subset @ SV188 @ SV206 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV23 @ SV188 ) @ ( cartesian_product2 @ SV134 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1905,plain,
! [SV189: $i,SV207: $i,SV136: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV136 ) )
= $true )
| ( ( relation_of2_as_subset @ SV207 @ SV189 @ SV136 )
= $true )
| ( ( relation_of2_as_subset @ SV207 @ SV189 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1906,plain,
! [SV190: $i,SV137: $i,SV26: $i] :
( ( ( subset @ SV26 @ SV137 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV190 @ SV26 ) @ ( relation_inverse_image @ SV190 @ SV137 ) )
= $true )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1907,plain,
! [SV27: $i,SV191: $i,SV138: $i] :
( ( ( subset @ SV138 @ SV191 )
= $false )
| ( ( subset @ SV27 @ SV138 )
= $false )
| ( ( subset @ SV27 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1908,plain,
! [SV208: $i,SV29: $i] :
( ( ( ( in @ SV29 @ SV208 )
| ( SV29 = SV208 ) )
= $true )
| ( ( in @ SV208 @ SV29 )
= $true )
| ( ( ordinal @ SV208 )
= $false )
| ( ( ordinal @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1909,plain,
! [SV34: $i,SV192: $i,SV143: $i] :
( ( ( in @ SV143 @ SV192 )
= $false )
| ( ( in @ SV34 @ SV143 )
= $false )
| ( ( ~ ( in @ SV192 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1910,plain,
! [SV193: $i,SV39: $i,SV316: $i] :
( ( ( ~ ( element @ SV316 @ SV39 ) )
= $true )
| ( ( ( in @ SV316 @ SV193 )
| ( in @ SV316 @ ( subset_complement @ SV39 @ SV193 ) ) )
= $true )
| ( ( element @ SV193 @ ( powerset @ SV39 ) )
= $false )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1911,plain,
! [SV194: $i,SV40: $i,SV147: $i] :
( ( ( in @ SV147 @ ( subset_complement @ SV40 @ SV194 ) )
= $false )
| ( ( ~ ( in @ SV147 @ SV194 ) )
= $true )
| ( ( element @ SV194 @ ( powerset @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1912,plain,
! [SV195: $i,SV149: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV149 )
= $false )
| ( ( disjoint @ SV149 @ SV195 )
= $false )
| ( ( disjoint @ SV43 @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1913,plain,
! [SV47: $i,SV153: $i,SV196: $i] :
( ( ( subset @ SV196 @ SV153 )
= $false )
| ( ( subset @ SV47 @ SV153 )
= $false )
| ( ( subset @ ( set_union2 @ SV47 @ SV196 ) @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1914,plain,
! [SV162: $i,SV64: $i,SV198: $i] :
( ( ( element @ SV198 @ ( powerset @ SV64 ) )
= $false )
| ( ( element @ SV162 @ ( powerset @ SV64 ) )
= $false )
| ( ( element @ ( subset_difference @ SV64 @ SV162 @ SV198 ) @ ( powerset @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1915,plain,
! [SV172: $i,SV84: $i,SV201: $i] :
( ( ( element @ SV201 @ ( powerset @ SV84 ) )
= $false )
| ( ( element @ SV172 @ ( powerset @ SV84 ) )
= $false )
| ( ( ( subset_difference @ SV84 @ SV172 @ SV201 )
= ( set_difference @ SV172 @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1916,plain,
! [SV202: $i,SV176: $i,SV92: $i] :
( ( ( in @ SV92 @ SV176 )
= $false )
| ( ( element @ SV176 @ ( powerset @ SV202 ) )
= $false )
| ( ( element @ SV92 @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1917,plain,
! [SV203: $i,SV177: $i,SV93: $i] :
( ( ( in @ SV93 @ SV177 )
= $false )
| ( ( element @ SV177 @ ( powerset @ SV203 ) )
= $false )
| ( ( ~ ( empty @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1918,plain,
! [SV265: $i] :
( ( ( ~ ! [SY714: $i] :
( ! [SY715: $i] :
( ( SY715 != SY714 )
| ~ ( in @ SY715 @ SV265 ) )
| ~ ( ordinal @ SY714 )
| ( in @ SY714 @ ( sK7_B @ SV265 ) ) ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1919,plain,
! [SV265: $i] :
( ( ( ~ ! [SY716: $i] :
( ~ ( in @ SY716 @ ( sK7_B @ SV265 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SY716 @ SV265 )
!= SY716 )
| ~ ( in @ ( sK8_D @ SY716 @ SV265 ) @ SV265 ) )
| ~ ( ordinal @ SY716 ) ) ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1920,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1921,plain,
( ( ( ~ ( ( sK10_SY386 != sK11_SY388 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1922,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) )
| ~ ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1923,plain,
! [SV267: $i,SV97: $i,SV318: $i] :
( ( ( ( SV318
!= ( set_union2 @ SV97 @ SV267 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY751: $i] :
( ~ ( in @ SY751 @ SV318 )
| ( in @ SY751 @ SV97 )
| ( in @ SY751 @ SV267 ) )
| ~ ~ ( ~ ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) )
| ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(1924,plain,
! [SV269: $i,SV212: $i,SV328: $i] :
( ( ( ~ ( in @ SV328 @ ( set_intersection2 @ SV212 @ SV269 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV212 @ SV269 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(1925,plain,
! [SV98: $i,SV180: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV180 )
| ~ ( in @ SV329 @ ( sK5_C @ SV180 @ SV98 ) ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(1926,plain,
! [SV180: $i,SV98: $i] :
( ( ( in @ SV98 @ SV180 )
= $false )
| ( ( in @ ( sK5_C @ SV180 @ SV98 ) @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1927,plain,
! [SV270: $i,SV213: $i] :
( ( ( ( set_difference @ SV213 @ SV270 )
= SV213 )
= $false )
| ( ( disjoint @ SV213 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1928,plain,
! [SV271: $i,SV214: $i] :
( ( ( disjoint @ SV214 @ SV271 )
= $false )
| ( ( ( set_difference @ SV214 @ SV271 )
= SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1929,plain,
! [SV272: $i,SV215: $i] :
( ( ( SV215 = SV272 )
= $true )
| ( ( ~ ( subset @ SV215 @ SV272 ) )
= $true )
| ( ( proper_subset @ SV215 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1930,plain,
! [SV330: $i] :
( ( ! [SY769: $i] :
( ~ ( proper_subset @ SV330 @ SY769 )
| ( SV330 != SY769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(1931,plain,
! [SV331: $i] :
( ( ! [SY770: $i] :
( ~ ( proper_subset @ SV331 @ SY770 )
| ( subset @ SV331 @ SY770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(1932,plain,
! [SV100: $i] :
( ( ( ordinal @ ( sK65_B @ SV100 ) )
= $false )
| ( ( ~ ( subset @ ( sK65_B @ SV100 ) @ SV100 ) )
= $true )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1933,plain,
! [SV101: $i,SV273: $i] :
( ( ( ~ ( subset @ SV273 @ ( sK67_B @ SV101 ) ) )
= $true )
| ( ( are_equipotent @ SV273 @ ( sK67_B @ SV101 ) )
= $true )
| ( ( in @ SV273 @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(1934,plain,
! [SV101: $i] :
( ( ! [SY542: $i] :
( ~ ( in @ SY542 @ ( sK67_B @ SV101 ) )
| ( in @ ( powerset @ SY542 ) @ ( sK67_B @ SV101 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1935,plain,
! [SV101: $i] :
( ( ~ ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) )
| ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1936,plain,
! [SV219: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ SV219 ) )
= $true )
| ( ( SV219 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(1937,plain,
! [SV274: $i,SV220: $i] :
( ( ( in @ SV220 @ SV274 )
= $false )
| ( ( subset @ ( singleton @ SV220 ) @ SV274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1938,plain,
! [SV275: $i,SV221: $i] :
( ( ( subset @ ( singleton @ SV221 ) @ SV275 )
= $false )
| ( ( in @ SV221 @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1939,plain,
! [SV276: $i,SV222: $i] :
( ( ( ( set_intersection2 @ SV222 @ SV276 )
= empty_set )
= $false )
| ( ( disjoint @ SV222 @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1940,plain,
! [SV277: $i,SV223: $i] :
( ( ( disjoint @ SV223 @ SV277 )
= $false )
| ( ( ( set_intersection2 @ SV223 @ SV277 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1941,plain,
! [SV278: $i,SV224: $i] :
( ( ( ( set_difference @ SV224 @ SV278 )
= empty_set )
= $false )
| ( ( subset @ SV224 @ SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1942,plain,
! [SV279: $i,SV225: $i] :
( ( ( subset @ SV225 @ SV279 )
= $false )
| ( ( ( set_difference @ SV225 @ SV279 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1943,plain,
! [SV226: $i] :
( ( ( ~ ! [SY673: $i,SY674: $i] :
( ( sK60_B @ SV226 )
!= ( ordered_pair @ SY673 @ SY674 ) ) )
= $false )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1815]) ).
thf(1944,plain,
! [SV226: $i] :
( ( ( ~ ( in @ ( sK60_B @ SV226 ) @ SV226 ) )
= $false )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1815]) ).
thf(1945,plain,
! [SV227: $i,SV333: $i] :
( ( ( ( SV333
= ( ordered_pair @ ( sK58_C @ SV333 @ SV227 ) @ ( sK59_SY431 @ SV333 @ SV227 ) ) )
| ~ ( in @ SV333 @ SV227 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(1946,plain,
! [SV280: $i,SV319: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV319 )
| ~ ( in @ SV280 @ SV319 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV102 @ SV280 ) @ SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(1947,plain,
! [SV102: $i] :
( ( ! [SY547: $i,SY548: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY547 ) @ SY548 )
| ( in @ SV102 @ SY548 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1948,plain,
! [SV102: $i] :
( ( ! [SY549: $i,SY550: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SY549 ) @ SY550 )
| ( in @ SY549 @ SY550 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1819]) ).
thf(1949,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) ) ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1950,plain,
! [SV282: $i,SV103: $i,SV321: $i] :
( ( ( ( SV321
!= ( set_intersection2 @ SV103 @ SV282 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SV103 )
| ~ ( in @ SY754 @ SV282 )
| ( in @ SY754 @ SV321 ) )
| ~ ~ ( ~ ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) )
| ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1951,plain,
! [SV228: $i,SV283: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ~ ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) )
| ~ ( ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) ) )
= $false )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1952,plain,
! [SV229: $i,SV284: $i] :
( ( ( SV284
= ( powerset @ SV229 ) )
= $false )
| ( ( ~ ( ~ ! [SY729: $i] :
( ~ ( in @ SY729 @ SV284 )
| ( subset @ SY729 @ SV229 ) )
| ~ ! [SY730: $i] :
( ~ ( subset @ SY730 @ SV229 )
| ( in @ SY730 @ SV284 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1953,plain,
! [SV104: $i,SV334: $i] :
( ( ( ~ ( relation @ SV334 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) ) )
| ( SV104 = SV334 ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(1954,plain,
! [SV104: $i,SV335: $i] :
( ( ( ~ ( relation @ SV335 )
| ( SV104 != SV335 )
| ~ ( ~ ! [SY771: $i,SY772: $i] :
( ~ ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV104 )
| ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV335 ) )
| ~ ! [SY773: $i,SY774: $i] :
( ~ ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV335 )
| ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(1955,plain,
! [SV105: $i] :
( ( ( ~ ( element @ ( sK28_B @ SV105 ) @ ( powerset @ SV105 ) ) )
= $false )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1956,plain,
! [SV105: $i] :
( ( ( ~ ~ ( empty @ ( sK28_B @ SV105 ) ) )
= $false )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1957,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
| ~ ( ( ( sK23_SY407 @ SV181 @ SV106 )
!= ( sK24_SY413 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1958,plain,
! [SV107: $i,SV285: $i] :
( ( ( ~ ( in @ SV285 @ SV107 ) )
= $true )
| ( ( ~ ( ordinal @ SV285 ) )
= $true )
| ( ( in @ SV285 @ ( sK68_B @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1959,plain,
! [SV107: $i] :
( ( ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK68_B @ SV107 ) )
| ( in @ SY573 @ SV107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(1960,plain,
! [SV107: $i] :
( ( ! [SY574: $i] :
( ~ ( in @ SY574 @ ( sK68_B @ SV107 ) )
| ( ordinal @ SY574 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1832]) ).
thf(1961,plain,
! [SV230: $i,SV286: $i] :
( ( ( ~ ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV230 )
| ~ ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV286 ) )
= $false )
| ( ( disjoint @ SV230 @ SV286 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1962,plain,
! [SV287: $i,SV231: $i,SV336: $i] :
( ( ( ~ ( in @ SV336 @ SV231 )
| ~ ( in @ SV336 @ SV287 ) )
= $true )
| ( ( ~ ( disjoint @ SV231 @ SV287 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(1963,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( ! [SY732: $i] :
( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SY732 )
| ~ ( in @ SY732 @ SV232 ) )
| ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
| ~ ( ~ ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) )
| ~ ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 ) )
| ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) ) )
= $false )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1964,plain,
! [SV233: $i,SV289: $i] :
( ( ( SV289
= ( union @ SV233 ) )
= $false )
| ( ( ~ ( ~ ! [SY733: $i] :
( ! [SY687: $i] :
( ~ ( in @ SY733 @ SY687 )
| ~ ( in @ SY687 @ SV233 ) )
| ( in @ SY733 @ SV289 ) )
| ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV289 )
| ~ ( ~ ( in @ SY735 @ ( sK39_D @ SY735 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SY735 @ SV289 @ SV233 ) @ SV233 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1965,plain,
! [SV337: $i] :
( ( ( empty @ SV337 )
| ! [SY775: $i] :
( ~ ( element @ SY775 @ SV337 )
| ( in @ SY775 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(1966,plain,
! [SV338: $i] :
( ( ( empty @ SV338 )
| ! [SY776: $i] :
( ~ ( in @ SY776 @ SV338 )
| ( element @ SY776 @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(1967,plain,
! [SV339: $i] :
( ( ~ ( empty @ SV339 )
| ! [SY777: $i] :
( ~ ( element @ SY777 @ SV339 )
| ( empty @ SY777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(1968,plain,
! [SV340: $i] :
( ( ~ ( empty @ SV340 )
| ! [SY778: $i] :
( ~ ( empty @ SY778 )
| ( element @ SY778 @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(1969,plain,
! [SV234: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK45_B @ SV234 )
!= ( sK46_SY427 @ SV234 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1970,plain,
! [SV234: $i] :
( ( ( ~ ~ ( in @ ( sK46_SY427 @ SV234 ) @ ( sK45_B @ SV234 ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1971,plain,
! [SV235: $i,SV341: $i] :
( ( ( ! [SY779: $i] :
( ( SV341 = SY779 )
| ~ ( in @ SV341 @ SV235 )
| ~ ( in @ SY779 @ SV235 )
| ( in @ SV341 @ SY779 )
| ( in @ SY779 @ SV341 ) ) )
= $true )
| ( ( epsilon_connected @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(1972,plain,
! [SV290: $i,SV236: $i] :
( ( ( ~ ( subset @ SV236 @ SV290 ) )
= $true )
| ( ( ~ ( subset @ SV290 @ SV236 ) )
= $true )
| ( ( SV236 = SV290 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1973,plain,
! [SV342: $i] :
( ( ! [SY780: $i] :
( ( SV342 != SY780 )
| ( subset @ SV342 @ SY780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(1974,plain,
! [SV343: $i] :
( ( ! [SY781: $i] :
( ( SV343 != SY781 )
| ( subset @ SY781 @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(1975,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 ) ) )
| ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(1976,plain,
! [SV323: $i,SV182: $i,SV108: $i,SV345: $i] :
( ( ( SV345
!= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
| ~ ( ~ ! [SY782: $i] :
( ~ ( in @ SY782 @ SV345 )
| ( SY782 = SV323 )
| ( SY782 = SV108 )
| ( SY782 = SV182 ) )
| ~ ~ ( ~ ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) )
| ~ ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(1977,plain,
! [SV291: $i,SV237: $i] :
( ( ( element @ SV237 @ ( powerset @ SV291 ) )
= $false )
| ( ( subset @ SV237 @ SV291 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1978,plain,
! [SV292: $i,SV238: $i] :
( ( ( subset @ SV238 @ SV292 )
= $false )
| ( ( element @ SV238 @ ( powerset @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1979,plain,
! [SV109: $i,SV183: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 ) )
= $true )
| ( ( ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) )
= $true )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(1980,plain,
! [SV109: $i,SV183: $i] :
( ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
= $true )
| ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 )
= $true )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(1981,plain,
! [SV293: $i,SV241: $i] :
( ( ( ( set_difference @ SV241 @ SV293 )
= empty_set )
= $false )
| ( ( subset @ SV241 @ SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1982,plain,
! [SV294: $i,SV242: $i] :
( ( ( subset @ SV242 @ SV294 )
= $false )
| ( ( ( set_difference @ SV242 @ SV294 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1983,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) ) ) )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(1984,plain,
! [SV296: $i,SV111: $i,SV325: $i] :
( ( ( ( SV325
!= ( set_difference @ SV111 @ SV296 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY763: $i] :
( ~ ( in @ SY763 @ SV111 )
| ( in @ SY763 @ SV296 )
| ( in @ SY763 @ SV325 ) )
| ~ ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) )
| ~ ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(1985,plain,
! [SV184: $i,SV112: $i] :
( ( ( ! [SY655: $i] :
( ~ ( element @ SY655 @ ( powerset @ SV112 ) )
| ~ ( disjoint @ SV184 @ SY655 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SY655 ) ) ) )
= $true )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1986,plain,
! [SV184: $i,SV112: $i] :
( ( ( ! [SY656: $i] :
( ~ ( element @ SY656 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SY656 ) )
| ( disjoint @ SV184 @ SY656 ) ) )
= $true )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(1987,plain,
! [SV297: $i,SV113: $i] :
( ( ( subset @ SV113 @ SV297 )
= $false )
| ( ( ! [SY741: $i] : ( subset @ ( cartesian_product2 @ SV113 @ SY741 ) @ ( cartesian_product2 @ SV297 @ SY741 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1988,plain,
! [SV298: $i,SV113: $i] :
( ( ( subset @ SV113 @ SV298 )
= $false )
| ( ( ! [SY742: $i] : ( subset @ ( cartesian_product2 @ SY742 @ SV113 ) @ ( cartesian_product2 @ SY742 @ SV298 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(1989,plain,
! [SV114: $i,SV299: $i] :
( ( ( ~ ( subset @ SV299 @ ( sK3_B @ SV114 ) ) )
= $true )
| ( ( are_equipotent @ SV299 @ ( sK3_B @ SV114 ) )
= $true )
| ( ( in @ SV299 @ ( sK3_B @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(1990,plain,
! [SV114: $i] :
( ( ! [SY600: $i] :
( ~ ( ~ ! [SY601: $i] :
( ~ ( subset @ SY601 @ SY600 )
| ( in @ SY601 @ ( sK4_SY376 @ SY600 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SY600 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SY600 @ ( sK3_B @ SV114 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(1991,plain,
! [SV114: $i] :
( ( ~ ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(1992,plain,
! [SV300: $i,SV243: $i] :
( ( ( in @ SV243 @ SV300 )
= $false )
| ( ( subset @ ( singleton @ SV243 ) @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1993,plain,
! [SV301: $i,SV244: $i] :
( ( ( subset @ ( singleton @ SV244 ) @ SV301 )
= $false )
| ( ( in @ SV244 @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1994,plain,
! [SV245: $i] :
( ( ( ~ ( in @ ( sK51_B @ SV245 ) @ SV245 ) )
= $false )
| ( ( epsilon_transitive @ SV245 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(1995,plain,
! [SV245: $i] :
( ( ( ~ ~ ( subset @ ( sK51_B @ SV245 ) @ SV245 ) )
= $false )
| ( ( epsilon_transitive @ SV245 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(1996,plain,
! [SV246: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ SV246 )
| ( subset @ SV346 @ SV246 ) )
= $true )
| ( ( epsilon_transitive @ SV246 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(1997,plain,
! [SV302: $i,SV247: $i] :
( ( ( ( set_difference @ SV247 @ ( singleton @ SV302 ) )
= SV247 )
= $false )
| ( ( ~ ( in @ SV302 @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1998,plain,
! [SV304: $i,SV249: $i] :
( ( ( subset @ SV249 @ ( singleton @ SV304 ) )
= $false )
| ( ( ( SV249 = empty_set )
| ( SV249
= ( singleton @ SV304 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1999,plain,
! [SV347: $i] :
( ( ( SV347 != empty_set )
| ! [SY786: $i] : ( subset @ SV347 @ ( singleton @ SY786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2000,plain,
! [SV348: $i] :
( ( ! [SY787: $i] :
( ( SV348
!= ( singleton @ SY787 ) )
| ( subset @ SV348 @ ( singleton @ SY787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2001,plain,
! [SV305: $i,SV252: $i] :
( ( ( ~ ( empty @ SV252 ) )
= $true )
| ( ( ~ ( relation @ SV305 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV305 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(2002,plain,
! [SV306: $i,SV253: $i] :
( ( ( ~ ( empty @ SV253 ) )
= $true )
| ( ( ~ ( relation @ SV306 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV306 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2003,plain,
! [SV116: $i,SV185: $i] :
( ( ( in @ ( sK69_C @ SV185 @ SV116 ) @ SV185 )
= $false )
| ( ( element @ SV116 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(2004,plain,
! [SV307: $i,SV254: $i] :
( ( ( subset @ SV254 @ ( singleton @ SV307 ) )
= $false )
| ( ( ( SV254 = empty_set )
| ( SV254
= ( singleton @ SV307 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(2005,plain,
! [SV349: $i] :
( ( ( SV349 != empty_set )
| ! [SY788: $i] : ( subset @ SV349 @ ( singleton @ SY788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2006,plain,
! [SV350: $i] :
( ( ! [SY789: $i] :
( ( SV350
!= ( singleton @ SY789 ) )
| ( subset @ SV350 @ ( singleton @ SY789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2007,plain,
! [SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1886]) ).
thf(2008,plain,
! [SV117: $i] :
( ( ( ( ( sK17_SY395 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1886]) ).
thf(2009,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2010,plain,
! [SV118: $i,SV351: $i] :
( ( ( ~ ( relation @ SV351 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV351 ) )
| ( subset @ SV118 @ SV351 ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2011,plain,
! [SV118: $i,SV352: $i] :
( ( ( ~ ( relation @ SV352 )
| ~ ( subset @ SV118 @ SV352 )
| ! [SY790: $i,SY791: $i] :
( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV118 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV352 ) ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2012,plain,
! [SV308: $i,SV255: $i] :
( ( ( ~ ( empty @ SV255 ) )
= $true )
| ( ( ~ ( relation @ SV308 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV255 @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2013,plain,
! [SV309: $i,SV256: $i] :
( ( ( ~ ( empty @ SV256 ) )
= $true )
| ( ( ~ ( relation @ SV309 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV256 @ SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2014,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) ) )
| ~ ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV119 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV310 ) ) ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2015,plain,
! [SV311: $i,SV119: $i,SV327: $i] :
( ( ( ( SV327
!= ( unordered_pair @ SV119 @ SV311 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY766: $i] :
( ~ ( in @ SY766 @ SV327 )
| ( SY766 = SV119 )
| ( SY766 = SV311 ) )
| ~ ~ ( ~ ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) )
| ~ ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2016,plain,
! [SV257: $i,SV312: $i] :
( ( ( ~ ( ( ( sK54_C @ SV312 @ SV257 )
!= SV257 )
| ~ ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) )
| ~ ( ( ( sK54_C @ SV312 @ SV257 )
= SV257 )
| ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) ) )
= $false )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(2017,plain,
! [SV258: $i,SV313: $i] :
( ( ( SV313
= ( singleton @ SV258 ) )
= $false )
| ( ( ~ ( ~ ! [SY748: $i] :
( ( SY748 != SV258 )
| ( in @ SY748 @ SV313 ) )
| ~ ! [SY749: $i] :
( ~ ( in @ SY749 @ SV313 )
| ( SY749 = SV258 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2018,plain,
! [SV259: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV259 )
| ~ ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV314 ) )
= $false )
| ( ( subset @ SV259 @ SV314 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(2019,plain,
! [SV315: $i,SV260: $i] :
( ( ( subset @ SV260 @ SV315 )
= $false )
| ( ( ! [SY750: $i] :
( ~ ( in @ SY750 @ SV260 )
| ( in @ SY750 @ SV315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(2020,plain,
! [SV353: $i] :
( ( ( SV353 = empty_set )
| ! [SY792: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SY792 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SY792 @ SV353 ) @ ( sK57_SY429 @ SY792 @ SV353 ) ) )
| ~ ( in @ ( sK56_C @ SY792 @ SV353 ) @ SY792 ) )
| ~ ( ! [SY793: $i] :
( ~ ( in @ SY793 @ SV353 )
| ( in @ ( sK56_C @ SY792 @ SV353 ) @ SY793 ) )
| ( in @ ( sK56_C @ SY792 @ SV353 ) @ SY792 ) ) )
| ( SY792
= ( set_meet @ SV353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2021,plain,
! [SV354: $i] :
( ( ( SV354 = empty_set )
| ! [SY794: $i] :
( ( SY794
!= ( set_meet @ SV354 ) )
| ~ ( ~ ! [SY795: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SY795 @ SY794 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SY795 @ ( sK55_D @ SY795 @ SY794 @ SV354 ) ) )
| ( in @ SY795 @ SY794 ) )
| ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ SY794 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ SV354 )
| ( in @ SY796 @ SY797 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2022,plain,
! [SV355: $i] :
( ( ( SV355 != empty_set )
| ! [SY798: $i] :
( ( SY798
!= ( set_meet @ SV355 ) )
| ( SY798 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2023,plain,
! [SV356: $i] :
( ( ( SV356 != empty_set )
| ! [SY799: $i] :
( ( SY799 != empty_set )
| ( SY799
= ( set_meet @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2024,plain,
! [SV134: $i,SV23: $i,SV206: $i,SV188: $i] :
( ( ( subset @ SV188 @ SV206 )
= $false )
| ( ( subset @ SV23 @ SV134 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV23 @ SV188 ) @ ( cartesian_product2 @ SV134 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(2025,plain,
! [SV189: $i,SV207: $i,SV136: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV136 )
= $false )
| ( ( relation_of2_as_subset @ SV207 @ SV189 @ SV136 )
= $true )
| ( ( relation_of2_as_subset @ SV207 @ SV189 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(2026,plain,
! [SV208: $i,SV29: $i] :
( ( ( in @ SV29 @ SV208 )
= $true )
| ( ( SV29 = SV208 )
= $true )
| ( ( in @ SV208 @ SV29 )
= $true )
| ( ( ordinal @ SV208 )
= $false )
| ( ( ordinal @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1908]) ).
thf(2027,plain,
! [SV143: $i,SV34: $i,SV192: $i] :
( ( ( in @ SV192 @ SV34 )
= $false )
| ( ( in @ SV34 @ SV143 )
= $false )
| ( ( in @ SV143 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2028,plain,
! [SV193: $i,SV39: $i,SV316: $i] :
( ( ( element @ SV316 @ SV39 )
= $false )
| ( ( ( in @ SV316 @ SV193 )
| ( in @ SV316 @ ( subset_complement @ SV39 @ SV193 ) ) )
= $true )
| ( ( element @ SV193 @ ( powerset @ SV39 ) )
= $false )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(2029,plain,
! [SV40: $i,SV194: $i,SV147: $i] :
( ( ( in @ SV147 @ SV194 )
= $false )
| ( ( in @ SV147 @ ( subset_complement @ SV40 @ SV194 ) )
= $false )
| ( ( element @ SV194 @ ( powerset @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(2030,plain,
! [SV93: $i,SV177: $i,SV203: $i] :
( ( ( empty @ SV203 )
= $false )
| ( ( element @ SV177 @ ( powerset @ SV203 ) )
= $false )
| ( ( in @ SV93 @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2031,plain,
! [SV265: $i] :
( ( ( ! [SY714: $i] :
( ! [SY715: $i] :
( ( SY715 != SY714 )
| ~ ( in @ SY715 @ SV265 ) )
| ~ ( ordinal @ SY714 )
| ( in @ SY714 @ ( sK7_B @ SV265 ) ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(2032,plain,
! [SV265: $i] :
( ( ( ! [SY716: $i] :
( ~ ( in @ SY716 @ ( sK7_B @ SV265 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SY716 @ SV265 )
!= SY716 )
| ~ ( in @ ( sK8_D @ SY716 @ SV265 ) @ SV265 ) )
| ~ ( ordinal @ SY716 ) ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(2033,plain,
( ( ( ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) ) )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(2034,plain,
( ( ( ( sK10_SY386 != sK11_SY388 ) )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(2035,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) )
| ~ ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) )
= $false )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(2036,plain,
! [SV267: $i,SV97: $i,SV318: $i] :
( ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false )
| ( ( ~ ( ~ ! [SY751: $i] :
( ~ ( in @ SY751 @ SV318 )
| ( in @ SY751 @ SV97 )
| ( in @ SY751 @ SV267 ) )
| ~ ~ ( ~ ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) )
| ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2037,plain,
! [SV269: $i,SV212: $i,SV328: $i] :
( ( ( in @ SV328 @ ( set_intersection2 @ SV212 @ SV269 ) )
= $false )
| ( ( ~ ( disjoint @ SV212 @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2038,plain,
! [SV98: $i,SV180: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV180 ) )
= $true )
| ( ( ~ ( in @ SV329 @ ( sK5_C @ SV180 @ SV98 ) ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2039,plain,
! [SV272: $i,SV215: $i] :
( ( ( subset @ SV215 @ SV272 )
= $false )
| ( ( SV215 = SV272 )
= $true )
| ( ( proper_subset @ SV215 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2040,plain,
! [SV357: $i,SV330: $i] :
( ( ~ ( proper_subset @ SV330 @ SV357 )
| ( SV330 != SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2041,plain,
! [SV358: $i,SV331: $i] :
( ( ~ ( proper_subset @ SV331 @ SV358 )
| ( subset @ SV331 @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2042,plain,
! [SV100: $i] :
( ( ( subset @ ( sK65_B @ SV100 ) @ SV100 )
= $false )
| ( ( ordinal @ ( sK65_B @ SV100 ) )
= $false )
| ( ( ordinal @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2043,plain,
! [SV101: $i,SV273: $i] :
( ( ( subset @ SV273 @ ( sK67_B @ SV101 ) )
= $false )
| ( ( are_equipotent @ SV273 @ ( sK67_B @ SV101 ) )
= $true )
| ( ( in @ SV273 @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2044,plain,
! [SV101: $i,SV359: $i] :
( ( ~ ( in @ SV359 @ ( sK67_B @ SV101 ) )
| ( in @ ( powerset @ SV359 ) @ ( sK67_B @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2045,plain,
! [SV101: $i] :
( ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) )
| ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2046,plain,
! [SV219: $i,SV332: $i] :
( ( ( in @ SV332 @ SV219 )
= $false )
| ( ( SV219 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2047,plain,
! [SV226: $i] :
( ( ( ! [SY673: $i,SY674: $i] :
( ( sK60_B @ SV226 )
!= ( ordered_pair @ SY673 @ SY674 ) ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(2048,plain,
! [SV226: $i] :
( ( ( in @ ( sK60_B @ SV226 ) @ SV226 )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2049,plain,
! [SV227: $i,SV333: $i] :
( ( ( SV333
= ( ordered_pair @ ( sK58_C @ SV333 @ SV227 ) @ ( sK59_SY431 @ SV333 @ SV227 ) ) )
= $true )
| ( ( ~ ( in @ SV333 @ SV227 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2050,plain,
! [SV280: $i,SV319: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV319 ) )
= $true )
| ( ( ~ ( in @ SV280 @ SV319 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV102 @ SV280 ) @ SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2051,plain,
! [SV360: $i,SV102: $i] :
( ( ! [SY800: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SV360 ) @ SY800 )
| ( in @ SV102 @ SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2052,plain,
! [SV361: $i,SV102: $i] :
( ( ! [SY801: $i] :
( ~ ( subset @ ( unordered_pair @ SV102 @ SV361 ) @ SY801 )
| ( in @ SV361 @ SY801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2053,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ~ ( ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) ) )
= $false )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2054,plain,
! [SV282: $i,SV103: $i,SV321: $i] :
( ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false )
| ( ( ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SV103 )
| ~ ( in @ SY754 @ SV282 )
| ( in @ SY754 @ SV321 ) )
| ~ ~ ( ~ ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) )
| ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2055,plain,
! [SV228: $i,SV283: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ~ ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) ) )
= $false )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1951]) ).
thf(2056,plain,
! [SV228: $i,SV283: $i] :
( ( ( ~ ( ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) ) )
= $false )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1951]) ).
thf(2057,plain,
! [SV229: $i,SV284: $i] :
( ( ( ~ ! [SY729: $i] :
( ~ ( in @ SY729 @ SV284 )
| ( subset @ SY729 @ SV229 ) )
| ~ ! [SY730: $i] :
( ~ ( subset @ SY730 @ SV229 )
| ( in @ SY730 @ SV284 ) ) )
= $false )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2058,plain,
! [SV104: $i,SV334: $i] :
( ( ( ~ ( relation @ SV334 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) ) )
| ( SV104 = SV334 ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2059,plain,
! [SV104: $i,SV335: $i] :
( ( ( ~ ( relation @ SV335 ) )
= $true )
| ( ( ( SV104 != SV335 )
| ~ ( ~ ! [SY771: $i,SY772: $i] :
( ~ ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV104 )
| ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV335 ) )
| ~ ! [SY773: $i,SY774: $i] :
( ~ ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV335 )
| ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2060,plain,
! [SV105: $i] :
( ( ( element @ ( sK28_B @ SV105 ) @ ( powerset @ SV105 ) )
= $true )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(2061,plain,
! [SV105: $i] :
( ( ( ~ ( empty @ ( sK28_B @ SV105 ) ) )
= $true )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(2062,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(2063,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ( ( sK23_SY407 @ SV181 @ SV106 )
!= ( sK24_SY413 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(2064,plain,
! [SV107: $i,SV285: $i] :
( ( ( in @ SV285 @ SV107 )
= $false )
| ( ( ~ ( ordinal @ SV285 ) )
= $true )
| ( ( in @ SV285 @ ( sK68_B @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2065,plain,
! [SV107: $i,SV362: $i] :
( ( ~ ( in @ SV362 @ ( sK68_B @ SV107 ) )
| ( in @ SV362 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2066,plain,
! [SV107: $i,SV363: $i] :
( ( ~ ( in @ SV363 @ ( sK68_B @ SV107 ) )
| ( ordinal @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2067,plain,
! [SV230: $i,SV286: $i] :
( ( ( ~ ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV230 ) )
= $false )
| ( ( disjoint @ SV230 @ SV286 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1961]) ).
thf(2068,plain,
! [SV230: $i,SV286: $i] :
( ( ( ~ ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV286 ) )
= $false )
| ( ( disjoint @ SV230 @ SV286 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1961]) ).
thf(2069,plain,
! [SV287: $i,SV231: $i,SV336: $i] :
( ( ( ~ ( in @ SV336 @ SV231 ) )
= $true )
| ( ( ~ ( in @ SV336 @ SV287 ) )
= $true )
| ( ( ~ ( disjoint @ SV231 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2070,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( ! [SY732: $i] :
( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SY732 )
| ~ ( in @ SY732 @ SV232 ) )
| ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) ) )
= $false )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1963]) ).
thf(2071,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) )
| ~ ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 ) )
| ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) ) )
= $false )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1963]) ).
thf(2072,plain,
! [SV289: $i,SV233: $i] :
( ( ( ~ ! [SY733: $i] :
( ! [SY687: $i] :
( ~ ( in @ SY733 @ SY687 )
| ~ ( in @ SY687 @ SV233 ) )
| ( in @ SY733 @ SV289 ) )
| ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV289 )
| ~ ( ~ ( in @ SY735 @ ( sK39_D @ SY735 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SY735 @ SV289 @ SV233 ) @ SV233 ) ) ) )
= $false )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2073,plain,
! [SV337: $i] :
( ( ( empty @ SV337 )
= $true )
| ( ( ! [SY775: $i] :
( ~ ( element @ SY775 @ SV337 )
| ( in @ SY775 @ SV337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2074,plain,
! [SV338: $i] :
( ( ( empty @ SV338 )
= $true )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ SV338 )
| ( element @ SY776 @ SV338 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2075,plain,
! [SV339: $i] :
( ( ( ~ ( empty @ SV339 ) )
= $true )
| ( ( ! [SY777: $i] :
( ~ ( element @ SY777 @ SV339 )
| ( empty @ SY777 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(2076,plain,
! [SV340: $i] :
( ( ( ~ ( empty @ SV340 ) )
= $true )
| ( ( ! [SY778: $i] :
( ~ ( empty @ SY778 )
| ( element @ SY778 @ SV340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2077,plain,
! [SV234: $i] :
( ( ( ~ ( ~ ( ( ( sK45_B @ SV234 )
!= ( sK46_SY427 @ SV234 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) ) ) )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1969]) ).
thf(2078,plain,
! [SV234: $i] :
( ( ( ~ ( in @ ( sK46_SY427 @ SV234 ) @ ( sK45_B @ SV234 ) ) )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2079,plain,
! [SV235: $i,SV364: $i,SV341: $i] :
( ( ( ( SV341 = SV364 )
| ~ ( in @ SV341 @ SV235 )
| ~ ( in @ SV364 @ SV235 )
| ( in @ SV341 @ SV364 )
| ( in @ SV364 @ SV341 ) )
= $true )
| ( ( epsilon_connected @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2080,plain,
! [SV290: $i,SV236: $i] :
( ( ( subset @ SV236 @ SV290 )
= $false )
| ( ( ~ ( subset @ SV290 @ SV236 ) )
= $true )
| ( ( SV236 = SV290 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2081,plain,
! [SV365: $i,SV342: $i] :
( ( ( SV342 != SV365 )
| ( subset @ SV342 @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2082,plain,
! [SV366: $i,SV343: $i] :
( ( ( SV343 != SV366 )
| ( subset @ SV366 @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2083,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 ) ) ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2084,plain,
! [SV323: $i,SV182: $i,SV108: $i,SV345: $i] :
( ( ( ( SV345
!= ( unordered_triple @ SV108 @ SV182 @ SV323 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY782: $i] :
( ~ ( in @ SY782 @ SV345 )
| ( SY782 = SV323 )
| ( SY782 = SV108 )
| ( SY782 = SV182 ) )
| ~ ~ ( ~ ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) )
| ~ ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2085,plain,
! [SV109: $i,SV183: $i] :
( ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
= $false )
| ( ( ~ ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 ) )
= $true )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2086,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) ) )
= $false )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2087,plain,
! [SV296: $i,SV111: $i,SV325: $i] :
( ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false )
| ( ( ~ ( ~ ! [SY763: $i] :
( ~ ( in @ SY763 @ SV111 )
| ( in @ SY763 @ SV296 )
| ( in @ SY763 @ SV325 ) )
| ~ ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) )
| ~ ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2088,plain,
! [SV184: $i,SV112: $i,SV367: $i] :
( ( ( ~ ( element @ SV367 @ ( powerset @ SV112 ) )
| ~ ( disjoint @ SV184 @ SV367 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SV367 ) ) )
= $true )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2089,plain,
! [SV184: $i,SV112: $i,SV368: $i] :
( ( ( ~ ( element @ SV368 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SV368 ) )
| ( disjoint @ SV184 @ SV368 ) )
= $true )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2090,plain,
! [SV297: $i,SV369: $i,SV113: $i] :
( ( ( subset @ ( cartesian_product2 @ SV113 @ SV369 ) @ ( cartesian_product2 @ SV297 @ SV369 ) )
= $true )
| ( ( subset @ SV113 @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2091,plain,
! [SV298: $i,SV113: $i,SV370: $i] :
( ( ( subset @ ( cartesian_product2 @ SV370 @ SV113 ) @ ( cartesian_product2 @ SV370 @ SV298 ) )
= $true )
| ( ( subset @ SV113 @ SV298 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2092,plain,
! [SV114: $i,SV299: $i] :
( ( ( subset @ SV299 @ ( sK3_B @ SV114 ) )
= $false )
| ( ( are_equipotent @ SV299 @ ( sK3_B @ SV114 ) )
= $true )
| ( ( in @ SV299 @ ( sK3_B @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2093,plain,
! [SV114: $i,SV371: $i] :
( ( ~ ( ~ ! [SY802: $i] :
( ~ ( subset @ SY802 @ SV371 )
| ( in @ SY802 @ ( sK4_SY376 @ SV371 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SV371 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2094,plain,
! [SV114: $i] :
( ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) )
| ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2095,plain,
! [SV245: $i] :
( ( ( in @ ( sK51_B @ SV245 ) @ SV245 )
= $true )
| ( ( epsilon_transitive @ SV245 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1994]) ).
thf(2096,plain,
! [SV245: $i] :
( ( ( ~ ( subset @ ( sK51_B @ SV245 ) @ SV245 ) )
= $true )
| ( ( epsilon_transitive @ SV245 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2097,plain,
! [SV246: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ SV246 ) )
= $true )
| ( ( subset @ SV346 @ SV246 )
= $true )
| ( ( epsilon_transitive @ SV246 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2098,plain,
! [SV247: $i,SV302: $i] :
( ( ( in @ SV302 @ SV247 )
= $false )
| ( ( ( set_difference @ SV247 @ ( singleton @ SV302 ) )
= SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2099,plain,
! [SV304: $i,SV249: $i] :
( ( ( SV249 = empty_set )
= $true )
| ( ( SV249
= ( singleton @ SV304 ) )
= $true )
| ( ( subset @ SV249 @ ( singleton @ SV304 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2100,plain,
! [SV347: $i] :
( ( ( ( SV347 != empty_set ) )
= $true )
| ( ( ! [SY786: $i] : ( subset @ SV347 @ ( singleton @ SY786 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1999]) ).
thf(2101,plain,
! [SV372: $i,SV348: $i] :
( ( ( SV348
!= ( singleton @ SV372 ) )
| ( subset @ SV348 @ ( singleton @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2102,plain,
! [SV305: $i,SV252: $i] :
( ( ( empty @ SV252 )
= $false )
| ( ( ~ ( relation @ SV305 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV305 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2103,plain,
! [SV306: $i,SV253: $i] :
( ( ( empty @ SV253 )
= $false )
| ( ( ~ ( relation @ SV306 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV306 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2104,plain,
! [SV307: $i,SV254: $i] :
( ( ( SV254 = empty_set )
= $true )
| ( ( SV254
= ( singleton @ SV307 ) )
= $true )
| ( ( subset @ SV254 @ ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2004]) ).
thf(2105,plain,
! [SV349: $i] :
( ( ( ( SV349 != empty_set ) )
= $true )
| ( ( ! [SY788: $i] : ( subset @ SV349 @ ( singleton @ SY788 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2106,plain,
! [SV373: $i,SV350: $i] :
( ( ( SV350
!= ( singleton @ SV373 ) )
| ( subset @ SV350 @ ( singleton @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2107,plain,
! [SV117: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2007]) ).
thf(2108,plain,
! [SV117: $i] :
( ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2109,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2110,plain,
! [SV117: $i] :
( ( ( ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2111,plain,
! [SV118: $i,SV351: $i] :
( ( ( ~ ( relation @ SV351 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV351 ) )
| ( subset @ SV118 @ SV351 ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2112,plain,
! [SV118: $i,SV352: $i] :
( ( ( ~ ( relation @ SV352 ) )
= $true )
| ( ( ~ ( subset @ SV118 @ SV352 )
| ! [SY790: $i,SY791: $i] :
( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV118 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV352 ) ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2113,plain,
! [SV308: $i,SV255: $i] :
( ( ( empty @ SV255 )
= $false )
| ( ( ~ ( relation @ SV308 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV255 @ SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2114,plain,
! [SV309: $i,SV256: $i] :
( ( ( empty @ SV256 )
= $false )
| ( ( ~ ( relation @ SV309 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV256 @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2115,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) ) )
| ~ ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV119 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV310 ) ) )
= $false )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2116,plain,
! [SV311: $i,SV119: $i,SV327: $i] :
( ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false )
| ( ( ~ ( ~ ! [SY766: $i] :
( ~ ( in @ SY766 @ SV327 )
| ( SY766 = SV119 )
| ( SY766 = SV311 ) )
| ~ ~ ( ~ ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) )
| ~ ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2117,plain,
! [SV257: $i,SV312: $i] :
( ( ( ~ ( ( ( sK54_C @ SV312 @ SV257 )
!= SV257 )
| ~ ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) ) )
= $false )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2118,plain,
! [SV257: $i,SV312: $i] :
( ( ( ~ ( ( ( sK54_C @ SV312 @ SV257 )
= SV257 )
| ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) ) )
= $false )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2119,plain,
! [SV313: $i,SV258: $i] :
( ( ( ~ ! [SY748: $i] :
( ( SY748 != SV258 )
| ( in @ SY748 @ SV313 ) )
| ~ ! [SY749: $i] :
( ~ ( in @ SY749 @ SV313 )
| ( SY749 = SV258 ) ) )
= $false )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2120,plain,
! [SV259: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV259 ) )
= $false )
| ( ( subset @ SV259 @ SV314 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2121,plain,
! [SV259: $i,SV314: $i] :
( ( ( ~ ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV314 ) )
= $false )
| ( ( subset @ SV259 @ SV314 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2122,plain,
! [SV315: $i,SV260: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ SV260 )
| ( in @ SV374 @ SV315 ) )
= $true )
| ( ( subset @ SV260 @ SV315 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2123,plain,
! [SV353: $i] :
( ( ( SV353 = empty_set )
= $true )
| ( ( ! [SY792: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SY792 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SY792 @ SV353 ) @ ( sK57_SY429 @ SY792 @ SV353 ) ) )
| ~ ( in @ ( sK56_C @ SY792 @ SV353 ) @ SY792 ) )
| ~ ( ! [SY793: $i] :
( ~ ( in @ SY793 @ SV353 )
| ( in @ ( sK56_C @ SY792 @ SV353 ) @ SY793 ) )
| ( in @ ( sK56_C @ SY792 @ SV353 ) @ SY792 ) ) )
| ( SY792
= ( set_meet @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2124,plain,
! [SV354: $i] :
( ( ( SV354 = empty_set )
= $true )
| ( ( ! [SY794: $i] :
( ( SY794
!= ( set_meet @ SV354 ) )
| ~ ( ~ ! [SY795: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SY795 @ SY794 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SY795 @ ( sK55_D @ SY795 @ SY794 @ SV354 ) ) )
| ( in @ SY795 @ SY794 ) )
| ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ SY794 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ SV354 )
| ( in @ SY796 @ SY797 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2125,plain,
! [SV355: $i] :
( ( ( ( SV355 != empty_set ) )
= $true )
| ( ( ! [SY798: $i] :
( ( SY798
!= ( set_meet @ SV355 ) )
| ( SY798 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2126,plain,
! [SV356: $i] :
( ( ( ( SV356 != empty_set ) )
= $true )
| ( ( ! [SY799: $i] :
( ( SY799 != empty_set )
| ( SY799
= ( set_meet @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2023]) ).
thf(2127,plain,
! [SV39: $i,SV193: $i,SV316: $i] :
( ( ( in @ SV316 @ SV193 )
= $true )
| ( ( in @ SV316 @ ( subset_complement @ SV39 @ SV193 ) )
= $true )
| ( ( element @ SV316 @ SV39 )
= $false )
| ( ( element @ SV193 @ ( powerset @ SV39 ) )
= $false )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2128,plain,
! [SV265: $i,SV375: $i] :
( ( ( ! [SY803: $i] :
( ( SY803 != SV375 )
| ~ ( in @ SY803 @ SV265 ) )
| ~ ( ordinal @ SV375 )
| ( in @ SV375 @ ( sK7_B @ SV265 ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2129,plain,
! [SV265: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ ( sK7_B @ SV265 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SV376 @ SV265 )
!= SV376 )
| ~ ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 ) )
| ~ ( ordinal @ SV376 ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2130,plain,
( ( ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
| ~ ( ordinal @ sK11_SY388 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2131,plain,
( ( ( sK10_SY386 = sK11_SY388 )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2132,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) ) )
= $false )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2035]) ).
thf(2133,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) )
= $false )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2035]) ).
thf(2134,plain,
! [SV267: $i,SV97: $i,SV318: $i] :
( ( ( ~ ! [SY751: $i] :
( ~ ( in @ SY751 @ SV318 )
| ( in @ SY751 @ SV97 )
| ( in @ SY751 @ SV267 ) )
| ~ ~ ( ~ ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) )
| ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) ) )
= $false )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2135,plain,
! [SV328: $i,SV269: $i,SV212: $i] :
( ( ( disjoint @ SV212 @ SV269 )
= $false )
| ( ( in @ SV328 @ ( set_intersection2 @ SV212 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2136,plain,
! [SV98: $i,SV180: $i,SV329: $i] :
( ( ( in @ SV329 @ SV180 )
= $false )
| ( ( ~ ( in @ SV329 @ ( sK5_C @ SV180 @ SV98 ) ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2137,plain,
! [SV357: $i,SV330: $i] :
( ( ( ~ ( proper_subset @ SV330 @ SV357 ) )
= $true )
| ( ( ( SV330 != SV357 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2138,plain,
! [SV358: $i,SV331: $i] :
( ( ( ~ ( proper_subset @ SV331 @ SV358 ) )
= $true )
| ( ( subset @ SV331 @ SV358 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2139,plain,
! [SV101: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ ( sK67_B @ SV101 ) ) )
= $true )
| ( ( in @ ( powerset @ SV359 ) @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2140,plain,
! [SV101: $i] :
( ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2141,plain,
! [SV101: $i] :
( ( ~ ( in @ SV101 @ ( sK67_B @ SV101 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2142,plain,
! [SV377: $i,SV226: $i] :
( ( ( ! [SY804: $i] :
( ( sK60_B @ SV226 )
!= ( ordered_pair @ SV377 @ SY804 ) ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2143,plain,
! [SV227: $i,SV333: $i] :
( ( ( in @ SV333 @ SV227 )
= $false )
| ( ( SV333
= ( ordered_pair @ ( sK58_C @ SV333 @ SV227 ) @ ( sK59_SY431 @ SV333 @ SV227 ) ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2144,plain,
! [SV280: $i,SV319: $i,SV102: $i] :
( ( ( in @ SV102 @ SV319 )
= $false )
| ( ( ~ ( in @ SV280 @ SV319 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV102 @ SV280 ) @ SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2145,plain,
! [SV378: $i,SV360: $i,SV102: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV102 @ SV360 ) @ SV378 )
| ( in @ SV102 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2146,plain,
! [SV379: $i,SV361: $i,SV102: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV102 @ SV361 ) @ SV379 )
| ( in @ SV361 @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2147,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) )
= $false )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2148,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) ) )
= $false )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2149,plain,
! [SV321: $i,SV282: $i,SV103: $i] :
( ( ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SV103 )
| ~ ( in @ SY754 @ SV282 )
| ( in @ SY754 @ SV321 ) )
| ~ ~ ( ~ ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) )
| ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) ) )
= $false )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2150,plain,
! [SV228: $i,SV283: $i] :
( ( ( ~ ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ~ ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) )
= $true )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2151,plain,
! [SV228: $i,SV283: $i] :
( ( ( ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
| ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) )
= $true )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2056]) ).
thf(2152,plain,
! [SV229: $i,SV284: $i] :
( ( ( ~ ! [SY729: $i] :
( ~ ( in @ SY729 @ SV284 )
| ( subset @ SY729 @ SV229 ) ) )
= $false )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2153,plain,
! [SV284: $i,SV229: $i] :
( ( ( ~ ! [SY730: $i] :
( ~ ( subset @ SY730 @ SV229 )
| ( in @ SY730 @ SV284 ) ) )
= $false )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2154,plain,
! [SV104: $i,SV334: $i] :
( ( ( relation @ SV334 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) ) )
| ( SV104 = SV334 ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2155,plain,
! [SV104: $i,SV335: $i] :
( ( ( relation @ SV335 )
= $false )
| ( ( ( SV104 != SV335 )
| ~ ( ~ ! [SY771: $i,SY772: $i] :
( ~ ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV104 )
| ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV335 ) )
| ~ ! [SY773: $i,SY774: $i] :
( ~ ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV335 )
| ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2156,plain,
! [SV105: $i] :
( ( ( empty @ ( sK28_B @ SV105 ) )
= $false )
| ( ( empty @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2157,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2158,plain,
! [SV106: $i,SV181: $i] :
( ( ( ( ( sK23_SY407 @ SV181 @ SV106 )
!= ( sK24_SY413 @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2063]) ).
thf(2159,plain,
! [SV107: $i,SV285: $i] :
( ( ( ordinal @ SV285 )
= $false )
| ( ( in @ SV285 @ SV107 )
= $false )
| ( ( in @ SV285 @ ( sK68_B @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2160,plain,
! [SV107: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ ( sK68_B @ SV107 ) ) )
= $true )
| ( ( in @ SV362 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2065]) ).
thf(2161,plain,
! [SV107: $i,SV363: $i] :
( ( ( ~ ( in @ SV363 @ ( sK68_B @ SV107 ) ) )
= $true )
| ( ( ordinal @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2162,plain,
! [SV230: $i,SV286: $i] :
( ( ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV230 )
= $true )
| ( ( disjoint @ SV230 @ SV286 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2163,plain,
! [SV230: $i,SV286: $i] :
( ( ( in @ ( sK64_C @ SV286 @ SV230 ) @ SV286 )
= $true )
| ( ( disjoint @ SV230 @ SV286 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2164,plain,
! [SV287: $i,SV231: $i,SV336: $i] :
( ( ( in @ SV336 @ SV231 )
= $false )
| ( ( ~ ( in @ SV336 @ SV287 ) )
= $true )
| ( ( ~ ( disjoint @ SV231 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2165,plain,
! [SV232: $i,SV288: $i] :
( ( ( ! [SY732: $i] :
( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SY732 )
| ~ ( in @ SY732 @ SV232 ) )
| ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2166,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) )
| ~ ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 ) )
| ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2167,plain,
! [SV289: $i,SV233: $i] :
( ( ( ~ ! [SY733: $i] :
( ! [SY687: $i] :
( ~ ( in @ SY733 @ SY687 )
| ~ ( in @ SY687 @ SV233 ) )
| ( in @ SY733 @ SV289 ) ) )
= $false )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2168,plain,
! [SV233: $i,SV289: $i] :
( ( ( ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV289 )
| ~ ( ~ ( in @ SY735 @ ( sK39_D @ SY735 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SY735 @ SV289 @ SV233 ) @ SV233 ) ) ) )
= $false )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2169,plain,
! [SV337: $i,SV380: $i] :
( ( ( ~ ( element @ SV380 @ SV337 )
| ( in @ SV380 @ SV337 ) )
= $true )
| ( ( empty @ SV337 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2170,plain,
! [SV338: $i,SV381: $i] :
( ( ( ~ ( in @ SV381 @ SV338 )
| ( element @ SV381 @ SV338 ) )
= $true )
| ( ( empty @ SV338 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2171,plain,
! [SV339: $i] :
( ( ( empty @ SV339 )
= $false )
| ( ( ! [SY777: $i] :
( ~ ( element @ SY777 @ SV339 )
| ( empty @ SY777 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2172,plain,
! [SV340: $i] :
( ( ( empty @ SV340 )
= $false )
| ( ( ! [SY778: $i] :
( ~ ( empty @ SY778 )
| ( element @ SY778 @ SV340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2173,plain,
! [SV234: $i] :
( ( ( ~ ( ( ( sK45_B @ SV234 )
!= ( sK46_SY427 @ SV234 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2174,plain,
! [SV234: $i] :
( ( ( in @ ( sK46_SY427 @ SV234 ) @ ( sK45_B @ SV234 ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2175,plain,
! [SV235: $i,SV364: $i,SV341: $i] :
( ( ( ( SV341 = SV364 )
| ~ ( in @ SV341 @ SV235 )
| ~ ( in @ SV364 @ SV235 )
| ( in @ SV341 @ SV364 ) )
= $true )
| ( ( in @ SV364 @ SV341 )
= $true )
| ( ( epsilon_connected @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2176,plain,
! [SV236: $i,SV290: $i] :
( ( ( subset @ SV290 @ SV236 )
= $false )
| ( ( subset @ SV236 @ SV290 )
= $false )
| ( ( SV236 = SV290 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2177,plain,
! [SV365: $i,SV342: $i] :
( ( ( ( SV342 != SV365 ) )
= $true )
| ( ( subset @ SV342 @ SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2178,plain,
! [SV366: $i,SV343: $i] :
( ( ( ( SV343 != SV366 ) )
= $true )
| ( ( subset @ SV366 @ SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2179,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) )
| ~ ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2180,plain,
! [SV323: $i,SV182: $i,SV108: $i,SV345: $i] :
( ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false )
| ( ( ~ ( ~ ! [SY782: $i] :
( ~ ( in @ SY782 @ SV345 )
| ( SY782 = SV323 )
| ( SY782 = SV108 )
| ( SY782 = SV182 ) )
| ~ ~ ( ~ ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) )
| ~ ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2181,plain,
! [SV109: $i,SV183: $i] :
( ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV183 )
= $false )
| ( ( in @ ( sK6_C @ SV183 @ SV109 ) @ SV109 )
= $false )
| ( ( SV109 = SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2182,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2086]) ).
thf(2183,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) ) )
= $false )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2086]) ).
thf(2184,plain,
! [SV325: $i,SV296: $i,SV111: $i] :
( ( ( ~ ! [SY763: $i] :
( ~ ( in @ SY763 @ SV111 )
| ( in @ SY763 @ SV296 )
| ( in @ SY763 @ SV325 ) )
| ~ ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) )
| ~ ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) ) )
= $false )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2185,plain,
! [SV184: $i,SV112: $i,SV367: $i] :
( ( ( ~ ( element @ SV367 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV184 @ SV367 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SV367 ) ) )
= $true )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2186,plain,
! [SV184: $i,SV112: $i,SV368: $i] :
( ( ( ~ ( element @ SV368 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SV368 ) )
| ( disjoint @ SV184 @ SV368 ) )
= $true )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2187,plain,
! [SV114: $i,SV371: $i] :
( ( ( ~ ( ~ ! [SY802: $i] :
( ~ ( subset @ SY802 @ SV371 )
| ( in @ SY802 @ ( sK4_SY376 @ SV371 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SV371 @ SV114 ) @ ( sK3_B @ SV114 ) ) ) )
= $true )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2188,plain,
! [SV114: $i] :
( ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2189,plain,
! [SV114: $i] :
( ( ~ ( in @ SV114 @ ( sK3_B @ SV114 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2190,plain,
! [SV245: $i] :
( ( ( subset @ ( sK51_B @ SV245 ) @ SV245 )
= $false )
| ( ( epsilon_transitive @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2191,plain,
! [SV246: $i,SV346: $i] :
( ( ( in @ SV346 @ SV246 )
= $false )
| ( ( subset @ SV346 @ SV246 )
= $true )
| ( ( epsilon_transitive @ SV246 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2192,plain,
! [SV347: $i] :
( ( ( SV347 = empty_set )
= $false )
| ( ( ! [SY786: $i] : ( subset @ SV347 @ ( singleton @ SY786 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2193,plain,
! [SV372: $i,SV348: $i] :
( ( ( ( SV348
!= ( singleton @ SV372 ) ) )
= $true )
| ( ( subset @ SV348 @ ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2194,plain,
! [SV252: $i,SV305: $i] :
( ( ( relation @ SV305 )
= $false )
| ( ( empty @ SV252 )
= $false )
| ( ( empty @ ( relation_composition @ SV305 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2195,plain,
! [SV253: $i,SV306: $i] :
( ( ( relation @ SV306 )
= $false )
| ( ( empty @ SV253 )
= $false )
| ( ( relation @ ( relation_composition @ SV306 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2196,plain,
! [SV349: $i] :
( ( ( SV349 = empty_set )
= $false )
| ( ( ! [SY788: $i] : ( subset @ SV349 @ ( singleton @ SY788 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2197,plain,
! [SV373: $i,SV350: $i] :
( ( ( ( SV350
!= ( singleton @ SV373 ) ) )
= $true )
| ( ( subset @ SV350 @ ( singleton @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2198,plain,
! [SV117: $i] :
( ( ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2199,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2200,plain,
! [SV117: $i] :
( ( ( ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2109]) ).
thf(2201,plain,
! [SV117: $i] :
( ( ( ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2202,plain,
! [SV118: $i,SV351: $i] :
( ( ( relation @ SV351 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV351 ) )
| ( subset @ SV118 @ SV351 ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2203,plain,
! [SV118: $i,SV352: $i] :
( ( ( relation @ SV352 )
= $false )
| ( ( ~ ( subset @ SV118 @ SV352 )
| ! [SY790: $i,SY791: $i] :
( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV118 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV352 ) ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2204,plain,
! [SV255: $i,SV308: $i] :
( ( ( relation @ SV308 )
= $false )
| ( ( empty @ SV255 )
= $false )
| ( ( empty @ ( relation_composition @ SV255 @ SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2205,plain,
! [SV256: $i,SV309: $i] :
( ( ( relation @ SV309 )
= $false )
| ( ( empty @ SV256 )
= $false )
| ( ( relation @ ( relation_composition @ SV256 @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2206,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) ) ) )
= $false )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2115]) ).
thf(2207,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV119 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV310 ) ) )
= $false )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2115]) ).
thf(2208,plain,
! [SV311: $i,SV119: $i,SV327: $i] :
( ( ( ~ ! [SY766: $i] :
( ~ ( in @ SY766 @ SV327 )
| ( SY766 = SV119 )
| ( SY766 = SV311 ) )
| ~ ~ ( ~ ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) )
| ~ ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) ) )
= $false )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2209,plain,
! [SV257: $i,SV312: $i] :
( ( ( ( ( sK54_C @ SV312 @ SV257 )
!= SV257 )
| ~ ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) )
= $true )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2210,plain,
! [SV257: $i,SV312: $i] :
( ( ( ( ( sK54_C @ SV312 @ SV257 )
= SV257 )
| ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) )
= $true )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2118]) ).
thf(2211,plain,
! [SV313: $i,SV258: $i] :
( ( ( ~ ! [SY748: $i] :
( ( SY748 != SV258 )
| ( in @ SY748 @ SV313 ) ) )
= $false )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2212,plain,
! [SV258: $i,SV313: $i] :
( ( ( ~ ! [SY749: $i] :
( ~ ( in @ SY749 @ SV313 )
| ( SY749 = SV258 ) ) )
= $false )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2213,plain,
! [SV259: $i,SV314: $i] :
( ( ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV259 )
= $true )
| ( ( subset @ SV259 @ SV314 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2214,plain,
! [SV259: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV314 ) )
= $true )
| ( ( subset @ SV259 @ SV314 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2215,plain,
! [SV315: $i,SV260: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ SV260 ) )
= $true )
| ( ( in @ SV374 @ SV315 )
= $true )
| ( ( subset @ SV260 @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2216,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) )
| ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
| ~ ( ! [SY805: $i] :
( ~ ( in @ SY805 @ SV353 )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SY805 ) )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) ) )
| ( SV382
= ( set_meet @ SV353 ) ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2217,plain,
! [SV354: $i,SV383: $i] :
( ( ( ( SV383
!= ( set_meet @ SV354 ) )
| ~ ( ~ ! [SY806: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SY806 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SY806 @ ( sK55_D @ SY806 @ SV383 @ SV354 ) ) )
| ( in @ SY806 @ SV383 ) )
| ~ ! [SY807: $i] :
( ~ ( in @ SY807 @ SV383 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ SV354 )
| ( in @ SY807 @ SY797 ) ) ) ) )
= $true )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2218,plain,
! [SV355: $i] :
( ( ( SV355 = empty_set )
= $false )
| ( ( ! [SY798: $i] :
( ( SY798
!= ( set_meet @ SV355 ) )
| ( SY798 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2219,plain,
! [SV356: $i] :
( ( ( SV356 = empty_set )
= $false )
| ( ( ! [SY799: $i] :
( ( SY799 != empty_set )
| ( SY799
= ( set_meet @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2220,plain,
! [SV265: $i,SV375: $i] :
( ( ( ! [SY803: $i] :
( ( SY803 != SV375 )
| ~ ( in @ SY803 @ SV265 ) )
| ~ ( ordinal @ SV375 ) )
= $true )
| ( ( in @ SV375 @ ( sK7_B @ SV265 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2221,plain,
! [SV265: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ ( sK7_B @ SV265 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK8_D @ SV376 @ SV265 )
!= SV376 )
| ~ ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 ) )
| ~ ( ordinal @ SV376 ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2222,plain,
( ( ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2130]) ).
thf(2223,plain,
( ( ( ~ ( ordinal @ sK11_SY388 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2130]) ).
thf(2224,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2132]) ).
thf(2225,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2133]) ).
thf(2226,plain,
! [SV267: $i,SV97: $i,SV318: $i] :
( ( ( ~ ! [SY751: $i] :
( ~ ( in @ SY751 @ SV318 )
| ( in @ SY751 @ SV97 )
| ( in @ SY751 @ SV267 ) ) )
= $false )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2134]) ).
thf(2227,plain,
! [SV267: $i,SV318: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) )
| ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) ) )
= $false )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2134]) ).
thf(2228,plain,
! [SV98: $i,SV180: $i,SV329: $i] :
( ( ( in @ SV329 @ ( sK5_C @ SV180 @ SV98 ) )
= $false )
| ( ( in @ SV329 @ SV180 )
= $false )
| ( ( ~ ( in @ SV98 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2229,plain,
! [SV357: $i,SV330: $i] :
( ( ( proper_subset @ SV330 @ SV357 )
= $false )
| ( ( ( SV330 != SV357 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2230,plain,
! [SV358: $i,SV331: $i] :
( ( ( proper_subset @ SV331 @ SV358 )
= $false )
| ( ( subset @ SV331 @ SV358 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2231,plain,
! [SV101: $i,SV359: $i] :
( ( ( in @ SV359 @ ( sK67_B @ SV101 ) )
= $false )
| ( ( in @ ( powerset @ SV359 ) @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2232,plain,
! [SV101: $i] :
( ( ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY544 @ SY543 )
| ( in @ SY544 @ ( sK67_B @ SV101 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2233,plain,
! [SV101: $i] :
( ( in @ SV101 @ ( sK67_B @ SV101 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2234,plain,
! [SV384: $i,SV377: $i,SV226: $i] :
( ( ( ( ( sK60_B @ SV226 )
!= ( ordered_pair @ SV377 @ SV384 ) ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2235,plain,
! [SV102: $i,SV319: $i,SV280: $i] :
( ( ( in @ SV280 @ SV319 )
= $false )
| ( ( in @ SV102 @ SV319 )
= $false )
| ( ( subset @ ( unordered_pair @ SV102 @ SV280 ) @ SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2236,plain,
! [SV378: $i,SV360: $i,SV102: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV102 @ SV360 ) @ SV378 ) )
= $true )
| ( ( in @ SV102 @ SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2237,plain,
! [SV379: $i,SV361: $i,SV102: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV102 @ SV361 ) @ SV379 ) )
= $true )
| ( ( in @ SV361 @ SV379 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2238,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2239,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2240,plain,
! [SV321: $i,SV282: $i,SV103: $i] :
( ( ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SV103 )
| ~ ( in @ SY754 @ SV282 )
| ( in @ SY754 @ SV321 ) ) )
= $false )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2241,plain,
! [SV282: $i,SV103: $i,SV321: $i] :
( ( ( ~ ~ ( ~ ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) )
| ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) ) )
= $false )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2242,plain,
! [SV228: $i,SV283: $i] :
( ( ( ~ ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 ) )
= $true )
| ( ( ~ ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) )
= $true )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2243,plain,
! [SV228: $i,SV283: $i] :
( ( ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
= $true )
| ( ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 )
= $true )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2244,plain,
! [SV229: $i,SV284: $i] :
( ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV284 )
| ( subset @ SY729 @ SV229 ) ) )
= $true )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2152]) ).
thf(2245,plain,
! [SV284: $i,SV229: $i] :
( ( ( ! [SY730: $i] :
( ~ ( subset @ SY730 @ SV229 )
| ( in @ SY730 @ SV284 ) ) )
= $true )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2153]) ).
thf(2246,plain,
! [SV104: $i,SV334: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) ) ) )
= $true )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2247,plain,
! [SV335: $i,SV104: $i] :
( ( ( ( SV104 != SV335 ) )
= $true )
| ( ( ~ ( ~ ! [SY771: $i,SY772: $i] :
( ~ ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV104 )
| ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV335 ) )
| ~ ! [SY773: $i,SY774: $i] :
( ~ ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV335 )
| ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2248,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2249,plain,
! [SV106: $i,SV181: $i] :
( ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2250,plain,
! [SV107: $i,SV362: $i] :
( ( ( in @ SV362 @ ( sK68_B @ SV107 ) )
= $false )
| ( ( in @ SV362 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2251,plain,
! [SV107: $i,SV363: $i] :
( ( ( in @ SV363 @ ( sK68_B @ SV107 ) )
= $false )
| ( ( ordinal @ SV363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2252,plain,
! [SV231: $i,SV287: $i,SV336: $i] :
( ( ( in @ SV336 @ SV287 )
= $false )
| ( ( in @ SV336 @ SV231 )
= $false )
| ( ( ~ ( disjoint @ SV231 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2253,plain,
! [SV232: $i,SV288: $i] :
( ( ( ! [SY732: $i] :
( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SY732 )
| ~ ( in @ SY732 @ SV232 ) ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2254,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) )
| ~ ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 ) ) )
= $true )
| ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2255,plain,
! [SV289: $i,SV233: $i] :
( ( ( ! [SY733: $i] :
( ! [SY687: $i] :
( ~ ( in @ SY733 @ SY687 )
| ~ ( in @ SY687 @ SV233 ) )
| ( in @ SY733 @ SV289 ) ) )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2167]) ).
thf(2256,plain,
! [SV233: $i,SV289: $i] :
( ( ( ! [SY735: $i] :
( ~ ( in @ SY735 @ SV289 )
| ~ ( ~ ( in @ SY735 @ ( sK39_D @ SY735 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SY735 @ SV289 @ SV233 ) @ SV233 ) ) ) )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2168]) ).
thf(2257,plain,
! [SV337: $i,SV380: $i] :
( ( ( ~ ( element @ SV380 @ SV337 ) )
= $true )
| ( ( in @ SV380 @ SV337 )
= $true )
| ( ( empty @ SV337 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2258,plain,
! [SV338: $i,SV381: $i] :
( ( ( ~ ( in @ SV381 @ SV338 ) )
= $true )
| ( ( element @ SV381 @ SV338 )
= $true )
| ( ( empty @ SV338 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2259,plain,
! [SV339: $i,SV385: $i] :
( ( ( ~ ( element @ SV385 @ SV339 )
| ( empty @ SV385 ) )
= $true )
| ( ( empty @ SV339 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2260,plain,
! [SV340: $i,SV386: $i] :
( ( ( ~ ( empty @ SV386 )
| ( element @ SV386 @ SV340 ) )
= $true )
| ( ( empty @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2261,plain,
! [SV234: $i] :
( ( ( ~ ( ( ( sK45_B @ SV234 )
!= ( sK46_SY427 @ SV234 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2262,plain,
! [SV234: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2263,plain,
! [SV235: $i,SV364: $i,SV341: $i] :
( ( ( SV341 = SV364 )
= $true )
| ( ( ~ ( in @ SV341 @ SV235 )
| ~ ( in @ SV364 @ SV235 )
| ( in @ SV341 @ SV364 ) )
= $true )
| ( ( in @ SV364 @ SV341 )
= $true )
| ( ( epsilon_connected @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2264,plain,
! [SV365: $i,SV342: $i] :
( ( ( SV342 = SV365 )
= $false )
| ( ( subset @ SV342 @ SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2265,plain,
! [SV366: $i,SV343: $i] :
( ( ( SV343 = SV366 )
= $false )
| ( ( subset @ SV366 @ SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2266,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2179]) ).
thf(2267,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2179]) ).
thf(2268,plain,
! [SV182: $i,SV108: $i,SV323: $i,SV345: $i] :
( ( ( ~ ! [SY782: $i] :
( ~ ( in @ SY782 @ SV345 )
| ( SY782 = SV323 )
| ( SY782 = SV108 )
| ( SY782 = SV182 ) )
| ~ ~ ( ~ ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) )
| ~ ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2269,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2182]) ).
thf(2270,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) ) )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2271,plain,
! [SV325: $i,SV296: $i,SV111: $i] :
( ( ( ~ ! [SY763: $i] :
( ~ ( in @ SY763 @ SV111 )
| ( in @ SY763 @ SV296 )
| ( in @ SY763 @ SV325 ) ) )
= $false )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2184]) ).
thf(2272,plain,
! [SV296: $i,SV111: $i,SV325: $i] :
( ( ( ~ ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) )
| ~ ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) ) )
= $false )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2184]) ).
thf(2273,plain,
! [SV184: $i,SV112: $i,SV367: $i] :
( ( ( element @ SV367 @ ( powerset @ SV112 ) )
= $false )
| ( ( ~ ( disjoint @ SV184 @ SV367 )
| ( subset @ SV184 @ ( subset_complement @ SV112 @ SV367 ) ) )
= $true )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2274,plain,
! [SV184: $i,SV112: $i,SV368: $i] :
( ( ( element @ SV368 @ ( powerset @ SV112 ) )
= $false )
| ( ( ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SV368 ) )
| ( disjoint @ SV184 @ SV368 ) )
= $true )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2275,plain,
! [SV114: $i,SV371: $i] :
( ( ( ~ ! [SY802: $i] :
( ~ ( subset @ SY802 @ SV371 )
| ( in @ SY802 @ ( sK4_SY376 @ SV371 @ SV114 ) ) )
| ~ ( in @ ( sK4_SY376 @ SV371 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
= $false )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2276,plain,
! [SV114: $i] :
( ( ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY603 @ SY602 )
| ( in @ SY603 @ ( sK3_B @ SV114 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2277,plain,
! [SV114: $i] :
( ( in @ SV114 @ ( sK3_B @ SV114 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2189]) ).
thf(2278,plain,
! [SV387: $i,SV347: $i] :
( ( ( subset @ SV347 @ ( singleton @ SV387 ) )
= $true )
| ( ( SV347 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2279,plain,
! [SV372: $i,SV348: $i] :
( ( ( SV348
= ( singleton @ SV372 ) )
= $false )
| ( ( subset @ SV348 @ ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2280,plain,
! [SV388: $i,SV349: $i] :
( ( ( subset @ SV349 @ ( singleton @ SV388 ) )
= $true )
| ( ( SV349 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2281,plain,
! [SV373: $i,SV350: $i] :
( ( ( SV350
= ( singleton @ SV373 ) )
= $false )
| ( ( subset @ SV350 @ ( singleton @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2282,plain,
! [SV117: $i] :
( ( ( ~ ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2198]) ).
thf(2283,plain,
! [SV117: $i] :
( ( ( ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2198]) ).
thf(2284,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $false )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2285,plain,
! [SV117: $i] :
( ( ( ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2286,plain,
! [SV389: $i,SV117: $i] :
( ( ( ! [SY809: $i] :
( ~ ( in @ SY809 @ SV117 )
| ( SV389
!= ( singleton @ SY809 ) ) )
| ( in @ SV389 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2287,plain,
! [SV117: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SV390 @ SV117 ) @ SV117 )
| ( SV390
!= ( singleton @ ( sK14_D @ SV390 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2288,plain,
! [SV118: $i,SV351: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV351 ) ) )
= $true )
| ( ( subset @ SV118 @ SV351 )
= $true )
| ( ( relation @ SV351 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2289,plain,
! [SV352: $i,SV118: $i] :
( ( ( ~ ( subset @ SV118 @ SV352 ) )
= $true )
| ( ( ! [SY790: $i,SY791: $i] :
( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV118 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV352 ) ) )
= $true )
| ( ( relation @ SV352 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2290,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) ) ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2206]) ).
thf(2291,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV119 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV310 ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2292,plain,
! [SV311: $i,SV119: $i,SV327: $i] :
( ( ( ~ ! [SY766: $i] :
( ~ ( in @ SY766 @ SV327 )
| ( SY766 = SV119 )
| ( SY766 = SV311 ) ) )
= $false )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2293,plain,
! [SV311: $i,SV327: $i,SV119: $i] :
( ( ( ~ ~ ( ~ ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) )
| ~ ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) ) )
= $false )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2294,plain,
! [SV257: $i,SV312: $i] :
( ( ( ( ( sK54_C @ SV312 @ SV257 )
!= SV257 ) )
= $true )
| ( ( ~ ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) )
= $true )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2295,plain,
! [SV257: $i,SV312: $i] :
( ( ( ( sK54_C @ SV312 @ SV257 )
= SV257 )
= $true )
| ( ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 )
= $true )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2296,plain,
! [SV313: $i,SV258: $i] :
( ( ( ! [SY748: $i] :
( ( SY748 != SV258 )
| ( in @ SY748 @ SV313 ) ) )
= $true )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2297,plain,
! [SV258: $i,SV313: $i] :
( ( ( ! [SY749: $i] :
( ~ ( in @ SY749 @ SV313 )
| ( SY749 = SV258 ) ) )
= $true )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2298,plain,
! [SV259: $i,SV314: $i] :
( ( ( in @ ( sK42_C @ SV314 @ SV259 ) @ SV314 )
= $false )
| ( ( subset @ SV259 @ SV314 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2299,plain,
! [SV315: $i,SV260: $i,SV374: $i] :
( ( ( in @ SV374 @ SV260 )
= $false )
| ( ( in @ SV374 @ SV315 )
= $true )
| ( ( subset @ SV260 @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2300,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) )
| ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
| ~ ( ! [SY805: $i] :
( ~ ( in @ SY805 @ SV353 )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SY805 ) )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) ) ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2301,plain,
! [SV354: $i,SV383: $i] :
( ( ( ( SV383
!= ( set_meet @ SV354 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY806: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SY806 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SY806 @ ( sK55_D @ SY806 @ SV383 @ SV354 ) ) )
| ( in @ SY806 @ SV383 ) )
| ~ ! [SY807: $i] :
( ~ ( in @ SY807 @ SV383 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ SV354 )
| ( in @ SY807 @ SY797 ) ) ) ) )
= $true )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2217]) ).
thf(2302,plain,
! [SV355: $i,SV391: $i] :
( ( ( ( SV391
!= ( set_meet @ SV355 ) )
| ( SV391 = empty_set ) )
= $true )
| ( ( SV355 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2303,plain,
! [SV356: $i,SV392: $i] :
( ( ( ( SV392 != empty_set )
| ( SV392
= ( set_meet @ SV356 ) ) )
= $true )
| ( ( SV356 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2304,plain,
! [SV265: $i,SV375: $i] :
( ( ( ! [SY803: $i] :
( ( SY803 != SV375 )
| ~ ( in @ SY803 @ SV265 ) ) )
= $true )
| ( ( ~ ( ordinal @ SV375 ) )
= $true )
| ( ( in @ SV375 @ ( sK7_B @ SV265 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2305,plain,
! [SV265: $i,SV376: $i] :
( ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK8_D @ SV376 @ SV265 )
!= SV376 )
| ~ ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 ) )
| ~ ( ordinal @ SV376 ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2306,plain,
( ( ( ~ ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) ) )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2307,plain,
( ( ( ordinal @ sK11_SY388 )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2223]) ).
thf(2308,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) )
= $false )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2309,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
= $true )
| ( ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 )
| ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2310,plain,
! [SV267: $i,SV97: $i,SV318: $i] :
( ( ( ! [SY751: $i] :
( ~ ( in @ SY751 @ SV318 )
| ( in @ SY751 @ SV97 )
| ( in @ SY751 @ SV267 ) ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2226]) ).
thf(2311,plain,
! [SV267: $i,SV318: $i,SV97: $i] :
( ( ( ~ ( ~ ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) )
| ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2227]) ).
thf(2312,plain,
! [SV329: $i,SV180: $i,SV98: $i] :
( ( ( in @ SV98 @ SV180 )
= $false )
| ( ( in @ SV329 @ SV180 )
= $false )
| ( ( in @ SV329 @ ( sK5_C @ SV180 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2313,plain,
! [SV357: $i,SV330: $i] :
( ( ( SV330 = SV357 )
= $false )
| ( ( proper_subset @ SV330 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2314,plain,
! [SV101: $i,SV393: $i] :
( ( ! [SY810: $i] :
( ~ ( in @ SV393 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SY810 @ SV393 )
| ( in @ SY810 @ ( sK67_B @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2315,plain,
! [SV384: $i,SV377: $i,SV226: $i] :
( ( ( ( sK60_B @ SV226 )
= ( ordered_pair @ SV377 @ SV384 ) )
= $false )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2316,plain,
! [SV378: $i,SV360: $i,SV102: $i] :
( ( ( subset @ ( unordered_pair @ SV102 @ SV360 ) @ SV378 )
= $false )
| ( ( in @ SV102 @ SV378 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2317,plain,
! [SV379: $i,SV361: $i,SV102: $i] :
( ( ( subset @ ( unordered_pair @ SV102 @ SV361 ) @ SV379 )
= $false )
| ( ( in @ SV361 @ SV379 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2318,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 ) )
= $true )
| ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2319,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
| ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) )
= $false )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2320,plain,
! [SV321: $i,SV282: $i,SV103: $i] :
( ( ( ! [SY754: $i] :
( ~ ( in @ SY754 @ SV103 )
| ~ ( in @ SY754 @ SV282 )
| ( in @ SY754 @ SV321 ) ) )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2321,plain,
! [SV282: $i,SV103: $i,SV321: $i] :
( ( ( ~ ( ~ ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) )
| ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) ) )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2322,plain,
! [SV228: $i,SV283: $i] :
( ( ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
= $false )
| ( ( ~ ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 ) )
= $true )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2323,plain,
! [SV229: $i,SV284: $i,SV394: $i] :
( ( ( ~ ( in @ SV394 @ SV284 )
| ( subset @ SV394 @ SV229 ) )
= $true )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2324,plain,
! [SV284: $i,SV229: $i,SV395: $i] :
( ( ( ~ ( subset @ SV395 @ SV229 )
| ( in @ SV395 @ SV284 ) )
= $true )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2325,plain,
! [SV104: $i,SV334: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) ) )
= $false )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2326,plain,
! [SV335: $i,SV104: $i] :
( ( ( SV104 = SV335 )
= $false )
| ( ( ~ ( ~ ! [SY771: $i,SY772: $i] :
( ~ ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV104 )
| ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV335 ) )
| ~ ! [SY773: $i,SY774: $i] :
( ~ ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV335 )
| ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2327,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2248]) ).
thf(2328,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2248]) ).
thf(2329,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2330,plain,
! [SV336: $i,SV287: $i,SV231: $i] :
( ( ( disjoint @ SV231 @ SV287 )
= $false )
| ( ( in @ SV336 @ SV231 )
= $false )
| ( ( in @ SV336 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2331,plain,
! [SV396: $i,SV232: $i,SV288: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV396 )
| ~ ( in @ SV396 @ SV232 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2332,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) )
| ~ ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 ) )
= $false )
| ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2333,plain,
! [SV289: $i,SV233: $i,SV397: $i] :
( ( ( ! [SY811: $i] :
( ~ ( in @ SV397 @ SY811 )
| ~ ( in @ SY811 @ SV233 ) )
| ( in @ SV397 @ SV289 ) )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2334,plain,
! [SV233: $i,SV289: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ SV289 )
| ~ ( ~ ( in @ SV398 @ ( sK39_D @ SV398 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SV398 @ SV289 @ SV233 ) @ SV233 ) ) )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2335,plain,
! [SV337: $i,SV380: $i] :
( ( ( element @ SV380 @ SV337 )
= $false )
| ( ( in @ SV380 @ SV337 )
= $true )
| ( ( empty @ SV337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2336,plain,
! [SV338: $i,SV381: $i] :
( ( ( in @ SV381 @ SV338 )
= $false )
| ( ( element @ SV381 @ SV338 )
= $true )
| ( ( empty @ SV338 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2337,plain,
! [SV339: $i,SV385: $i] :
( ( ( ~ ( element @ SV385 @ SV339 ) )
= $true )
| ( ( empty @ SV385 )
= $true )
| ( ( empty @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2338,plain,
! [SV340: $i,SV386: $i] :
( ( ( ~ ( empty @ SV386 ) )
= $true )
| ( ( element @ SV386 @ SV340 )
= $true )
| ( ( empty @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2339,plain,
! [SV234: $i] :
( ( ( ( ( sK45_B @ SV234 )
!= ( sK46_SY427 @ SV234 ) ) )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2261]) ).
thf(2340,plain,
! [SV234: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2341,plain,
! [SV364: $i,SV235: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV235 )
| ~ ( in @ SV364 @ SV235 ) )
= $true )
| ( ( in @ SV341 @ SV364 )
= $true )
| ( ( SV341 = SV364 )
= $true )
| ( ( in @ SV364 @ SV341 )
= $true )
| ( ( epsilon_connected @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2342,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2343,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2267]) ).
thf(2344,plain,
! [SV182: $i,SV108: $i,SV323: $i,SV345: $i] :
( ( ( ~ ! [SY782: $i] :
( ~ ( in @ SY782 @ SV345 )
| ( SY782 = SV323 )
| ( SY782 = SV108 )
| ( SY782 = SV182 ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2268]) ).
thf(2345,plain,
! [SV182: $i,SV108: $i,SV345: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) )
| ~ ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2268]) ).
thf(2346,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2347,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2348,plain,
! [SV325: $i,SV296: $i,SV111: $i] :
( ( ( ! [SY763: $i] :
( ~ ( in @ SY763 @ SV111 )
| ( in @ SY763 @ SV296 )
| ( in @ SY763 @ SV325 ) ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2349,plain,
! [SV296: $i,SV111: $i,SV325: $i] :
( ( ( ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) )
| ~ ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2272]) ).
thf(2350,plain,
! [SV112: $i,SV367: $i,SV184: $i] :
( ( ( ~ ( disjoint @ SV184 @ SV367 ) )
= $true )
| ( ( subset @ SV184 @ ( subset_complement @ SV112 @ SV367 ) )
= $true )
| ( ( element @ SV367 @ ( powerset @ SV112 ) )
= $false )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2351,plain,
! [SV368: $i,SV112: $i,SV184: $i] :
( ( ( ~ ( subset @ SV184 @ ( subset_complement @ SV112 @ SV368 ) ) )
= $true )
| ( ( disjoint @ SV184 @ SV368 )
= $true )
| ( ( element @ SV368 @ ( powerset @ SV112 ) )
= $false )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2352,plain,
! [SV114: $i,SV371: $i] :
( ( ( ~ ! [SY802: $i] :
( ~ ( subset @ SY802 @ SV371 )
| ( in @ SY802 @ ( sK4_SY376 @ SV371 @ SV114 ) ) ) )
= $false )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2275]) ).
thf(2353,plain,
! [SV114: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK4_SY376 @ SV371 @ SV114 ) @ ( sK3_B @ SV114 ) ) )
= $false )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2275]) ).
thf(2354,plain,
! [SV114: $i,SV399: $i] :
( ( ! [SY812: $i] :
( ~ ( in @ SV399 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SY812 @ SV399 )
| ( in @ SY812 @ ( sK3_B @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2355,plain,
! [SV117: $i] :
( ( ( ~ ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2282]) ).
thf(2356,plain,
! [SV117: $i] :
( ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2357,plain,
! [SV117: $i] :
( ( ( ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2284]) ).
thf(2358,plain,
! [SV117: $i] :
( ( ( ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2285]) ).
thf(2359,plain,
! [SV389: $i,SV117: $i] :
( ( ( ! [SY809: $i] :
( ~ ( in @ SY809 @ SV117 )
| ( SV389
!= ( singleton @ SY809 ) ) ) )
= $true )
| ( ( in @ SV389 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2360,plain,
! [SV117: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV390 @ SV117 ) @ SV117 )
| ( SV390
!= ( singleton @ ( sK14_D @ SV390 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2361,plain,
! [SV118: $i,SV351: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV118 )
| ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV351 ) )
= $false )
| ( ( subset @ SV118 @ SV351 )
= $true )
| ( ( relation @ SV351 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2362,plain,
! [SV352: $i,SV118: $i] :
( ( ( subset @ SV118 @ SV352 )
= $false )
| ( ( ! [SY790: $i,SY791: $i] :
( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV118 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV352 ) ) )
= $true )
| ( ( relation @ SV352 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2363,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
| ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) ) )
= $false )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2364,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
= $true )
| ( ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV119 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV310 ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2365,plain,
! [SV311: $i,SV119: $i,SV327: $i] :
( ( ( ! [SY766: $i] :
( ~ ( in @ SY766 @ SV327 )
| ( SY766 = SV119 )
| ( SY766 = SV311 ) ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2366,plain,
! [SV311: $i,SV327: $i,SV119: $i] :
( ( ( ~ ( ~ ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) )
| ~ ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2367,plain,
! [SV257: $i,SV312: $i] :
( ( ( ( sK54_C @ SV312 @ SV257 )
= SV257 )
= $false )
| ( ( ~ ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 ) )
= $true )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2368,plain,
! [SV313: $i,SV258: $i,SV400: $i] :
( ( ( ( SV400 != SV258 )
| ( in @ SV400 @ SV313 ) )
= $true )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2369,plain,
! [SV258: $i,SV313: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV313 )
| ( SV401 = SV258 ) )
= $true )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2370,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) )
| ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
| ~ ( ! [SY805: $i] :
( ~ ( in @ SY805 @ SV353 )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SY805 ) )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) ) )
= $false )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2371,plain,
! [SV354: $i,SV383: $i] :
( ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( ~ ( ~ ! [SY806: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SY806 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SY806 @ ( sK55_D @ SY806 @ SV383 @ SV354 ) ) )
| ( in @ SY806 @ SV383 ) )
| ~ ! [SY807: $i] :
( ~ ( in @ SY807 @ SV383 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ SV354 )
| ( in @ SY807 @ SY797 ) ) ) ) )
= $true )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2372,plain,
! [SV355: $i,SV391: $i] :
( ( ( ( SV391
!= ( set_meet @ SV355 ) ) )
= $true )
| ( ( SV391 = empty_set )
= $true )
| ( ( SV355 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2373,plain,
! [SV356: $i,SV392: $i] :
( ( ( ( SV392 != empty_set ) )
= $true )
| ( ( SV392
= ( set_meet @ SV356 ) )
= $true )
| ( ( SV356 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2374,plain,
! [SV265: $i,SV375: $i,SV402: $i] :
( ( ( ( SV402 != SV375 )
| ~ ( in @ SV402 @ SV265 ) )
= $true )
| ( ( ~ ( ordinal @ SV375 ) )
= $true )
| ( ( in @ SV375 @ ( sK7_B @ SV265 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2375,plain,
! [SV265: $i,SV376: $i] :
( ( ( ~ ~ ( ( ( sK8_D @ SV376 @ SV265 )
!= SV376 )
| ~ ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 ) )
| ~ ( ordinal @ SV376 ) )
= $false )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2376,plain,
( ( ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
| ( sK9_B != sK11_SY388 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2377,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) ) )
= $false )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2308]) ).
thf(2378,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) ) )
= $false )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2308]) ).
thf(2379,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 )
= $true )
| ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 )
= $true )
| ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2380,plain,
! [SV267: $i,SV97: $i,SV318: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV318 )
| ( in @ SV403 @ SV97 )
| ( in @ SV403 @ SV267 ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2381,plain,
! [SV267: $i,SV318: $i,SV97: $i] :
( ( ( ~ ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) )
| ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) )
= $false )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2382,plain,
! [SV404: $i,SV101: $i,SV393: $i] :
( ( ~ ( in @ SV393 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SV404 @ SV393 )
| ( in @ SV404 @ ( sK67_B @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2383,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 ) )
= $true )
| ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 ) )
= $true )
| ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2384,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) )
= $false )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2319]) ).
thf(2385,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ~ ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) ) )
= $false )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2319]) ).
thf(2386,plain,
! [SV321: $i,SV282: $i,SV103: $i,SV405: $i] :
( ( ( ~ ( in @ SV405 @ SV103 )
| ~ ( in @ SV405 @ SV282 )
| ( in @ SV405 @ SV321 ) )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2387,plain,
! [SV282: $i,SV103: $i,SV321: $i] :
( ( ( ~ ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) )
| ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) )
= $false )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2388,plain,
! [SV228: $i,SV283: $i] :
( ( ( subset @ ( sK52_C @ SV283 @ SV228 ) @ SV228 )
= $false )
| ( ( in @ ( sK52_C @ SV283 @ SV228 ) @ SV283 )
= $false )
| ( ( SV283
= ( powerset @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2389,plain,
! [SV229: $i,SV284: $i,SV394: $i] :
( ( ( ~ ( in @ SV394 @ SV284 ) )
= $true )
| ( ( subset @ SV394 @ SV229 )
= $true )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2390,plain,
! [SV284: $i,SV229: $i,SV395: $i] :
( ( ( ~ ( subset @ SV395 @ SV229 ) )
= $true )
| ( ( in @ SV395 @ SV284 )
= $true )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2391,plain,
! [SV104: $i,SV334: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) ) )
= $false )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2392,plain,
! [SV104: $i,SV334: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) ) )
= $false )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2393,plain,
! [SV335: $i,SV104: $i] :
( ( ( ~ ! [SY771: $i,SY772: $i] :
( ~ ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV104 )
| ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV335 ) )
| ~ ! [SY773: $i,SY774: $i] :
( ~ ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV335 )
| ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV104 ) ) )
= $false )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2394,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2327]) ).
thf(2395,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2328]) ).
thf(2396,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2329]) ).
thf(2397,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2329]) ).
thf(2398,plain,
! [SV396: $i,SV232: $i,SV288: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV396 ) )
= $true )
| ( ( ~ ( in @ SV396 @ SV232 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2399,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) ) )
= $false )
| ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2332]) ).
thf(2400,plain,
! [SV232: $i,SV288: $i] :
( ( ( ~ ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 ) )
= $false )
| ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2332]) ).
thf(2401,plain,
! [SV289: $i,SV233: $i,SV397: $i] :
( ( ( ! [SY811: $i] :
( ~ ( in @ SV397 @ SY811 )
| ~ ( in @ SY811 @ SV233 ) ) )
= $true )
| ( ( in @ SV397 @ SV289 )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2402,plain,
! [SV233: $i,SV289: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ SV289 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV398 @ ( sK39_D @ SV398 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SV398 @ SV289 @ SV233 ) @ SV233 ) ) )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2403,plain,
! [SV339: $i,SV385: $i] :
( ( ( element @ SV385 @ SV339 )
= $false )
| ( ( empty @ SV385 )
= $true )
| ( ( empty @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2404,plain,
! [SV340: $i,SV386: $i] :
( ( ( empty @ SV386 )
= $false )
| ( ( element @ SV386 @ SV340 )
= $true )
| ( ( empty @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2405,plain,
! [SV234: $i] :
( ( ( ( sK45_B @ SV234 )
= ( sK46_SY427 @ SV234 ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2406,plain,
! [SV234: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
| ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2407,plain,
! [SV364: $i,SV235: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV235 ) )
= $true )
| ( ( ~ ( in @ SV364 @ SV235 ) )
= $true )
| ( ( in @ SV341 @ SV364 )
= $true )
| ( ( SV341 = SV364 )
= $true )
| ( ( in @ SV364 @ SV341 )
= $true )
| ( ( epsilon_connected @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2408,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2409,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $true )
| ( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2410,plain,
! [SV182: $i,SV108: $i,SV323: $i,SV345: $i] :
( ( ( ! [SY782: $i] :
( ~ ( in @ SY782 @ SV345 )
| ( SY782 = SV323 )
| ( SY782 = SV108 )
| ( SY782 = SV182 ) ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2344]) ).
thf(2411,plain,
! [SV182: $i,SV108: $i,SV345: $i,SV323: $i] :
( ( ( ~ ( ~ ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) )
| ~ ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2412,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 ) )
= $true )
| ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2413,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2347]) ).
thf(2414,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2347]) ).
thf(2415,plain,
! [SV325: $i,SV296: $i,SV111: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ SV111 )
| ( in @ SV406 @ SV296 )
| ( in @ SV406 @ SV325 ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2416,plain,
! [SV296: $i,SV111: $i,SV325: $i] :
( ( ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) )
| ~ ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) )
= $false )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2417,plain,
! [SV112: $i,SV367: $i,SV184: $i] :
( ( ( disjoint @ SV184 @ SV367 )
= $false )
| ( ( subset @ SV184 @ ( subset_complement @ SV112 @ SV367 ) )
= $true )
| ( ( element @ SV367 @ ( powerset @ SV112 ) )
= $false )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2418,plain,
! [SV368: $i,SV112: $i,SV184: $i] :
( ( ( subset @ SV184 @ ( subset_complement @ SV112 @ SV368 ) )
= $false )
| ( ( disjoint @ SV184 @ SV368 )
= $true )
| ( ( element @ SV368 @ ( powerset @ SV112 ) )
= $false )
| ( ( element @ SV184 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2419,plain,
! [SV114: $i,SV371: $i] :
( ( ( ! [SY802: $i] :
( ~ ( subset @ SY802 @ SV371 )
| ( in @ SY802 @ ( sK4_SY376 @ SV371 @ SV114 ) ) ) )
= $true )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2420,plain,
! [SV114: $i,SV371: $i] :
( ( ( in @ ( sK4_SY376 @ SV371 @ SV114 ) @ ( sK3_B @ SV114 ) )
= $true )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2421,plain,
! [SV407: $i,SV114: $i,SV399: $i] :
( ( ~ ( in @ SV399 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SV407 @ SV399 )
| ( in @ SV407 @ ( sK3_B @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2422,plain,
! [SV117: $i] :
( ( ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) )
| ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2423,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2424,plain,
! [SV408: $i,SV117: $i] :
( ( ( ! [SY813: $i] :
( ~ ( in @ SY813 @ SV117 )
| ( SV408
!= ( singleton @ SY813 ) ) )
| ( in @ SV408 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2425,plain,
! [SV117: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SV409 @ SV117 ) @ SV117 )
| ( SV409
!= ( singleton @ ( sK14_D @ SV409 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2426,plain,
! [SV389: $i,SV117: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ SV117 )
| ( SV389
!= ( singleton @ SV410 ) ) )
= $true )
| ( ( in @ SV389 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2427,plain,
! [SV117: $i,SV390: $i] :
( ( ( in @ SV390 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV390 @ SV117 ) @ SV117 )
| ( SV390
!= ( singleton @ ( sK14_D @ SV390 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2428,plain,
! [SV118: $i,SV351: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV118 ) )
= $false )
| ( ( subset @ SV118 @ SV351 )
= $true )
| ( ( relation @ SV351 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2429,plain,
! [SV118: $i,SV351: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV351 ) )
= $false )
| ( ( subset @ SV118 @ SV351 )
= $true )
| ( ( relation @ SV351 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2430,plain,
! [SV352: $i,SV118: $i,SV411: $i] :
( ( ( ! [SY814: $i] :
( ~ ( in @ ( ordered_pair @ SV411 @ SY814 ) @ SV118 )
| ( in @ ( ordered_pair @ SV411 @ SY814 ) @ SV352 ) ) )
= $true )
| ( ( subset @ SV118 @ SV352 )
= $false )
| ( ( relation @ SV352 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2431,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) ) )
= $false )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2432,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) ) )
= $false )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2433,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV119 )
= $true )
| ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV310 )
= $true )
| ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2434,plain,
! [SV311: $i,SV119: $i,SV327: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV327 )
| ( SV412 = SV119 )
| ( SV412 = SV311 ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2435,plain,
! [SV311: $i,SV327: $i,SV119: $i] :
( ( ( ~ ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) )
| ~ ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) )
= $false )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2436,plain,
! [SV257: $i,SV312: $i] :
( ( ( in @ ( sK54_C @ SV312 @ SV257 ) @ SV312 )
= $false )
| ( ( ( sK54_C @ SV312 @ SV257 )
= SV257 )
= $false )
| ( ( SV312
= ( singleton @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2437,plain,
! [SV313: $i,SV258: $i,SV400: $i] :
( ( ( ( SV400 != SV258 ) )
= $true )
| ( ( in @ SV400 @ SV313 )
= $true )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2438,plain,
! [SV258: $i,SV313: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV313 ) )
= $true )
| ( ( SV401 = SV258 )
= $true )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2439,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) )
| ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) ) )
= $false )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2370]) ).
thf(2440,plain,
! [SV382: $i,SV353: $i] :
( ( ( ~ ( ! [SY805: $i] :
( ~ ( in @ SY805 @ SV353 )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SY805 ) )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) ) )
= $false )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2370]) ).
thf(2441,plain,
! [SV354: $i,SV383: $i] :
( ( ( ~ ! [SY806: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SY806 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SY806 @ ( sK55_D @ SY806 @ SV383 @ SV354 ) ) )
| ( in @ SY806 @ SV383 ) )
| ~ ! [SY807: $i] :
( ~ ( in @ SY807 @ SV383 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ SV354 )
| ( in @ SY807 @ SY797 ) ) ) )
= $false )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2442,plain,
! [SV355: $i,SV391: $i] :
( ( ( SV391
= ( set_meet @ SV355 ) )
= $false )
| ( ( SV391 = empty_set )
= $true )
| ( ( SV355 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2443,plain,
! [SV356: $i,SV392: $i] :
( ( ( SV392 = empty_set )
= $false )
| ( ( SV392
= ( set_meet @ SV356 ) )
= $true )
| ( ( SV356 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2444,plain,
! [SV265: $i,SV375: $i,SV402: $i] :
( ( ( ( SV402 != SV375 ) )
= $true )
| ( ( ~ ( in @ SV402 @ SV265 ) )
= $true )
| ( ( ~ ( ordinal @ SV375 ) )
= $true )
| ( ( in @ SV375 @ ( sK7_B @ SV265 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2374]) ).
thf(2445,plain,
! [SV265: $i,SV376: $i] :
( ( ( ~ ~ ( ( ( sK8_D @ SV376 @ SV265 )
!= SV376 )
| ~ ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2446,plain,
! [SV265: $i,SV376: $i] :
( ( ( ~ ( ordinal @ SV376 ) )
= $false )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2447,plain,
( ( ( ~ ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2448,plain,
( ( ( ( sK9_B != sK11_SY388 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2449,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2377]) ).
thf(2450,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
| ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2451,plain,
! [SV267: $i,SV97: $i,SV318: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV318 ) )
= $true )
| ( ( ( in @ SV403 @ SV97 )
| ( in @ SV403 @ SV267 ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2452,plain,
! [SV267: $i,SV318: $i,SV97: $i] :
( ( ( ~ ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) ) )
= $false )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2381]) ).
thf(2453,plain,
! [SV97: $i,SV318: $i,SV267: $i] :
( ( ( ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) )
= $false )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2381]) ).
thf(2454,plain,
! [SV404: $i,SV101: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ ( sK67_B @ SV101 ) )
| ~ ( subset @ SV404 @ SV393 ) )
= $true )
| ( ( in @ SV404 @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2455,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
= $false )
| ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 ) )
= $true )
| ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2456,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2384]) ).
thf(2457,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
| ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2385]) ).
thf(2458,plain,
! [SV321: $i,SV282: $i,SV103: $i,SV405: $i] :
( ( ( ~ ( in @ SV405 @ SV103 )
| ~ ( in @ SV405 @ SV282 ) )
= $true )
| ( ( in @ SV405 @ SV321 )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2459,plain,
! [SV282: $i,SV103: $i,SV321: $i] :
( ( ( ~ ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) ) )
= $false )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2460,plain,
! [SV103: $i,SV282: $i,SV321: $i] :
( ( ( ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) )
= $false )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2461,plain,
! [SV229: $i,SV284: $i,SV394: $i] :
( ( ( in @ SV394 @ SV284 )
= $false )
| ( ( subset @ SV394 @ SV229 )
= $true )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2462,plain,
! [SV284: $i,SV229: $i,SV395: $i] :
( ( ( subset @ SV395 @ SV229 )
= $false )
| ( ( in @ SV395 @ SV284 )
= $true )
| ( ( SV284
= ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2463,plain,
! [SV104: $i,SV334: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
= $true )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2391]) ).
thf(2464,plain,
! [SV104: $i,SV334: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
| ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
= $true )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2392]) ).
thf(2465,plain,
! [SV335: $i,SV104: $i] :
( ( ( ~ ! [SY771: $i,SY772: $i] :
( ~ ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV104 )
| ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV335 ) ) )
= $false )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2393]) ).
thf(2466,plain,
! [SV104: $i,SV335: $i] :
( ( ( ~ ! [SY773: $i,SY774: $i] :
( ~ ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV335 )
| ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV104 ) ) )
= $false )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2393]) ).
thf(2467,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2468,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2469,plain,
! [SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2470,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2471,plain,
! [SV396: $i,SV232: $i,SV288: $i] :
( ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV396 )
= $false )
| ( ( ~ ( in @ SV396 @ SV232 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2472,plain,
! [SV232: $i,SV288: $i] :
( ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ ( sK41_SY425 @ SV288 @ SV232 ) )
= $true )
| ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2473,plain,
! [SV232: $i,SV288: $i] :
( ( ( in @ ( sK41_SY425 @ SV288 @ SV232 ) @ SV232 )
= $true )
| ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2400]) ).
thf(2474,plain,
! [SV289: $i,SV233: $i,SV413: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV413 )
| ~ ( in @ SV413 @ SV233 ) )
= $true )
| ( ( in @ SV397 @ SV289 )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2475,plain,
! [SV233: $i,SV289: $i,SV398: $i] :
( ( ( in @ SV398 @ SV289 )
= $false )
| ( ( ~ ( ~ ( in @ SV398 @ ( sK39_D @ SV398 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SV398 @ SV289 @ SV233 ) @ SV233 ) ) )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2476,plain,
! [SV234: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2477,plain,
! [SV234: $i] :
( ( ( ~ ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2478,plain,
! [SV364: $i,SV235: $i,SV341: $i] :
( ( ( in @ SV341 @ SV235 )
= $false )
| ( ( ~ ( in @ SV364 @ SV235 ) )
= $true )
| ( ( in @ SV341 @ SV364 )
= $true )
| ( ( SV341 = SV364 )
= $true )
| ( ( in @ SV364 @ SV341 )
= $true )
| ( ( epsilon_connected @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2479,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2480,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2481,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
= $true )
| ( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 ) )
= $true )
| ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2482,plain,
! [SV182: $i,SV108: $i,SV323: $i,SV345: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV345 )
| ( SV414 = SV323 )
| ( SV414 = SV108 )
| ( SV414 = SV182 ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2483,plain,
! [SV182: $i,SV108: $i,SV345: $i,SV323: $i] :
( ( ( ~ ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) )
| ~ ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2484,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
= $false )
| ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2485,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2413]) ).
thf(2486,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
| ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2414]) ).
thf(2487,plain,
! [SV325: $i,SV296: $i,SV111: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ SV111 )
| ( in @ SV406 @ SV296 ) )
= $true )
| ( ( in @ SV406 @ SV325 )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2488,plain,
! [SV296: $i,SV111: $i,SV325: $i] :
( ( ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) ) )
= $false )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2416]) ).
thf(2489,plain,
! [SV111: $i,SV296: $i,SV325: $i] :
( ( ( ~ ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) )
= $false )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2416]) ).
thf(2490,plain,
! [SV114: $i,SV371: $i,SV415: $i] :
( ( ( ~ ( subset @ SV415 @ SV371 )
| ( in @ SV415 @ ( sK4_SY376 @ SV371 @ SV114 ) ) )
= $true )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2491,plain,
! [SV114: $i,SV371: $i] :
( ( ( in @ SV371 @ ( sK3_B @ SV114 ) )
= $false )
| ( ( in @ ( sK4_SY376 @ SV371 @ SV114 ) @ ( sK3_B @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2492,plain,
! [SV407: $i,SV114: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ ( sK3_B @ SV114 ) )
| ~ ( subset @ SV407 @ SV399 ) )
= $true )
| ( ( in @ SV407 @ ( sK3_B @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2493,plain,
! [SV117: $i] :
( ( ( ( ( sK16_SY393 @ SV117 )
!= ( singleton @ ( sK15_B @ SV117 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2422]) ).
thf(2494,plain,
! [SV117: $i] :
( ( ( ~ ( in @ ( sK15_B @ SV117 ) @ SV117 ) )
= $false )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2422]) ).
thf(2495,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2496,plain,
! [SV117: $i] :
( ( ( ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2497,plain,
! [SV408: $i,SV117: $i] :
( ( ( ! [SY813: $i] :
( ~ ( in @ SY813 @ SV117 )
| ( SV408
!= ( singleton @ SY813 ) ) ) )
= $true )
| ( ( in @ SV408 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2498,plain,
! [SV117: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV409 @ SV117 ) @ SV117 )
| ( SV409
!= ( singleton @ ( sK14_D @ SV409 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2499,plain,
! [SV389: $i,SV117: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ SV117 ) )
= $true )
| ( ( ( SV389
!= ( singleton @ SV410 ) ) )
= $true )
| ( ( in @ SV389 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2500,plain,
! [SV117: $i,SV390: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV390 @ SV117 ) @ SV117 )
| ( SV390
!= ( singleton @ ( sK14_D @ SV390 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV390 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2501,plain,
! [SV118: $i,SV351: $i] :
( ( ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV118 )
= $true )
| ( ( subset @ SV118 @ SV351 )
= $true )
| ( ( relation @ SV351 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2428]) ).
thf(2502,plain,
! [SV118: $i,SV351: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV351 ) )
= $true )
| ( ( subset @ SV118 @ SV351 )
= $true )
| ( ( relation @ SV351 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2429]) ).
thf(2503,plain,
! [SV352: $i,SV118: $i,SV416: $i,SV411: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV411 @ SV416 ) @ SV118 )
| ( in @ ( ordered_pair @ SV411 @ SV416 ) @ SV352 ) )
= $true )
| ( ( subset @ SV118 @ SV352 )
= $false )
| ( ( relation @ SV352 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2504,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2431]) ).
thf(2505,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
| ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2432]) ).
thf(2506,plain,
! [SV311: $i,SV119: $i,SV327: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV327 ) )
= $true )
| ( ( ( SV412 = SV119 )
| ( SV412 = SV311 ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2507,plain,
! [SV311: $i,SV327: $i,SV119: $i] :
( ( ( ~ ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) ) )
= $false )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2508,plain,
! [SV119: $i,SV327: $i,SV311: $i] :
( ( ( ~ ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) )
= $false )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2509,plain,
! [SV313: $i,SV258: $i,SV400: $i] :
( ( ( SV400 = SV258 )
= $false )
| ( ( in @ SV400 @ SV313 )
= $true )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2510,plain,
! [SV258: $i,SV313: $i,SV401: $i] :
( ( ( in @ SV401 @ SV313 )
= $false )
| ( ( SV401 = SV258 )
= $true )
| ( ( SV313
= ( singleton @ SV258 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2511,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) )
| ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2439]) ).
thf(2512,plain,
! [SV382: $i,SV353: $i] :
( ( ( ! [SY805: $i] :
( ~ ( in @ SY805 @ SV353 )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SY805 ) )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2513,plain,
! [SV354: $i,SV383: $i] :
( ( ( ~ ! [SY806: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SY806 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SY806 @ ( sK55_D @ SY806 @ SV383 @ SV354 ) ) )
| ( in @ SY806 @ SV383 ) ) )
= $false )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2514,plain,
! [SV354: $i,SV383: $i] :
( ( ( ~ ! [SY807: $i] :
( ~ ( in @ SY807 @ SV383 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ SV354 )
| ( in @ SY807 @ SY797 ) ) ) )
= $false )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2515,plain,
! [SV265: $i,SV375: $i,SV402: $i] :
( ( ( SV402 = SV375 )
= $false )
| ( ( ~ ( in @ SV402 @ SV265 ) )
= $true )
| ( ( ~ ( ordinal @ SV375 ) )
= $true )
| ( ( in @ SV375 @ ( sK7_B @ SV265 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2516,plain,
! [SV265: $i,SV376: $i] :
( ( ( ~ ( ( ( sK8_D @ SV376 @ SV265 )
!= SV376 )
| ~ ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2445]) ).
thf(2517,plain,
! [SV265: $i,SV376: $i] :
( ( ( ordinal @ SV376 )
= $true )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2446]) ).
thf(2518,plain,
( ( ( ~ ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) ) )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2447]) ).
thf(2519,plain,
( ( ( sK9_B = sK11_SY388 )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2448]) ).
thf(2520,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2449]) ).
thf(2521,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(2522,plain,
! [SV267: $i,SV97: $i,SV318: $i,SV403: $i] :
( ( ( in @ SV403 @ SV318 )
= $false )
| ( ( ( in @ SV403 @ SV97 )
| ( in @ SV403 @ SV267 ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2523,plain,
! [SV267: $i,SV318: $i,SV97: $i] :
( ( ( ! [SY752: $i] :
( ~ ( in @ SY752 @ SV97 )
| ( in @ SY752 @ SV318 ) ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2452]) ).
thf(2524,plain,
! [SV97: $i,SV318: $i,SV267: $i] :
( ( ( ! [SY753: $i] :
( ~ ( in @ SY753 @ SV267 )
| ( in @ SY753 @ SV318 ) ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2453]) ).
thf(2525,plain,
! [SV404: $i,SV101: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ ( sK67_B @ SV101 ) ) )
= $true )
| ( ( ~ ( subset @ SV404 @ SV393 ) )
= $true )
| ( ( in @ SV404 @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2526,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
= $false )
| ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
= $false )
| ( ( ~ ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 ) )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2527,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
= $true )
| ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2528,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
= $true )
| ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 )
= $true )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2529,plain,
! [SV321: $i,SV282: $i,SV103: $i,SV405: $i] :
( ( ( ~ ( in @ SV405 @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV405 @ SV282 ) )
= $true )
| ( ( in @ SV405 @ SV321 )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2530,plain,
! [SV282: $i,SV103: $i,SV321: $i] :
( ( ( ! [SY755: $i] :
( ~ ( in @ SY755 @ SV321 )
| ( in @ SY755 @ SV103 ) ) )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2459]) ).
thf(2531,plain,
! [SV103: $i,SV282: $i,SV321: $i] :
( ( ( ! [SY756: $i] :
( ~ ( in @ SY756 @ SV321 )
| ( in @ SY756 @ SV282 ) ) )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2460]) ).
thf(2532,plain,
! [SV104: $i,SV334: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
= $true )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2533,plain,
! [SV104: $i,SV334: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 )
= $true )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2534,plain,
! [SV335: $i,SV104: $i] :
( ( ( ! [SY771: $i,SY772: $i] :
( ~ ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV104 )
| ( in @ ( ordered_pair @ SY771 @ SY772 ) @ SV335 ) ) )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2465]) ).
thf(2535,plain,
! [SV104: $i,SV335: $i] :
( ( ( ! [SY773: $i,SY774: $i] :
( ~ ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV335 )
| ( in @ ( ordered_pair @ SY773 @ SY774 ) @ SV104 ) ) )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2536,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2537,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2538,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2468]) ).
thf(2539,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2468]) ).
thf(2540,plain,
! [SV181: $i,SV417: $i,SV106: $i] :
( ( ( ! [SY815: $i] :
( ~ ( in @ SY815 @ SV106 )
| ! [SY816: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY816 @ SY815 @ SV417 @ SV181 @ SV106 ) @ SY816 )
| ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SY816 @ SY815 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY815 != SY816 )
| ~ ( in @ SV417 @ SY816 ) ) )
| ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2541,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV418 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2542,plain,
! [SV288: $i,SV232: $i,SV396: $i] :
( ( ( in @ SV396 @ SV232 )
= $false )
| ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV396 )
= $false )
| ( ( ~ ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 ) )
= $true )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2543,plain,
! [SV289: $i,SV233: $i,SV413: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV413 ) )
= $true )
| ( ( ~ ( in @ SV413 @ SV233 ) )
= $true )
| ( ( in @ SV397 @ SV289 )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2544,plain,
! [SV233: $i,SV289: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ ( sK39_D @ SV398 @ SV289 @ SV233 ) )
| ~ ( in @ ( sK39_D @ SV398 @ SV289 @ SV233 ) @ SV233 ) )
= $false )
| ( ( in @ SV398 @ SV289 )
= $false )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2545,plain,
! [SV234: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) ) )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2476]) ).
thf(2546,plain,
! [SV234: $i] :
( ( ( ~ ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) ) )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2477]) ).
thf(2547,plain,
! [SV341: $i,SV235: $i,SV364: $i] :
( ( ( in @ SV364 @ SV235 )
= $false )
| ( ( in @ SV341 @ SV235 )
= $false )
| ( ( in @ SV341 @ SV364 )
= $true )
| ( ( SV341 = SV364 )
= $true )
| ( ( in @ SV364 @ SV341 )
= $true )
| ( ( epsilon_connected @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2548,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2479]) ).
thf(2549,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2480]) ).
thf(2550,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
= $true )
| ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 )
= $true )
| ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
= $true )
| ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2481]) ).
thf(2551,plain,
! [SV182: $i,SV108: $i,SV323: $i,SV345: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV345 ) )
= $true )
| ( ( ( SV414 = SV323 )
| ( SV414 = SV108 )
| ( SV414 = SV182 ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2552,plain,
! [SV182: $i,SV108: $i,SV345: $i,SV323: $i] :
( ( ( ~ ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2483]) ).
thf(2553,plain,
! [SV323: $i,SV182: $i,SV345: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2483]) ).
thf(2554,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 )
= $false )
| ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
= $true )
| ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
= $false )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2555,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2485]) ).
thf(2556,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 ) )
= $true )
| ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(2557,plain,
! [SV325: $i,SV296: $i,SV111: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ SV111 ) )
= $true )
| ( ( in @ SV406 @ SV296 )
= $true )
| ( ( in @ SV406 @ SV325 )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2558,plain,
! [SV296: $i,SV111: $i,SV325: $i] :
( ( ( ! [SY764: $i] :
( ~ ( in @ SY764 @ SV325 )
| ( in @ SY764 @ SV111 ) ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2559,plain,
! [SV111: $i,SV296: $i,SV325: $i] :
( ( ( ! [SY765: $i] :
( ~ ( in @ SY765 @ SV325 )
| ~ ( in @ SY765 @ SV296 ) ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2489]) ).
thf(2560,plain,
! [SV114: $i,SV371: $i,SV415: $i] :
( ( ( ~ ( subset @ SV415 @ SV371 ) )
= $true )
| ( ( in @ SV415 @ ( sK4_SY376 @ SV371 @ SV114 ) )
= $true )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2490]) ).
thf(2561,plain,
! [SV407: $i,SV114: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ ( sK3_B @ SV114 ) ) )
= $true )
| ( ( ~ ( subset @ SV407 @ SV399 ) )
= $true )
| ( ( in @ SV407 @ ( sK3_B @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2562,plain,
! [SV117: $i] :
( ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2493]) ).
thf(2563,plain,
! [SV117: $i] :
( ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true )
| ( ( ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2494]) ).
thf(2564,plain,
! [SV117: $i] :
( ( ( ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2565,plain,
! [SV117: $i] :
( ( ( ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2566,plain,
! [SV408: $i,SV117: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ SV117 )
| ( SV408
!= ( singleton @ SV419 ) ) )
= $true )
| ( ( in @ SV408 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2567,plain,
! [SV117: $i,SV409: $i] :
( ( ( in @ SV409 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV409 @ SV117 ) @ SV117 )
| ( SV409
!= ( singleton @ ( sK14_D @ SV409 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2568,plain,
! [SV389: $i,SV117: $i,SV410: $i] :
( ( ( in @ SV410 @ SV117 )
= $false )
| ( ( ( SV389
!= ( singleton @ SV410 ) ) )
= $true )
| ( ( in @ SV389 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2569,plain,
! [SV117: $i,SV390: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV390 @ SV117 ) @ SV117 ) )
= $false )
| ( ( in @ SV390 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2570,plain,
! [SV117: $i,SV390: $i] :
( ( ( ( SV390
!= ( singleton @ ( sK14_D @ SV390 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV390 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2571,plain,
! [SV118: $i,SV351: $i] :
( ( ( in @ ( ordered_pair @ ( sK43_C @ SV351 @ SV118 ) @ ( sK44_SY426 @ SV351 @ SV118 ) ) @ SV351 )
= $false )
| ( ( subset @ SV118 @ SV351 )
= $true )
| ( ( relation @ SV351 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2572,plain,
! [SV352: $i,SV118: $i,SV416: $i,SV411: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV411 @ SV416 ) @ SV118 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV411 @ SV416 ) @ SV352 )
= $true )
| ( ( subset @ SV118 @ SV352 )
= $false )
| ( ( relation @ SV352 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2573,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 ) )
= $true )
| ( ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2574,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 ) )
= $true )
| ( ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2575,plain,
! [SV311: $i,SV119: $i,SV327: $i,SV412: $i] :
( ( ( in @ SV412 @ SV327 )
= $false )
| ( ( ( SV412 = SV119 )
| ( SV412 = SV311 ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2576,plain,
! [SV311: $i,SV327: $i,SV119: $i] :
( ( ( ! [SY767: $i] :
( ( SY767 != SV119 )
| ( in @ SY767 @ SV327 ) ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2577,plain,
! [SV119: $i,SV327: $i,SV311: $i] :
( ( ( ! [SY768: $i] :
( ( SY768 != SV311 )
| ( in @ SY768 @ SV327 ) ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2578,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2579,plain,
! [SV382: $i,SV353: $i] :
( ( ( ! [SY805: $i] :
( ~ ( in @ SY805 @ SV353 )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SY805 ) ) )
= $true )
| ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2580,plain,
! [SV354: $i,SV383: $i] :
( ( ( ! [SY806: $i] :
( ~ ( ~ ( in @ ( sK55_D @ SY806 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SY806 @ ( sK55_D @ SY806 @ SV383 @ SV354 ) ) )
| ( in @ SY806 @ SV383 ) ) )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2513]) ).
thf(2581,plain,
! [SV354: $i,SV383: $i] :
( ( ( ! [SY807: $i] :
( ~ ( in @ SY807 @ SV383 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ SV354 )
| ( in @ SY807 @ SY797 ) ) ) )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2514]) ).
thf(2582,plain,
! [SV375: $i,SV265: $i,SV402: $i] :
( ( ( in @ SV402 @ SV265 )
= $false )
| ( ( SV402 = SV375 )
= $false )
| ( ( ~ ( ordinal @ SV375 ) )
= $true )
| ( ( in @ SV375 @ ( sK7_B @ SV265 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2583,plain,
! [SV265: $i,SV376: $i] :
( ( ( ( ( sK8_D @ SV376 @ SV265 )
!= SV376 )
| ~ ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 ) )
= $false )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2584,plain,
( ( ( ( sK9_B != sK10_SY386 )
| ~ ( ordinal @ sK10_SY386 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2585,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
= $false )
| ( ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2586,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
= $false )
| ( ( ~ ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 ) )
= $true )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2587,plain,
! [SV318: $i,SV267: $i,SV97: $i,SV403: $i] :
( ( ( in @ SV403 @ SV97 )
= $true )
| ( ( in @ SV403 @ SV267 )
= $true )
| ( ( in @ SV403 @ SV318 )
= $false )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2588,plain,
! [SV267: $i,SV318: $i,SV97: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV97 )
| ( in @ SV420 @ SV318 ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(2589,plain,
! [SV97: $i,SV318: $i,SV267: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ SV267 )
| ( in @ SV421 @ SV318 ) )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(2590,plain,
! [SV404: $i,SV101: $i,SV393: $i] :
( ( ( in @ SV393 @ ( sK67_B @ SV101 ) )
= $false )
| ( ( ~ ( subset @ SV404 @ SV393 ) )
= $true )
| ( ( in @ SV404 @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2591,plain,
! [SV103: $i,SV281: $i,SV320: $i] :
( ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV320 )
= $false )
| ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV103 )
= $false )
| ( ( in @ ( sK71_D @ SV320 @ SV281 @ SV103 ) @ SV281 )
= $false )
| ( ( SV320
= ( set_intersection2 @ SV103 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2592,plain,
! [SV321: $i,SV282: $i,SV103: $i,SV405: $i] :
( ( ( in @ SV405 @ SV103 )
= $false )
| ( ( ~ ( in @ SV405 @ SV282 ) )
= $true )
| ( ( in @ SV405 @ SV321 )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2593,plain,
! [SV282: $i,SV103: $i,SV321: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV321 )
| ( in @ SV422 @ SV103 ) )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(2594,plain,
! [SV103: $i,SV282: $i,SV321: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV321 )
| ( in @ SV423 @ SV282 ) )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(2595,plain,
! [SV104: $i,SV334: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 ) )
= $true )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2596,plain,
! [SV335: $i,SV104: $i,SV424: $i] :
( ( ( ! [SY818: $i] :
( ~ ( in @ ( ordered_pair @ SV424 @ SY818 ) @ SV104 )
| ( in @ ( ordered_pair @ SV424 @ SY818 ) @ SV335 ) ) )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(2597,plain,
! [SV104: $i,SV335: $i,SV425: $i] :
( ( ( ! [SY819: $i] :
( ~ ( in @ ( ordered_pair @ SV425 @ SY819 ) @ SV335 )
| ( in @ ( ordered_pair @ SV425 @ SY819 ) @ SV104 ) ) )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(2598,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2536]) ).
thf(2599,plain,
! [SV106: $i,SV181: $i] :
( ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2537]) ).
thf(2600,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY641: $i] :
( ~ ( in @ SY641 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SY641 ) @ SV181 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2538]) ).
thf(2601,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2602,plain,
! [SV181: $i,SV417: $i,SV106: $i] :
( ( ( ! [SY815: $i] :
( ~ ( in @ SY815 @ SV106 )
| ! [SY816: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY816 @ SY815 @ SV417 @ SV181 @ SV106 ) @ SY816 )
| ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SY816 @ SY815 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY815 != SY816 )
| ~ ( in @ SV417 @ SY816 ) ) ) )
= $true )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2603,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV418 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2604,plain,
! [SV396: $i,SV232: $i,SV288: $i] :
( ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV288 )
= $false )
| ( ( in @ ( sK40_C @ SV288 @ SV232 ) @ SV396 )
= $false )
| ( ( in @ SV396 @ SV232 )
= $false )
| ( ( SV288
= ( union @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2605,plain,
! [SV289: $i,SV233: $i,SV413: $i,SV397: $i] :
( ( ( in @ SV397 @ SV413 )
= $false )
| ( ( ~ ( in @ SV413 @ SV233 ) )
= $true )
| ( ( in @ SV397 @ SV289 )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2606,plain,
! [SV233: $i,SV289: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ ( sK39_D @ SV398 @ SV289 @ SV233 ) ) )
= $false )
| ( ( in @ SV398 @ SV289 )
= $false )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2607,plain,
! [SV233: $i,SV289: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK39_D @ SV398 @ SV289 @ SV233 ) @ SV233 ) )
= $false )
| ( ( in @ SV398 @ SV289 )
= $false )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2608,plain,
! [SV234: $i] :
( ( ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 )
| ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2609,plain,
! [SV234: $i] :
( ( ( in @ ( sK45_B @ SV234 ) @ ( sK46_SY427 @ SV234 ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2610,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 ) )
= $true )
| ( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2548]) ).
thf(2611,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
| ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2612,plain,
! [SV182: $i,SV108: $i,SV323: $i,SV345: $i,SV414: $i] :
( ( ( in @ SV414 @ SV345 )
= $false )
| ( ( ( SV414 = SV323 )
| ( SV414 = SV108 )
| ( SV414 = SV182 ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2613,plain,
! [SV182: $i,SV108: $i,SV345: $i,SV323: $i] :
( ( ( ! [SY783: $i] :
( ( SY783 != SV323 )
| ( in @ SY783 @ SV345 ) ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2614,plain,
! [SV323: $i,SV182: $i,SV345: $i,SV108: $i] :
( ( ( ~ ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2553]) ).
thf(2615,plain,
! [SV111: $i,SV295: $i,SV324: $i] :
( ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV295 )
= $false )
| ( ( in @ ( sK38_D @ SV324 @ SV295 @ SV111 ) @ SV324 )
= $true )
| ( ( SV324
= ( set_difference @ SV111 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2616,plain,
! [SV325: $i,SV296: $i,SV111: $i,SV406: $i] :
( ( ( in @ SV406 @ SV111 )
= $false )
| ( ( in @ SV406 @ SV296 )
= $true )
| ( ( in @ SV406 @ SV325 )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2617,plain,
! [SV296: $i,SV111: $i,SV325: $i,SV426: $i] :
( ( ( ~ ( in @ SV426 @ SV325 )
| ( in @ SV426 @ SV111 ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(2618,plain,
! [SV111: $i,SV296: $i,SV325: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV325 )
| ~ ( in @ SV427 @ SV296 ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(2619,plain,
! [SV114: $i,SV371: $i,SV415: $i] :
( ( ( subset @ SV415 @ SV371 )
= $false )
| ( ( in @ SV415 @ ( sK4_SY376 @ SV371 @ SV114 ) )
= $true )
| ( ( ~ ( in @ SV371 @ ( sK3_B @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2620,plain,
! [SV407: $i,SV114: $i,SV399: $i] :
( ( ( in @ SV399 @ ( sK3_B @ SV114 ) )
= $false )
| ( ( ~ ( subset @ SV407 @ SV399 ) )
= $true )
| ( ( in @ SV407 @ ( sK3_B @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2621,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2622,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2623,plain,
! [SV428: $i,SV117: $i] :
( ( ( ! [SY820: $i] :
( ~ ( in @ SY820 @ SV117 )
| ( SV428
!= ( singleton @ SY820 ) ) )
| ( in @ SV428 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2624,plain,
! [SV117: $i,SV429: $i] :
( ( ( ~ ( in @ SV429 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SV429 @ SV117 ) @ SV117 )
| ( SV429
!= ( singleton @ ( sK14_D @ SV429 @ SV117 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2625,plain,
! [SV408: $i,SV117: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ SV117 ) )
= $true )
| ( ( ( SV408
!= ( singleton @ SV419 ) ) )
= $true )
| ( ( in @ SV408 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2626,plain,
! [SV117: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV409 @ SV117 ) @ SV117 )
| ( SV409
!= ( singleton @ ( sK14_D @ SV409 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV409 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2627,plain,
! [SV117: $i,SV410: $i,SV389: $i] :
( ( ( SV389
= ( singleton @ SV410 ) )
= $false )
| ( ( in @ SV410 @ SV117 )
= $false )
| ( ( in @ SV389 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(2628,plain,
! [SV117: $i,SV390: $i] :
( ( ( in @ ( sK14_D @ SV390 @ SV117 ) @ SV117 )
= $true )
| ( ( in @ SV390 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2569]) ).
thf(2629,plain,
! [SV117: $i,SV390: $i] :
( ( ( SV390
= ( singleton @ ( sK14_D @ SV390 @ SV117 ) ) )
= $true )
| ( ( in @ SV390 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( sK17_SY395 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2630,plain,
! [SV352: $i,SV118: $i,SV416: $i,SV411: $i] :
( ( ( in @ ( ordered_pair @ SV411 @ SV416 ) @ SV118 )
= $false )
| ( ( in @ ( ordered_pair @ SV411 @ SV416 ) @ SV352 )
= $true )
| ( ( subset @ SV118 @ SV352 )
= $false )
| ( ( relation @ SV352 )
= $false )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2631,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
= $false )
| ( ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV119 ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2632,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
= $false )
| ( ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
!= SV310 ) )
= $true )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2633,plain,
! [SV327: $i,SV311: $i,SV119: $i,SV412: $i] :
( ( ( SV412 = SV119 )
= $true )
| ( ( SV412 = SV311 )
= $true )
| ( ( in @ SV412 @ SV327 )
= $false )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2575]) ).
thf(2634,plain,
! [SV311: $i,SV327: $i,SV119: $i,SV430: $i] :
( ( ( ( SV430 != SV119 )
| ( in @ SV430 @ SV327 ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(2635,plain,
! [SV119: $i,SV327: $i,SV311: $i,SV431: $i] :
( ( ( ( SV431 != SV311 )
| ( in @ SV431 @ SV327 ) )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(2636,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
| ~ ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) )
= $false )
| ( ( ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2637,plain,
! [SV382: $i,SV353: $i,SV432: $i] :
( ( ( ~ ( in @ SV432 @ SV353 )
| ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV432 ) )
= $true )
| ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(2638,plain,
! [SV354: $i,SV383: $i,SV433: $i] :
( ( ( ~ ( ~ ( in @ ( sK55_D @ SV433 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SV433 @ ( sK55_D @ SV433 @ SV383 @ SV354 ) ) )
| ( in @ SV433 @ SV383 ) )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(2639,plain,
! [SV354: $i,SV383: $i,SV434: $i] :
( ( ( ~ ( in @ SV434 @ SV383 )
| ! [SY821: $i] :
( ~ ( in @ SY821 @ SV354 )
| ( in @ SV434 @ SY821 ) ) )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(2640,plain,
! [SV265: $i,SV402: $i,SV375: $i] :
( ( ( ordinal @ SV375 )
= $false )
| ( ( SV402 = SV375 )
= $false )
| ( ( in @ SV402 @ SV265 )
= $false )
| ( ( in @ SV375 @ ( sK7_B @ SV265 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2641,plain,
! [SV265: $i,SV376: $i] :
( ( ( ( ( sK8_D @ SV376 @ SV265 )
!= SV376 ) )
= $false )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2583]) ).
thf(2642,plain,
! [SV265: $i,SV376: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 ) )
= $false )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2583]) ).
thf(2643,plain,
( ( ( ( sK9_B != sK10_SY386 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2584]) ).
thf(2644,plain,
( ( ( ~ ( ordinal @ sK10_SY386 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2584]) ).
thf(2645,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV97 )
= $false )
| ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
= $false )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2646,plain,
! [SV97: $i,SV266: $i,SV317: $i] :
( ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV266 )
= $false )
| ( ( in @ ( sK47_D @ SV317 @ SV266 @ SV97 ) @ SV317 )
= $false )
| ( ( SV317
= ( set_union2 @ SV97 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2647,plain,
! [SV267: $i,SV318: $i,SV97: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV97 ) )
= $true )
| ( ( in @ SV420 @ SV318 )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2648,plain,
! [SV97: $i,SV318: $i,SV267: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ SV267 ) )
= $true )
| ( ( in @ SV421 @ SV318 )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2649,plain,
! [SV101: $i,SV393: $i,SV404: $i] :
( ( ( subset @ SV404 @ SV393 )
= $false )
| ( ( in @ SV393 @ ( sK67_B @ SV101 ) )
= $false )
| ( ( in @ SV404 @ ( sK67_B @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2650,plain,
! [SV321: $i,SV103: $i,SV282: $i,SV405: $i] :
( ( ( in @ SV405 @ SV282 )
= $false )
| ( ( in @ SV405 @ SV103 )
= $false )
| ( ( in @ SV405 @ SV321 )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2651,plain,
! [SV282: $i,SV103: $i,SV321: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV321 ) )
= $true )
| ( ( in @ SV422 @ SV103 )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2652,plain,
! [SV103: $i,SV282: $i,SV321: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV321 ) )
= $true )
| ( ( in @ SV423 @ SV282 )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2653,plain,
! [SV104: $i,SV334: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV334 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_C @ SV334 @ SV104 ) @ ( sK50_SY428 @ SV334 @ SV104 ) ) @ SV104 )
= $false )
| ( ( SV104 = SV334 )
= $true )
| ( ( relation @ SV334 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2654,plain,
! [SV335: $i,SV104: $i,SV435: $i,SV424: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV424 @ SV435 ) @ SV104 )
| ( in @ ( ordered_pair @ SV424 @ SV435 ) @ SV335 ) )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(2655,plain,
! [SV104: $i,SV335: $i,SV436: $i,SV425: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV425 @ SV436 ) @ SV335 )
| ( in @ ( ordered_pair @ SV425 @ SV436 ) @ SV104 ) )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(2656,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
| ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2657,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2658,plain,
! [SV106: $i,SV181: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(2659,plain,
! [SV106: $i,SV181: $i] :
( ( ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2660,plain,
! [SV181: $i,SV417: $i,SV106: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV106 )
| ! [SY822: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY822 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SY822 )
| ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SY822 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV438 != SY822 )
| ~ ( in @ SV417 @ SY822 ) ) )
= $true )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(2661,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV418 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2662,plain,
! [SV289: $i,SV397: $i,SV233: $i,SV413: $i] :
( ( ( in @ SV413 @ SV233 )
= $false )
| ( ( in @ SV397 @ SV413 )
= $false )
| ( ( in @ SV397 @ SV289 )
= $true )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2663,plain,
! [SV233: $i,SV289: $i,SV398: $i] :
( ( ( in @ SV398 @ ( sK39_D @ SV398 @ SV289 @ SV233 ) )
= $true )
| ( ( in @ SV398 @ SV289 )
= $false )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2606]) ).
thf(2664,plain,
! [SV233: $i,SV289: $i,SV398: $i] :
( ( ( in @ ( sK39_D @ SV398 @ SV289 @ SV233 ) @ SV233 )
= $true )
| ( ( in @ SV398 @ SV289 )
= $false )
| ( ( SV289
= ( union @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2607]) ).
thf(2665,plain,
! [SV234: $i] :
( ( ( ~ ( in @ ( sK45_B @ SV234 ) @ SV234 ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2608]) ).
thf(2666,plain,
! [SV234: $i] :
( ( ( ~ ( in @ ( sK46_SY427 @ SV234 ) @ SV234 ) )
= $false )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2608]) ).
thf(2667,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $false )
| ( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV322 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2668,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2611]) ).
thf(2669,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) ) )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2611]) ).
thf(2670,plain,
! [SV345: $i,SV182: $i,SV108: $i,SV323: $i,SV414: $i] :
( ( ( SV414 = SV323 )
= $true )
| ( ( ( SV414 = SV108 )
| ( SV414 = SV182 ) )
= $true )
| ( ( in @ SV414 @ SV345 )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2671,plain,
! [SV182: $i,SV108: $i,SV345: $i,SV323: $i,SV439: $i] :
( ( ( ( SV439 != SV323 )
| ( in @ SV439 @ SV345 ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(2672,plain,
! [SV323: $i,SV182: $i,SV345: $i,SV108: $i] :
( ( ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) )
| ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2673,plain,
! [SV296: $i,SV111: $i,SV325: $i,SV426: $i] :
( ( ( ~ ( in @ SV426 @ SV325 ) )
= $true )
| ( ( in @ SV426 @ SV111 )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2617]) ).
thf(2674,plain,
! [SV111: $i,SV296: $i,SV325: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV325 ) )
= $true )
| ( ( ~ ( in @ SV427 @ SV296 ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2618]) ).
thf(2675,plain,
! [SV415: $i,SV114: $i,SV371: $i] :
( ( ( in @ SV371 @ ( sK3_B @ SV114 ) )
= $false )
| ( ( in @ SV415 @ ( sK4_SY376 @ SV371 @ SV114 ) )
= $true )
| ( ( subset @ SV415 @ SV371 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2676,plain,
! [SV114: $i,SV399: $i,SV407: $i] :
( ( ( subset @ SV407 @ SV399 )
= $false )
| ( ( in @ SV399 @ ( sK3_B @ SV114 ) )
= $false )
| ( ( in @ SV407 @ ( sK3_B @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2677,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2621]) ).
thf(2678,plain,
! [SV117: $i] :
( ( ( ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2621]) ).
thf(2679,plain,
! [SV117: $i] :
( ( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2622]) ).
thf(2680,plain,
! [SV117: $i] :
( ( ( ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2622]) ).
thf(2681,plain,
! [SV428: $i,SV117: $i] :
( ( ( ! [SY820: $i] :
( ~ ( in @ SY820 @ SV117 )
| ( SV428
!= ( singleton @ SY820 ) ) ) )
= $true )
| ( ( in @ SV428 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2682,plain,
! [SV117: $i,SV429: $i] :
( ( ( ~ ( in @ SV429 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV429 @ SV117 ) @ SV117 )
| ( SV429
!= ( singleton @ ( sK14_D @ SV429 @ SV117 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2683,plain,
! [SV408: $i,SV117: $i,SV419: $i] :
( ( ( in @ SV419 @ SV117 )
= $false )
| ( ( ( SV408
!= ( singleton @ SV419 ) ) )
= $true )
| ( ( in @ SV408 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2684,plain,
! [SV117: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV409 @ SV117 ) @ SV117 ) )
= $false )
| ( ( in @ SV409 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2626]) ).
thf(2685,plain,
! [SV117: $i,SV409: $i] :
( ( ( ( SV409
!= ( singleton @ ( sK14_D @ SV409 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV409 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2626]) ).
thf(2686,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV119 )
= $false )
| ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
= $false )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2687,plain,
! [SV119: $i,SV310: $i,SV326: $i] :
( ( ( ( sK48_D @ SV326 @ SV310 @ SV119 )
= SV310 )
= $false )
| ( ( in @ ( sK48_D @ SV326 @ SV310 @ SV119 ) @ SV326 )
= $false )
| ( ( SV326
= ( unordered_pair @ SV119 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2688,plain,
! [SV311: $i,SV327: $i,SV119: $i,SV430: $i] :
( ( ( ( SV430 != SV119 ) )
= $true )
| ( ( in @ SV430 @ SV327 )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2689,plain,
! [SV119: $i,SV327: $i,SV311: $i,SV431: $i] :
( ( ( ( SV431 != SV311 ) )
= $true )
| ( ( in @ SV431 @ SV327 )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2690,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 ) )
= $false )
| ( ( ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2636]) ).
thf(2691,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) )
= $false )
| ( ( ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2636]) ).
thf(2692,plain,
! [SV382: $i,SV353: $i,SV432: $i] :
( ( ( ~ ( in @ SV432 @ SV353 ) )
= $true )
| ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV432 )
= $true )
| ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2637]) ).
thf(2693,plain,
! [SV354: $i,SV383: $i,SV433: $i] :
( ( ( ~ ( ~ ( in @ ( sK55_D @ SV433 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SV433 @ ( sK55_D @ SV433 @ SV383 @ SV354 ) ) ) )
= $true )
| ( ( in @ SV433 @ SV383 )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2638]) ).
thf(2694,plain,
! [SV354: $i,SV383: $i,SV434: $i] :
( ( ( ~ ( in @ SV434 @ SV383 ) )
= $true )
| ( ( ! [SY821: $i] :
( ~ ( in @ SY821 @ SV354 )
| ( in @ SV434 @ SY821 ) ) )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2695,plain,
! [SV265: $i,SV376: $i] :
( ( ( ( sK8_D @ SV376 @ SV265 )
= SV376 )
= $true )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2641]) ).
thf(2696,plain,
! [SV265: $i,SV376: $i] :
( ( ( in @ ( sK8_D @ SV376 @ SV265 ) @ SV265 )
= $true )
| ( ( in @ SV376 @ ( sK7_B @ SV265 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2642]) ).
thf(2697,plain,
( ( ( sK9_B = sK10_SY386 )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2643]) ).
thf(2698,plain,
( ( ( ordinal @ sK10_SY386 )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2644]) ).
thf(2699,plain,
! [SV267: $i,SV318: $i,SV97: $i,SV420: $i] :
( ( ( in @ SV420 @ SV97 )
= $false )
| ( ( in @ SV420 @ SV318 )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2700,plain,
! [SV97: $i,SV318: $i,SV267: $i,SV421: $i] :
( ( ( in @ SV421 @ SV267 )
= $false )
| ( ( in @ SV421 @ SV318 )
= $true )
| ( ( SV318
= ( set_union2 @ SV97 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2701,plain,
! [SV282: $i,SV103: $i,SV321: $i,SV422: $i] :
( ( ( in @ SV422 @ SV321 )
= $false )
| ( ( in @ SV422 @ SV103 )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2702,plain,
! [SV103: $i,SV282: $i,SV321: $i,SV423: $i] :
( ( ( in @ SV423 @ SV321 )
= $false )
| ( ( in @ SV423 @ SV282 )
= $true )
| ( ( SV321
= ( set_intersection2 @ SV103 @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2703,plain,
! [SV335: $i,SV104: $i,SV435: $i,SV424: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV424 @ SV435 ) @ SV104 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV424 @ SV435 ) @ SV335 )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2704,plain,
! [SV104: $i,SV335: $i,SV436: $i,SV425: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV425 @ SV436 ) @ SV335 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV425 @ SV436 ) @ SV104 )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2705,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2656]) ).
thf(2706,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2656]) ).
thf(2707,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2657]) ).
thf(2708,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2657]) ).
thf(2709,plain,
! [SV106: $i,SV181: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(2710,plain,
! [SV106: $i,SV181: $i] :
( ( ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK25_SY420 @ SV181 @ SV106 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2659]) ).
thf(2711,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2659]) ).
thf(2712,plain,
! [SV181: $i,SV417: $i,SV106: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV106 ) )
= $true )
| ( ( ! [SY822: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY822 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SY822 )
| ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SY822 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV438 != SY822 )
| ~ ( in @ SV417 @ SY822 ) ) )
= $true )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2713,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV418 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2714,plain,
! [SV234: $i] :
( ( ( in @ ( sK45_B @ SV234 ) @ SV234 )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2715,plain,
! [SV234: $i] :
( ( ( in @ ( sK46_SY427 @ SV234 ) @ SV234 )
= $true )
| ( ( epsilon_connected @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2666]) ).
thf(2716,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV322 )
= $false )
| ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2717,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2668]) ).
thf(2718,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
| ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2719,plain,
! [SV345: $i,SV323: $i,SV182: $i,SV108: $i,SV414: $i] :
( ( ( SV414 = SV108 )
= $true )
| ( ( SV414 = SV182 )
= $true )
| ( ( SV414 = SV323 )
= $true )
| ( ( in @ SV414 @ SV345 )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2720,plain,
! [SV182: $i,SV108: $i,SV345: $i,SV323: $i,SV439: $i] :
( ( ( ( SV439 != SV323 ) )
= $true )
| ( ( in @ SV439 @ SV345 )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2721,plain,
! [SV323: $i,SV182: $i,SV345: $i,SV108: $i] :
( ( ( ~ ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2722,plain,
! [SV323: $i,SV108: $i,SV345: $i,SV182: $i] :
( ( ( ~ ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) )
= $false )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2723,plain,
! [SV296: $i,SV111: $i,SV325: $i,SV426: $i] :
( ( ( in @ SV426 @ SV325 )
= $false )
| ( ( in @ SV426 @ SV111 )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2724,plain,
! [SV111: $i,SV296: $i,SV325: $i,SV427: $i] :
( ( ( in @ SV427 @ SV325 )
= $false )
| ( ( ~ ( in @ SV427 @ SV296 ) )
= $true )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2725,plain,
! [SV117: $i] :
( ( ( ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2677]) ).
thf(2726,plain,
! [SV117: $i] :
( ( ( ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2678]) ).
thf(2727,plain,
! [SV117: $i] :
( ( ( ! [SY605: $i] :
( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV117 )
| ( SY605
!= ( singleton @ SY606 ) ) )
| ( in @ SY605 @ ( sK13_B @ SV117 ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2679]) ).
thf(2728,plain,
! [SV117: $i] :
( ( ( ! [SY607: $i] :
( ~ ( in @ SY607 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SY607 @ SV117 ) @ SV117 )
| ( SY607
!= ( singleton @ ( sK14_D @ SY607 @ SV117 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2729,plain,
! [SV428: $i,SV117: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV117 )
| ( SV428
!= ( singleton @ SV440 ) ) )
= $true )
| ( ( in @ SV428 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(2730,plain,
! [SV117: $i,SV429: $i] :
( ( ( in @ SV429 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV429 @ SV117 ) @ SV117 )
| ( SV429
!= ( singleton @ ( sK14_D @ SV429 @ SV117 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2731,plain,
! [SV117: $i,SV419: $i,SV408: $i] :
( ( ( SV408
= ( singleton @ SV419 ) )
= $false )
| ( ( in @ SV419 @ SV117 )
= $false )
| ( ( in @ SV408 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2732,plain,
! [SV117: $i,SV409: $i] :
( ( ( in @ ( sK14_D @ SV409 @ SV117 ) @ SV117 )
= $true )
| ( ( in @ SV409 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2684]) ).
thf(2733,plain,
! [SV117: $i,SV409: $i] :
( ( ( SV409
= ( singleton @ ( sK14_D @ SV409 @ SV117 ) ) )
= $true )
| ( ( in @ SV409 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK17_SY395 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2685]) ).
thf(2734,plain,
! [SV311: $i,SV327: $i,SV119: $i,SV430: $i] :
( ( ( SV430 = SV119 )
= $false )
| ( ( in @ SV430 @ SV327 )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2735,plain,
! [SV119: $i,SV327: $i,SV311: $i,SV431: $i] :
( ( ( SV431 = SV311 )
= $false )
| ( ( in @ SV431 @ SV327 )
= $true )
| ( ( SV327
= ( unordered_pair @ SV119 @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2736,plain,
! [SV353: $i,SV382: $i] :
( ( ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
= $true )
| ( ( ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2690]) ).
thf(2737,plain,
! [SV353: $i,SV382: $i] :
( ( ( ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2738,plain,
! [SV382: $i,SV353: $i,SV432: $i] :
( ( ( in @ SV432 @ SV353 )
= $false )
| ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV432 )
= $true )
| ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2739,plain,
! [SV354: $i,SV383: $i,SV433: $i] :
( ( ( ~ ( in @ ( sK55_D @ SV433 @ SV383 @ SV354 ) @ SV354 )
| ~ ~ ( in @ SV433 @ ( sK55_D @ SV433 @ SV383 @ SV354 ) ) )
= $false )
| ( ( in @ SV433 @ SV383 )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2740,plain,
! [SV354: $i,SV383: $i,SV434: $i] :
( ( ( in @ SV434 @ SV383 )
= $false )
| ( ( ! [SY821: $i] :
( ~ ( in @ SY821 @ SV354 )
| ( in @ SV434 @ SY821 ) ) )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2741,plain,
! [SV335: $i,SV104: $i,SV435: $i,SV424: $i] :
( ( ( in @ ( ordered_pair @ SV424 @ SV435 ) @ SV104 )
= $false )
| ( ( in @ ( ordered_pair @ SV424 @ SV435 ) @ SV335 )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2742,plain,
! [SV104: $i,SV335: $i,SV436: $i,SV425: $i] :
( ( ( in @ ( ordered_pair @ SV425 @ SV436 ) @ SV335 )
= $false )
| ( ( in @ ( ordered_pair @ SV425 @ SV436 ) @ SV104 )
= $true )
| ( ( SV104 = SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2743,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2705]) ).
thf(2744,plain,
! [SV106: $i,SV181: $i] :
( ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2706]) ).
thf(2745,plain,
! [SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2707]) ).
thf(2746,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2708]) ).
thf(2747,plain,
! [SV106: $i,SV181: $i,SV437: $i] :
( ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2748,plain,
! [SV106: $i,SV181: $i] :
( ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2710]) ).
thf(2749,plain,
! [SV106: $i,SV181: $i] :
( ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2711]) ).
thf(2750,plain,
! [SV181: $i,SV417: $i,SV106: $i,SV438: $i] :
( ( ( in @ SV438 @ SV106 )
= $false )
| ( ( ! [SY822: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY822 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SY822 )
| ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SY822 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV438 != SY822 )
| ~ ( in @ SV417 @ SY822 ) ) )
= $true )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2751,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV418 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2713]) ).
thf(2752,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2713]) ).
thf(2753,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 ) )
= $true )
| ( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2717]) ).
thf(2754,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ~ ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 ) )
= $true )
| ( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(2755,plain,
! [SV182: $i,SV108: $i,SV345: $i,SV323: $i,SV439: $i] :
( ( ( SV439 = SV323 )
= $false )
| ( ( in @ SV439 @ SV345 )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2756,plain,
! [SV323: $i,SV182: $i,SV345: $i,SV108: $i] :
( ( ( ! [SY784: $i] :
( ( SY784 != SV108 )
| ( in @ SY784 @ SV345 ) ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2721]) ).
thf(2757,plain,
! [SV323: $i,SV108: $i,SV345: $i,SV182: $i] :
( ( ( ! [SY785: $i] :
( ( SY785 != SV182 )
| ( in @ SY785 @ SV345 ) ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2722]) ).
thf(2758,plain,
! [SV111: $i,SV325: $i,SV296: $i,SV427: $i] :
( ( ( in @ SV427 @ SV296 )
= $false )
| ( ( in @ SV427 @ SV325 )
= $false )
| ( ( SV325
= ( set_difference @ SV111 @ SV296 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2759,plain,
! [SV441: $i,SV117: $i] :
( ( ( ! [SY823: $i] :
( ~ ( in @ SY823 @ SV117 )
| ( SV441
!= ( singleton @ SY823 ) ) )
| ( in @ SV441 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(2760,plain,
! [SV117: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SV442 @ SV117 ) @ SV117 )
| ( SV442
!= ( singleton @ ( sK14_D @ SV442 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(2761,plain,
! [SV443: $i,SV117: $i] :
( ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV117 )
| ( SV443
!= ( singleton @ SY824 ) ) )
| ( in @ SV443 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(2762,plain,
! [SV117: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( sK13_B @ SV117 ) )
| ~ ( ~ ( in @ ( sK14_D @ SV444 @ SV117 ) @ SV117 )
| ( SV444
!= ( singleton @ ( sK14_D @ SV444 @ SV117 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(2763,plain,
! [SV428: $i,SV117: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV117 ) )
= $true )
| ( ( ( SV428
!= ( singleton @ SV440 ) ) )
= $true )
| ( ( in @ SV428 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(2764,plain,
! [SV117: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV429 @ SV117 ) @ SV117 )
| ( SV429
!= ( singleton @ ( sK14_D @ SV429 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV429 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(2765,plain,
! [SV353: $i,SV382: $i] :
( ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 )
= $false )
| ( ( in @ ( sK57_SY429 @ SV382 @ SV353 ) @ SV353 )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2766,plain,
! [SV353: $i,SV382: $i] :
( ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) )
= $false )
| ( ( ~ ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 ) )
= $true )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2767,plain,
! [SV354: $i,SV383: $i,SV433: $i] :
( ( ( ~ ( in @ ( sK55_D @ SV433 @ SV383 @ SV354 ) @ SV354 ) )
= $false )
| ( ( in @ SV433 @ SV383 )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2768,plain,
! [SV354: $i,SV383: $i,SV433: $i] :
( ( ( ~ ~ ( in @ SV433 @ ( sK55_D @ SV433 @ SV383 @ SV354 ) ) )
= $false )
| ( ( in @ SV433 @ SV383 )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2769,plain,
! [SV383: $i,SV434: $i,SV354: $i,SV445: $i] :
( ( ( ~ ( in @ SV445 @ SV354 )
| ( in @ SV434 @ SV445 ) )
= $true )
| ( ( in @ SV434 @ SV383 )
= $false )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(2770,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) )
| ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2771,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2772,plain,
! [SV181: $i,SV446: $i,SV106: $i] :
( ( ( ! [SY825: $i] :
( ~ ( in @ SY825 @ SV106 )
| ! [SY826: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY826 @ SY825 @ SV446 @ SV181 @ SV106 ) @ SY826 )
| ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SY826 @ SY825 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY825 != SY826 )
| ~ ( in @ SV446 @ SY826 ) ) )
| ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(2773,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV447 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(2774,plain,
! [SV437: $i,SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(2775,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2748]) ).
thf(2776,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(2777,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV438: $i,SV448: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SV448 )
| ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV438 != SV448 )
| ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(2778,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( in @ ( sK19_E @ SV418 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2751]) ).
thf(2779,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(2780,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $false )
| ( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV108 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2781,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $false )
| ( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
!= SV182 ) )
= $true )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2782,plain,
! [SV323: $i,SV182: $i,SV345: $i,SV108: $i,SV449: $i] :
( ( ( ( SV449 != SV108 )
| ( in @ SV449 @ SV345 ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(2783,plain,
! [SV323: $i,SV108: $i,SV345: $i,SV182: $i,SV450: $i] :
( ( ( ( SV450 != SV182 )
| ( in @ SV450 @ SV345 ) )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(2784,plain,
! [SV441: $i,SV117: $i] :
( ( ( ! [SY823: $i] :
( ~ ( in @ SY823 @ SV117 )
| ( SV441
!= ( singleton @ SY823 ) ) ) )
= $true )
| ( ( in @ SV441 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(2785,plain,
! [SV117: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV442 @ SV117 ) @ SV117 )
| ( SV442
!= ( singleton @ ( sK14_D @ SV442 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2760]) ).
thf(2786,plain,
! [SV443: $i,SV117: $i] :
( ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV117 )
| ( SV443
!= ( singleton @ SY824 ) ) ) )
= $true )
| ( ( in @ SV443 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(2787,plain,
! [SV117: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( sK13_B @ SV117 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV444 @ SV117 ) @ SV117 )
| ( SV444
!= ( singleton @ ( sK14_D @ SV444 @ SV117 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(2788,plain,
! [SV428: $i,SV117: $i,SV440: $i] :
( ( ( in @ SV440 @ SV117 )
= $false )
| ( ( ( SV428
!= ( singleton @ SV440 ) ) )
= $true )
| ( ( in @ SV428 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2789,plain,
! [SV117: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV429 @ SV117 ) @ SV117 ) )
= $false )
| ( ( in @ SV429 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2764]) ).
thf(2790,plain,
! [SV117: $i,SV429: $i] :
( ( ( ( SV429
!= ( singleton @ ( sK14_D @ SV429 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV429 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2764]) ).
thf(2791,plain,
! [SV353: $i,SV382: $i] :
( ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ SV382 )
= $false )
| ( ( in @ ( sK56_C @ SV382 @ SV353 ) @ ( sK57_SY429 @ SV382 @ SV353 ) )
= $false )
| ( ( SV382
= ( set_meet @ SV353 ) )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(2792,plain,
! [SV354: $i,SV383: $i,SV433: $i] :
( ( ( in @ ( sK55_D @ SV433 @ SV383 @ SV354 ) @ SV354 )
= $true )
| ( ( in @ SV433 @ SV383 )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2767]) ).
thf(2793,plain,
! [SV354: $i,SV383: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK55_D @ SV433 @ SV383 @ SV354 ) ) )
= $true )
| ( ( in @ SV433 @ SV383 )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2794,plain,
! [SV383: $i,SV434: $i,SV354: $i,SV445: $i] :
( ( ( ~ ( in @ SV445 @ SV354 ) )
= $true )
| ( ( in @ SV434 @ SV445 )
= $true )
| ( ( in @ SV434 @ SV383 )
= $false )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(2795,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2770]) ).
thf(2796,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2770]) ).
thf(2797,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2798,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2799,plain,
! [SV181: $i,SV446: $i,SV106: $i] :
( ( ( ! [SY825: $i] :
( ~ ( in @ SY825 @ SV106 )
| ! [SY826: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY826 @ SY825 @ SV446 @ SV181 @ SV106 ) @ SY826 )
| ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SY826 @ SY825 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY825 != SY826 )
| ~ ( in @ SV446 @ SY826 ) ) ) )
= $true )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(2800,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV447 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2801,plain,
! [SV437: $i,SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2802,plain,
! [SV437: $i,SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2803,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2804,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2805,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2776]) ).
thf(2806,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2776]) ).
thf(2807,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV438: $i,SV448: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SV448 )
| ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV438 != SV448 )
| ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2808,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(2809,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV108 )
= $false )
| ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2810,plain,
! [SV108: $i,SV182: $i,SV322: $i,SV344: $i] :
( ( ( ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 )
= SV182 )
= $false )
| ( ( in @ ( sK61_E @ SV344 @ SV322 @ SV182 @ SV108 ) @ SV344 )
= $false )
| ( ( SV344
= ( unordered_triple @ SV108 @ SV182 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2811,plain,
! [SV323: $i,SV182: $i,SV345: $i,SV108: $i,SV449: $i] :
( ( ( ( SV449 != SV108 ) )
= $true )
| ( ( in @ SV449 @ SV345 )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2812,plain,
! [SV323: $i,SV108: $i,SV345: $i,SV182: $i,SV450: $i] :
( ( ( ( SV450 != SV182 ) )
= $true )
| ( ( in @ SV450 @ SV345 )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(2813,plain,
! [SV441: $i,SV117: $i,SV451: $i] :
( ( ( ~ ( in @ SV451 @ SV117 )
| ( SV441
!= ( singleton @ SV451 ) ) )
= $true )
| ( ( in @ SV441 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(2814,plain,
! [SV117: $i,SV442: $i] :
( ( ( in @ SV442 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV442 @ SV117 ) @ SV117 )
| ( SV442
!= ( singleton @ ( sK14_D @ SV442 @ SV117 ) ) ) ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(2815,plain,
! [SV443: $i,SV117: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ SV117 )
| ( SV443
!= ( singleton @ SV452 ) ) )
= $true )
| ( ( in @ SV443 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(2816,plain,
! [SV117: $i,SV444: $i] :
( ( ( in @ SV444 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK14_D @ SV444 @ SV117 ) @ SV117 )
| ( SV444
!= ( singleton @ ( sK14_D @ SV444 @ SV117 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2817,plain,
! [SV117: $i,SV440: $i,SV428: $i] :
( ( ( SV428
= ( singleton @ SV440 ) )
= $false )
| ( ( in @ SV440 @ SV117 )
= $false )
| ( ( in @ SV428 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(2818,plain,
! [SV117: $i,SV429: $i] :
( ( ( in @ ( sK14_D @ SV429 @ SV117 ) @ SV117 )
= $true )
| ( ( in @ SV429 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2789]) ).
thf(2819,plain,
! [SV117: $i,SV429: $i] :
( ( ( SV429
= ( singleton @ ( sK14_D @ SV429 @ SV117 ) ) )
= $true )
| ( ( in @ SV429 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2820,plain,
! [SV354: $i,SV383: $i,SV433: $i] :
( ( ( in @ SV433 @ ( sK55_D @ SV433 @ SV383 @ SV354 ) )
= $false )
| ( ( in @ SV433 @ SV383 )
= $true )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2821,plain,
! [SV383: $i,SV434: $i,SV354: $i,SV445: $i] :
( ( ( in @ SV445 @ SV354 )
= $false )
| ( ( in @ SV434 @ SV445 )
= $true )
| ( ( in @ SV434 @ SV383 )
= $false )
| ( ( SV383
= ( set_meet @ SV354 ) )
= $false )
| ( ( SV354 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(2822,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY640: $i] :
( ~ ( in @ SY640 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SY640 ) @ SV181 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2795]) ).
thf(2823,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2796]) ).
thf(2824,plain,
! [SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2797]) ).
thf(2825,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(2826,plain,
! [SV181: $i,SV446: $i,SV106: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV106 )
| ! [SY828: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY828 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SY828 )
| ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SY828 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV453 != SY828 )
| ~ ( in @ SV446 @ SY828 ) ) )
= $true )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(2827,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV447 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(2828,plain,
! [SV437: $i,SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2801]) ).
thf(2829,plain,
! [SV437: $i,SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2802]) ).
thf(2830,plain,
! [SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2831,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2804]) ).
thf(2832,plain,
! [SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2833,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2806]) ).
thf(2834,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV438: $i,SV448: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SV448 )
| ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV438 != SV448 )
| ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2835,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2808]) ).
thf(2836,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2808]) ).
thf(2837,plain,
! [SV323: $i,SV182: $i,SV345: $i,SV108: $i,SV449: $i] :
( ( ( SV449 = SV108 )
= $false )
| ( ( in @ SV449 @ SV345 )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(2838,plain,
! [SV323: $i,SV108: $i,SV345: $i,SV182: $i,SV450: $i] :
( ( ( SV450 = SV182 )
= $false )
| ( ( in @ SV450 @ SV345 )
= $true )
| ( ( SV345
= ( unordered_triple @ SV108 @ SV182 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(2839,plain,
! [SV441: $i,SV117: $i,SV451: $i] :
( ( ( ~ ( in @ SV451 @ SV117 ) )
= $true )
| ( ( ( SV441
!= ( singleton @ SV451 ) ) )
= $true )
| ( ( in @ SV441 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2813]) ).
thf(2840,plain,
! [SV117: $i,SV442: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV442 @ SV117 ) @ SV117 )
| ( SV442
!= ( singleton @ ( sK14_D @ SV442 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV442 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2841,plain,
! [SV443: $i,SV117: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ SV117 ) )
= $true )
| ( ( ( SV443
!= ( singleton @ SV452 ) ) )
= $true )
| ( ( in @ SV443 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(2842,plain,
! [SV117: $i,SV444: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV444 @ SV117 ) @ SV117 )
| ( SV444
!= ( singleton @ ( sK14_D @ SV444 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV444 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2816]) ).
thf(2843,plain,
! [SV106: $i,SV181: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(2844,plain,
! [SV106: $i,SV181: $i] :
( ( ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) )
| ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2845,plain,
! [SV181: $i,SV455: $i,SV106: $i] :
( ( ( ! [SY829: $i] :
( ~ ( in @ SY829 @ SV106 )
| ! [SY830: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY830 @ SY829 @ SV455 @ SV181 @ SV106 ) @ SY830 )
| ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SY830 @ SY829 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY829 != SY830 )
| ~ ( in @ SV455 @ SY830 ) ) )
| ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(2846,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV456 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(2847,plain,
! [SV181: $i,SV446: $i,SV106: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV106 ) )
= $true )
| ( ( ! [SY828: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY828 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SY828 )
| ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SY828 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV453 != SY828 )
| ~ ( in @ SV446 @ SY828 ) ) )
= $true )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(2848,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV447 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(2849,plain,
! [SV437: $i,SV181: $i,SV457: $i,SV106: $i] :
( ( ( ! [SY832: $i] :
( ~ ( in @ SY832 @ SV106 )
| ! [SY833: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY833 @ SY832 @ SV457 @ SV181 @ SV106 ) @ SY833 )
| ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SY833 @ SY832 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY832 != SY833 )
| ~ ( in @ SV457 @ SY833 ) ) )
| ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(2850,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV458 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(2851,plain,
! [SV181: $i,SV459: $i,SV106: $i] :
( ( ( ! [SY835: $i] :
( ~ ( in @ SY835 @ SV106 )
| ! [SY836: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY836 @ SY835 @ SV459 @ SV181 @ SV106 ) @ SY836 )
| ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SY836 @ SY835 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY835 != SY836 )
| ~ ( in @ SV459 @ SY836 ) ) )
| ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(2852,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV460 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(2853,plain,
! [SV181: $i,SV461: $i,SV106: $i] :
( ( ( ! [SY838: $i] :
( ~ ( in @ SY838 @ SV106 )
| ! [SY839: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY839 @ SY838 @ SV461 @ SV181 @ SV106 ) @ SY839 )
| ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SY839 @ SY838 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY838 != SY839 )
| ~ ( in @ SV461 @ SY839 ) ) )
| ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(2854,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV462 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(2855,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV438: $i,SV448: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SV448 ) )
= $false )
| ( ( ( SV438 != SV448 )
| ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2834]) ).
thf(2856,plain,
! [SV106: $i,SV181: $i,SV438: $i,SV448: $i,SV417: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV438 != SV448 )
| ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2834]) ).
thf(2857,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SY817 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2858,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(2859,plain,
! [SV441: $i,SV117: $i,SV451: $i] :
( ( ( in @ SV451 @ SV117 )
= $false )
| ( ( ( SV441
!= ( singleton @ SV451 ) ) )
= $true )
| ( ( in @ SV441 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2860,plain,
! [SV117: $i,SV442: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV442 @ SV117 ) @ SV117 ) )
= $false )
| ( ( in @ SV442 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2840]) ).
thf(2861,plain,
! [SV117: $i,SV442: $i] :
( ( ( ( SV442
!= ( singleton @ ( sK14_D @ SV442 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV442 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2840]) ).
thf(2862,plain,
! [SV443: $i,SV117: $i,SV452: $i] :
( ( ( in @ SV452 @ SV117 )
= $false )
| ( ( ( SV443
!= ( singleton @ SV452 ) ) )
= $true )
| ( ( in @ SV443 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(2863,plain,
! [SV117: $i,SV444: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV444 @ SV117 ) @ SV117 ) )
= $false )
| ( ( in @ SV444 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2864,plain,
! [SV117: $i,SV444: $i] :
( ( ( ( SV444
!= ( singleton @ ( sK14_D @ SV444 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV444 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2865,plain,
! [SV106: $i,SV181: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(2866,plain,
! [SV106: $i,SV181: $i] :
( ( ( ( ( sK22_C @ SV181 @ SV106 )
!= ( sK26_SY414 @ SV181 @ SV106 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2867,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2868,plain,
! [SV181: $i,SV455: $i,SV106: $i] :
( ( ( ! [SY829: $i] :
( ~ ( in @ SY829 @ SV106 )
| ! [SY830: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY830 @ SY829 @ SV455 @ SV181 @ SV106 ) @ SY830 )
| ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SY830 @ SY829 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY829 != SY830 )
| ~ ( in @ SV455 @ SY830 ) ) ) )
= $true )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(2869,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV456 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2846]) ).
thf(2870,plain,
! [SV181: $i,SV446: $i,SV106: $i,SV453: $i] :
( ( ( in @ SV453 @ SV106 )
= $false )
| ( ( ! [SY828: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY828 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SY828 )
| ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SY828 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV453 != SY828 )
| ~ ( in @ SV446 @ SY828 ) ) )
= $true )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(2871,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV447 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2872,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ~ ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2873,plain,
! [SV437: $i,SV181: $i,SV457: $i,SV106: $i] :
( ( ( ! [SY832: $i] :
( ~ ( in @ SY832 @ SV106 )
| ! [SY833: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY833 @ SY832 @ SV457 @ SV181 @ SV106 ) @ SY833 )
| ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SY833 @ SY832 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY832 != SY833 )
| ~ ( in @ SV457 @ SY833 ) ) ) )
= $true )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(2874,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV458 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2850]) ).
thf(2875,plain,
! [SV181: $i,SV459: $i,SV106: $i] :
( ( ( ! [SY835: $i] :
( ~ ( in @ SY835 @ SV106 )
| ! [SY836: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY836 @ SY835 @ SV459 @ SV181 @ SV106 ) @ SY836 )
| ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SY836 @ SY835 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY835 != SY836 )
| ~ ( in @ SV459 @ SY836 ) ) ) )
= $true )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(2876,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV460 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(2877,plain,
! [SV181: $i,SV461: $i,SV106: $i] :
( ( ( ! [SY838: $i] :
( ~ ( in @ SY838 @ SV106 )
| ! [SY839: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY839 @ SY838 @ SV461 @ SV181 @ SV106 ) @ SY839 )
| ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SY839 @ SY838 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY838 != SY839 )
| ~ ( in @ SV461 @ SY839 ) ) ) )
= $true )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(2878,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV462 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(2879,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV438: $i,SV448: $i] :
( ( ( in @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SV448 )
= $true )
| ( ( ( SV438 != SV448 )
| ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2855]) ).
thf(2880,plain,
! [SV106: $i,SV181: $i,SV438: $i,SV448: $i,SV417: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV438 != SV448 )
| ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2856]) ).
thf(2881,plain,
! [SV106: $i,SV181: $i,SV418: $i,SV463: $i] :
( ( ( ~ ( in @ SV463 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV418 @ SV463 ) @ SV181 ) )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(2882,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
| ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2883,plain,
! [SV117: $i,SV451: $i,SV441: $i] :
( ( ( SV441
= ( singleton @ SV451 ) )
= $false )
| ( ( in @ SV451 @ SV117 )
= $false )
| ( ( in @ SV441 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(2884,plain,
! [SV117: $i,SV442: $i] :
( ( ( in @ ( sK14_D @ SV442 @ SV117 ) @ SV117 )
= $true )
| ( ( in @ SV442 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(2885,plain,
! [SV117: $i,SV442: $i] :
( ( ( SV442
= ( singleton @ ( sK14_D @ SV442 @ SV117 ) ) )
= $true )
| ( ( in @ SV442 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( ( sK16_SY393 @ SV117 )
= ( singleton @ ( sK15_B @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2861]) ).
thf(2886,plain,
! [SV117: $i,SV452: $i,SV443: $i] :
( ( ( SV443
= ( singleton @ SV452 ) )
= $false )
| ( ( in @ SV452 @ SV117 )
= $false )
| ( ( in @ SV443 @ ( sK13_B @ SV117 ) )
= $true )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(2887,plain,
! [SV117: $i,SV444: $i] :
( ( ( in @ ( sK14_D @ SV444 @ SV117 ) @ SV117 )
= $true )
| ( ( in @ SV444 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2863]) ).
thf(2888,plain,
! [SV117: $i,SV444: $i] :
( ( ( SV444
= ( singleton @ ( sK14_D @ SV444 @ SV117 ) ) )
= $true )
| ( ( in @ SV444 @ ( sK13_B @ SV117 ) )
= $false )
| ( ( in @ ( sK15_B @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2864]) ).
thf(2889,plain,
! [SV106: $i,SV181: $i,SV454: $i] :
( ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2890,plain,
! [SV106: $i,SV181: $i] :
( ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2866]) ).
thf(2891,plain,
! [SV106: $i,SV181: $i] :
( ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2867]) ).
thf(2892,plain,
! [SV181: $i,SV455: $i,SV106: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ SV106 )
| ! [SY841: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY841 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SY841 )
| ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SY841 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV464 != SY841 )
| ~ ( in @ SV455 @ SY841 ) ) )
= $true )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(2893,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV456 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(2894,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV453: $i,SV465: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SV465 )
| ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV453 != SV465 )
| ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(2895,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( in @ ( sK19_E @ SV447 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(2896,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(2897,plain,
! [SV437: $i,SV181: $i,SV457: $i,SV106: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ SV106 )
| ! [SY842: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY842 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SY842 )
| ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SY842 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV466 != SY842 )
| ~ ( in @ SV457 @ SY842 ) ) )
= $true )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(2898,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV458 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2899,plain,
! [SV181: $i,SV459: $i,SV106: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ SV106 )
| ! [SY843: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY843 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SY843 )
| ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SY843 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV467 != SY843 )
| ~ ( in @ SV459 @ SY843 ) ) )
= $true )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(2900,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV460 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(2901,plain,
! [SV181: $i,SV461: $i,SV106: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV106 )
| ! [SY844: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY844 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SY844 )
| ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SY844 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV468 != SY844 )
| ~ ( in @ SV461 @ SY844 ) ) )
= $true )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(2902,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV462 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2903,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV448: $i,SV438: $i] :
( ( ( ( SV438 != SV448 ) )
= $true )
| ( ( ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SV448 )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2879]) ).
thf(2904,plain,
! [SV106: $i,SV181: $i,SV438: $i,SV448: $i,SV417: $i] :
( ( ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV438 != SV448 )
| ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(2905,plain,
! [SV106: $i,SV181: $i,SV418: $i,SV463: $i] :
( ( ( ~ ( in @ SV463 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV418 @ SV463 ) @ SV181 )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(2906,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2882]) ).
thf(2907,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2882]) ).
thf(2908,plain,
! [SV454: $i,SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2909,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(2910,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2891]) ).
thf(2911,plain,
! [SV181: $i,SV455: $i,SV106: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ SV106 ) )
= $true )
| ( ( ! [SY841: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY841 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SY841 )
| ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SY841 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV464 != SY841 )
| ~ ( in @ SV455 @ SY841 ) ) )
= $true )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2892]) ).
thf(2912,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV456 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(2913,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV453: $i,SV465: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SV465 )
| ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV453 != SV465 )
| ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(2914,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(2915,plain,
! [SV437: $i,SV181: $i,SV457: $i,SV106: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ SV106 ) )
= $true )
| ( ( ! [SY842: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY842 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SY842 )
| ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SY842 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV466 != SY842 )
| ~ ( in @ SV457 @ SY842 ) ) )
= $true )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(2916,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV458 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(2917,plain,
! [SV181: $i,SV459: $i,SV106: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ SV106 ) )
= $true )
| ( ( ! [SY843: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY843 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SY843 )
| ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SY843 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV467 != SY843 )
| ~ ( in @ SV459 @ SY843 ) ) )
= $true )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2899]) ).
thf(2918,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV460 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(2919,plain,
! [SV181: $i,SV461: $i,SV106: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV106 ) )
= $true )
| ( ( ! [SY844: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY844 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SY844 )
| ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SY844 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV468 != SY844 )
| ~ ( in @ SV461 @ SY844 ) ) )
= $true )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2901]) ).
thf(2920,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV462 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(2921,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV448: $i,SV438: $i] :
( ( ( SV438 = SV448 )
= $false )
| ( ( ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SV448 )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2922,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV448: $i,SV438: $i] :
( ( ( ( SV438 != SV448 ) )
= $true )
| ( ( ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(2923,plain,
! [SV106: $i,SV181: $i,SV418: $i,SV463: $i] :
( ( ( in @ SV463 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV418 @ SV463 ) @ SV181 )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(2924,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( ( sK19_E @ SV418 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2906]) ).
thf(2925,plain,
! [SV106: $i,SV181: $i,SV418: $i] :
( ( ( in @ SV418 @ ( sK20_SY404 @ SV418 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV418 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2907]) ).
thf(2926,plain,
! [SV454: $i,SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2908]) ).
thf(2927,plain,
! [SV454: $i,SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2908]) ).
thf(2928,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(2929,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(2930,plain,
! [SV181: $i,SV106: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2910]) ).
thf(2931,plain,
! [SV106: $i,SV181: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2910]) ).
thf(2932,plain,
! [SV181: $i,SV455: $i,SV106: $i,SV464: $i] :
( ( ( in @ SV464 @ SV106 )
= $false )
| ( ( ! [SY841: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY841 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SY841 )
| ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SY841 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV464 != SY841 )
| ~ ( in @ SV455 @ SY841 ) ) )
= $true )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(2933,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV456 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2912]) ).
thf(2934,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ~ ( ~ ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2912]) ).
thf(2935,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV453: $i,SV465: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SV465 )
| ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV453 != SV465 )
| ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(2936,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2914]) ).
thf(2937,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2914]) ).
thf(2938,plain,
! [SV437: $i,SV181: $i,SV457: $i,SV106: $i,SV466: $i] :
( ( ( in @ SV466 @ SV106 )
= $false )
| ( ( ! [SY842: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY842 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SY842 )
| ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SY842 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV466 != SY842 )
| ~ ( in @ SV457 @ SY842 ) ) )
= $true )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(2939,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV458 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2916]) ).
thf(2940,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ~ ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2916]) ).
thf(2941,plain,
! [SV181: $i,SV459: $i,SV106: $i,SV467: $i] :
( ( ( in @ SV467 @ SV106 )
= $false )
| ( ( ! [SY843: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY843 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SY843 )
| ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SY843 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV467 != SY843 )
| ~ ( in @ SV459 @ SY843 ) ) )
= $true )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(2942,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV460 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2918]) ).
thf(2943,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ~ ( ~ ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2918]) ).
thf(2944,plain,
! [SV181: $i,SV461: $i,SV106: $i,SV468: $i] :
( ( ( in @ SV468 @ SV106 )
= $false )
| ( ( ! [SY844: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY844 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SY844 )
| ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SY844 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV468 != SY844 )
| ~ ( in @ SV461 @ SY844 ) ) )
= $true )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(2945,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV462 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2920]) ).
thf(2946,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2920]) ).
thf(2947,plain,
! [SV106: $i,SV181: $i,SV438: $i,SV448: $i,SV417: $i] :
( ( ( in @ SV417 @ SV448 )
= $false )
| ( ( SV438 = SV448 )
= $false )
| ( ( in @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) @ SV448 )
= $true )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(2948,plain,
! [SV106: $i,SV181: $i,SV417: $i,SV448: $i,SV438: $i] :
( ( ( SV438 = SV448 )
= $false )
| ( ( ~ ( in @ SV417 @ SV448 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(2949,plain,
! [SV454: $i,SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(2950,plain,
! [SV454: $i,SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(2951,plain,
! [SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(2952,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(2953,plain,
! [SV181: $i,SV106: $i] :
( ( ( ! [SY642: $i] :
( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV106 )
| ! [SY644: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) @ SY644 )
| ~ ~ ( in @ ( ordered_pair @ SY642 @ ( sK21_K @ SY644 @ SY643 @ SY642 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY643 != SY644 )
| ~ ( in @ SY642 @ SY644 ) ) )
| ( in @ SY642 @ ( sK18_C @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2930]) ).
thf(2954,plain,
! [SV106: $i,SV181: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SY645 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SY645 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) )
| ~ ( in @ SY645 @ ( sK20_SY404 @ SY645 @ SV181 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2931]) ).
thf(2955,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV464: $i,SV469: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SV469 )
| ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV464 != SV469 )
| ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(2956,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( in @ ( sK19_E @ SV456 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2933]) ).
thf(2957,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ( ~ ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2934]) ).
thf(2958,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV453: $i,SV465: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SV465 ) )
= $false )
| ( ( ( SV453 != SV465 )
| ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2935]) ).
thf(2959,plain,
! [SV106: $i,SV181: $i,SV453: $i,SV465: $i,SV446: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV453 != SV465 )
| ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2935]) ).
thf(2960,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ! [SY827: $i] :
( ~ ( in @ SY827 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SY827 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2936]) ).
thf(2961,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(2962,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV466: $i,SV470: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SV470 )
| ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV466 != SV470 )
| ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(2963,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( in @ ( sK19_E @ SV458 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2939]) ).
thf(2964,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2940]) ).
thf(2965,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV467: $i,SV471: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SV471 )
| ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV467 != SV471 )
| ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(2966,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( in @ ( sK19_E @ SV460 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2942]) ).
thf(2967,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ( ~ ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2943]) ).
thf(2968,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV468: $i,SV472: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SV472 )
| ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV468 != SV472 )
| ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(2969,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( in @ ( sK19_E @ SV462 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2945]) ).
thf(2970,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2946]) ).
thf(2971,plain,
! [SV106: $i,SV181: $i,SV438: $i,SV448: $i,SV417: $i] :
( ( ( in @ SV417 @ SV448 )
= $false )
| ( ( SV438 = SV448 )
= $false )
| ( ( in @ ( ordered_pair @ SV417 @ ( sK21_K @ SV448 @ SV438 @ SV417 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV438 @ SV106 )
= $false )
| ( ( in @ SV417 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK23_SY407 @ SV181 @ SV106 )
= ( sK24_SY413 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(2972,plain,
! [SV454: $i,SV181: $i,SV473: $i,SV106: $i] :
( ( ( ! [SY845: $i] :
( ~ ( in @ SY845 @ SV106 )
| ! [SY846: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY846 @ SY845 @ SV473 @ SV181 @ SV106 ) @ SY846 )
| ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SY846 @ SY845 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY845 != SY846 )
| ~ ( in @ SV473 @ SY846 ) ) )
| ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(2973,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV474 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(2974,plain,
! [SV181: $i,SV475: $i,SV106: $i] :
( ( ( ! [SY848: $i] :
( ~ ( in @ SY848 @ SV106 )
| ! [SY849: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY849 @ SY848 @ SV475 @ SV181 @ SV106 ) @ SY849 )
| ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SY849 @ SY848 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY848 != SY849 )
| ~ ( in @ SV475 @ SY849 ) ) )
| ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(2975,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV476 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(2976,plain,
! [SV181: $i,SV477: $i,SV106: $i] :
( ( ( ! [SY851: $i] :
( ~ ( in @ SY851 @ SV106 )
| ! [SY852: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY852 @ SY851 @ SV477 @ SV181 @ SV106 ) @ SY852 )
| ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SY852 @ SY851 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY851 != SY852 )
| ~ ( in @ SV477 @ SY852 ) ) )
| ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(2977,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
| ~ ( ~ ( in @ ( sK19_E @ SV478 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(2978,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV464: $i,SV469: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SV469 )
| ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV464 != SV469 )
| ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2955]) ).
thf(2979,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(2980,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV453: $i,SV465: $i] :
( ( ( in @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SV465 )
= $true )
| ( ( ( SV453 != SV465 )
| ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2958]) ).
thf(2981,plain,
! [SV106: $i,SV181: $i,SV453: $i,SV465: $i,SV446: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV453 != SV465 )
| ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2959]) ).
thf(2982,plain,
! [SV106: $i,SV181: $i,SV447: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV447 @ SV479 ) @ SV181 ) )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(2983,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
| ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(2984,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV466: $i,SV470: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SV470 )
| ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV466 != SV470 )
| ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2962]) ).
thf(2985,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(2986,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV467: $i,SV471: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SV471 )
| ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV467 != SV471 )
| ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2965]) ).
thf(2987,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(2988,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV468: $i,SV472: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SV472 )
| ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV468 != SV472 )
| ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(2989,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(2990,plain,
! [SV454: $i,SV181: $i,SV473: $i,SV106: $i] :
( ( ( ! [SY845: $i] :
( ~ ( in @ SY845 @ SV106 )
| ! [SY846: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY846 @ SY845 @ SV473 @ SV181 @ SV106 ) @ SY846 )
| ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SY846 @ SY845 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY845 != SY846 )
| ~ ( in @ SV473 @ SY846 ) ) ) )
= $true )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2972]) ).
thf(2991,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV474 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(2992,plain,
! [SV181: $i,SV475: $i,SV106: $i] :
( ( ( ! [SY848: $i] :
( ~ ( in @ SY848 @ SV106 )
| ! [SY849: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY849 @ SY848 @ SV475 @ SV181 @ SV106 ) @ SY849 )
| ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SY849 @ SY848 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY848 != SY849 )
| ~ ( in @ SV475 @ SY849 ) ) ) )
= $true )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(2993,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV476 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(2994,plain,
! [SV181: $i,SV477: $i,SV106: $i] :
( ( ( ! [SY851: $i] :
( ~ ( in @ SY851 @ SV106 )
| ! [SY852: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY852 @ SY851 @ SV477 @ SV181 @ SV106 ) @ SY852 )
| ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SY852 @ SY851 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SY851 != SY852 )
| ~ ( in @ SV477 @ SY852 ) ) ) )
= $true )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(2995,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV478 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(2996,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV464: $i,SV469: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SV469 )
| ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV464 != SV469 )
| ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(2997,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2979]) ).
thf(2998,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2979]) ).
thf(2999,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV465: $i,SV453: $i] :
( ( ( ( SV453 != SV465 ) )
= $true )
| ( ( ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SV465 )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3000,plain,
! [SV106: $i,SV181: $i,SV453: $i,SV465: $i,SV446: $i] :
( ( ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV453 != SV465 )
| ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3001,plain,
! [SV106: $i,SV181: $i,SV447: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV447 @ SV479 ) @ SV181 )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2982]) ).
thf(3002,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2983]) ).
thf(3003,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2983]) ).
thf(3004,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV466: $i,SV470: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SV470 )
| ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV466 != SV470 )
| ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3005,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2985]) ).
thf(3006,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2985]) ).
thf(3007,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV467: $i,SV471: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SV471 )
| ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV467 != SV471 )
| ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3008,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2987]) ).
thf(3009,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2987]) ).
thf(3010,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV468: $i,SV472: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SV472 )
| ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV468 != SV472 )
| ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3011,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2989]) ).
thf(3012,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2989]) ).
thf(3013,plain,
! [SV454: $i,SV181: $i,SV473: $i,SV106: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV106 )
| ! [SY854: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY854 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SY854 )
| ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SY854 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV480 != SY854 )
| ~ ( in @ SV473 @ SY854 ) ) )
= $true )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3014,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV474 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3015,plain,
! [SV181: $i,SV475: $i,SV106: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV106 )
| ! [SY855: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY855 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SY855 )
| ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SY855 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV481 != SY855 )
| ~ ( in @ SV475 @ SY855 ) ) )
= $true )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3016,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV476 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3017,plain,
! [SV181: $i,SV477: $i,SV106: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV106 )
| ! [SY856: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY856 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SY856 )
| ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SY856 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV482 != SY856 )
| ~ ( in @ SV477 @ SY856 ) ) )
= $true )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3018,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK19_E @ SV478 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3019,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV464: $i,SV469: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SV469 ) )
= $false )
| ( ( ( SV464 != SV469 )
| ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2996]) ).
thf(3020,plain,
! [SV106: $i,SV181: $i,SV464: $i,SV469: $i,SV455: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV464 != SV469 )
| ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2996]) ).
thf(3021,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ! [SY831: $i] :
( ~ ( in @ SY831 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SY831 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2997]) ).
thf(3022,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2998]) ).
thf(3023,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV465: $i,SV453: $i] :
( ( ( SV453 = SV465 )
= $false )
| ( ( ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SV465 )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3024,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV465: $i,SV453: $i] :
( ( ( ( SV453 != SV465 ) )
= $true )
| ( ( ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3025,plain,
! [SV106: $i,SV181: $i,SV447: $i,SV479: $i] :
( ( ( in @ SV479 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV447 @ SV479 ) @ SV181 )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3026,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( ( sK19_E @ SV447 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3027,plain,
! [SV106: $i,SV181: $i,SV447: $i] :
( ( ( in @ SV447 @ ( sK20_SY404 @ SV447 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV447 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3003]) ).
thf(3028,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV466: $i,SV470: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SV470 ) )
= $false )
| ( ( ( SV466 != SV470 )
| ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3004]) ).
thf(3029,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV466: $i,SV470: $i,SV457: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV466 != SV470 )
| ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3004]) ).
thf(3030,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SY834 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3031,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3006]) ).
thf(3032,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV467: $i,SV471: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SV471 ) )
= $false )
| ( ( ( SV467 != SV471 )
| ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3007]) ).
thf(3033,plain,
! [SV106: $i,SV181: $i,SV467: $i,SV471: $i,SV459: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV467 != SV471 )
| ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3007]) ).
thf(3034,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ! [SY837: $i] :
( ~ ( in @ SY837 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SY837 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3008]) ).
thf(3035,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3009]) ).
thf(3036,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV468: $i,SV472: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SV472 ) )
= $false )
| ( ( ( SV468 != SV472 )
| ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3010]) ).
thf(3037,plain,
! [SV106: $i,SV181: $i,SV468: $i,SV472: $i,SV461: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV468 != SV472 )
| ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3010]) ).
thf(3038,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ! [SY840: $i] :
( ~ ( in @ SY840 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SY840 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3011]) ).
thf(3039,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3012]) ).
thf(3040,plain,
! [SV454: $i,SV181: $i,SV473: $i,SV106: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV106 ) )
= $true )
| ( ( ! [SY854: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY854 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SY854 )
| ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SY854 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV480 != SY854 )
| ~ ( in @ SV473 @ SY854 ) ) )
= $true )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3041,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV474 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3042,plain,
! [SV181: $i,SV475: $i,SV106: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV106 ) )
= $true )
| ( ( ! [SY855: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY855 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SY855 )
| ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SY855 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV481 != SY855 )
| ~ ( in @ SV475 @ SY855 ) ) )
= $true )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3015]) ).
thf(3043,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV476 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3044,plain,
! [SV181: $i,SV477: $i,SV106: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV106 ) )
= $true )
| ( ( ! [SY856: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY856 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SY856 )
| ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SY856 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV482 != SY856 )
| ~ ( in @ SV477 @ SY856 ) ) )
= $true )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3045,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV478 @ SV181 @ SV106 ) @ SV106 )
| ~ ~ ( ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3046,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV464: $i,SV469: $i] :
( ( ( in @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SV469 )
= $true )
| ( ( ( SV464 != SV469 )
| ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3047,plain,
! [SV106: $i,SV181: $i,SV464: $i,SV469: $i,SV455: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV464 != SV469 )
| ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3020]) ).
thf(3048,plain,
! [SV106: $i,SV181: $i,SV456: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV456 @ SV483 ) @ SV181 ) )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3049,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
| ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3050,plain,
! [SV106: $i,SV181: $i,SV453: $i,SV465: $i,SV446: $i] :
( ( ( in @ SV446 @ SV465 )
= $false )
| ( ( SV453 = SV465 )
= $false )
| ( ( in @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) @ SV465 )
= $true )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3051,plain,
! [SV106: $i,SV181: $i,SV446: $i,SV465: $i,SV453: $i] :
( ( ( SV453 = SV465 )
= $false )
| ( ( ~ ( in @ SV446 @ SV465 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3052,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV466: $i,SV470: $i] :
( ( ( in @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SV470 )
= $true )
| ( ( ( SV466 != SV470 )
| ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3028]) ).
thf(3053,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV466: $i,SV470: $i,SV457: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV466 != SV470 )
| ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3029]) ).
thf(3054,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV458 @ SV484 ) @ SV181 ) )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3055,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
| ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3056,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV467: $i,SV471: $i] :
( ( ( in @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SV471 )
= $true )
| ( ( ( SV467 != SV471 )
| ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3032]) ).
thf(3057,plain,
! [SV106: $i,SV181: $i,SV467: $i,SV471: $i,SV459: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV467 != SV471 )
| ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3033]) ).
thf(3058,plain,
! [SV106: $i,SV181: $i,SV460: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV460 @ SV485 ) @ SV181 ) )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3059,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
| ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3060,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV468: $i,SV472: $i] :
( ( ( in @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SV472 )
= $true )
| ( ( ( SV468 != SV472 )
| ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3036]) ).
thf(3061,plain,
! [SV106: $i,SV181: $i,SV468: $i,SV472: $i,SV461: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV468 != SV472 )
| ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3037]) ).
thf(3062,plain,
! [SV106: $i,SV181: $i,SV462: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV462 @ SV486 ) @ SV181 ) )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3063,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
| ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3064,plain,
! [SV454: $i,SV181: $i,SV473: $i,SV106: $i,SV480: $i] :
( ( ( in @ SV480 @ SV106 )
= $false )
| ( ( ! [SY854: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY854 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SY854 )
| ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SY854 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV480 != SY854 )
| ~ ( in @ SV473 @ SY854 ) ) )
= $true )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3065,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV474 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3041]) ).
thf(3066,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3041]) ).
thf(3067,plain,
! [SV181: $i,SV475: $i,SV106: $i,SV481: $i] :
( ( ( in @ SV481 @ SV106 )
= $false )
| ( ( ! [SY855: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY855 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SY855 )
| ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SY855 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV481 != SY855 )
| ~ ( in @ SV475 @ SY855 ) ) )
= $true )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3042]) ).
thf(3068,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV476 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3069,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3070,plain,
! [SV181: $i,SV477: $i,SV106: $i,SV482: $i] :
( ( ( in @ SV482 @ SV106 )
= $false )
| ( ( ! [SY856: $i] :
( ~ ( ~ ( in @ ( sK21_K @ SY856 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SY856 )
| ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SY856 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV482 != SY856 )
| ~ ( in @ SV477 @ SY856 ) ) )
= $true )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3071,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ( in @ ( sK19_E @ SV478 @ SV181 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3045]) ).
thf(3072,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ~ ( ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3045]) ).
thf(3073,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV469: $i,SV464: $i] :
( ( ( ( SV464 != SV469 ) )
= $true )
| ( ( ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SV469 )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3046]) ).
thf(3074,plain,
! [SV106: $i,SV181: $i,SV464: $i,SV469: $i,SV455: $i] :
( ( ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV464 != SV469 )
| ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3075,plain,
! [SV106: $i,SV181: $i,SV456: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV456 @ SV483 ) @ SV181 )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3048]) ).
thf(3076,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3077,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3078,plain,
! [SV106: $i,SV181: $i,SV453: $i,SV465: $i,SV446: $i] :
( ( ( in @ SV446 @ SV465 )
= $false )
| ( ( SV453 = SV465 )
= $false )
| ( ( in @ ( ordered_pair @ SV446 @ ( sK21_K @ SV465 @ SV453 @ SV446 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV453 @ SV106 )
= $false )
| ( ( in @ SV446 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3079,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV470: $i,SV466: $i] :
( ( ( ( SV466 != SV470 ) )
= $true )
| ( ( ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SV470 )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3052]) ).
thf(3080,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV466: $i,SV470: $i,SV457: $i] :
( ( ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV466 != SV470 )
| ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3081,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV458 @ SV484 ) @ SV181 )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3082,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3083,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3084,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV471: $i,SV467: $i] :
( ( ( ( SV467 != SV471 ) )
= $true )
| ( ( ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SV471 )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3085,plain,
! [SV106: $i,SV181: $i,SV467: $i,SV471: $i,SV459: $i] :
( ( ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV467 != SV471 )
| ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3086,plain,
! [SV106: $i,SV181: $i,SV460: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV460 @ SV485 ) @ SV181 )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3058]) ).
thf(3087,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3088,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3089,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV472: $i,SV468: $i] :
( ( ( ( SV468 != SV472 ) )
= $true )
| ( ( ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SV472 )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3090,plain,
! [SV106: $i,SV181: $i,SV468: $i,SV472: $i,SV461: $i] :
( ( ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV468 != SV472 )
| ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3091,plain,
! [SV106: $i,SV181: $i,SV462: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV462 @ SV486 ) @ SV181 )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3092,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3063]) ).
thf(3093,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3063]) ).
thf(3094,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV480: $i,SV487: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SV487 )
| ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV480 != SV487 )
| ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3095,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( in @ ( sK19_E @ SV474 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3065]) ).
thf(3096,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ( ~ ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3066]) ).
thf(3097,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV481: $i,SV488: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SV488 )
| ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV481 != SV488 )
| ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3098,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( in @ ( sK19_E @ SV476 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3068]) ).
thf(3099,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3069]) ).
thf(3100,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV482: $i,SV489: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SV489 )
| ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
| ( SV482 != SV489 )
| ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3101,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( in @ ( sK19_E @ SV478 @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3071]) ).
thf(3102,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ( ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) ) )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3072]) ).
thf(3103,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV469: $i,SV464: $i] :
( ( ( SV464 = SV469 )
= $false )
| ( ( ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SV469 )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3104,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV469: $i,SV464: $i] :
( ( ( ( SV464 != SV469 ) )
= $true )
| ( ( ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3074]) ).
thf(3105,plain,
! [SV106: $i,SV181: $i,SV456: $i,SV483: $i] :
( ( ( in @ SV483 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV456 @ SV483 ) @ SV181 )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3106,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( ( sK19_E @ SV456 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3076]) ).
thf(3107,plain,
! [SV106: $i,SV181: $i,SV456: $i] :
( ( ( in @ SV456 @ ( sK20_SY404 @ SV456 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV456 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3077]) ).
thf(3108,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV470: $i,SV466: $i] :
( ( ( SV466 = SV470 )
= $false )
| ( ( ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SV470 )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3109,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV470: $i,SV466: $i] :
( ( ( ( SV466 != SV470 ) )
= $true )
| ( ( ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3110,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i,SV484: $i] :
( ( ( in @ SV484 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV458 @ SV484 ) @ SV181 )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3111,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( ( sK19_E @ SV458 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3112,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV458: $i] :
( ( ( in @ SV458 @ ( sK20_SY404 @ SV458 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV458 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3083]) ).
thf(3113,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV471: $i,SV467: $i] :
( ( ( SV467 = SV471 )
= $false )
| ( ( ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SV471 )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3114,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV471: $i,SV467: $i] :
( ( ( ( SV467 != SV471 ) )
= $true )
| ( ( ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3085]) ).
thf(3115,plain,
! [SV106: $i,SV181: $i,SV460: $i,SV485: $i] :
( ( ( in @ SV485 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV460 @ SV485 ) @ SV181 )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3116,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( ( sK19_E @ SV460 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3087]) ).
thf(3117,plain,
! [SV106: $i,SV181: $i,SV460: $i] :
( ( ( in @ SV460 @ ( sK20_SY404 @ SV460 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV460 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3088]) ).
thf(3118,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV472: $i,SV468: $i] :
( ( ( SV468 = SV472 )
= $false )
| ( ( ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SV472 )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3119,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV472: $i,SV468: $i] :
( ( ( ( SV468 != SV472 ) )
= $true )
| ( ( ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3120,plain,
! [SV106: $i,SV181: $i,SV462: $i,SV486: $i] :
( ( ( in @ SV486 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV462 @ SV486 ) @ SV181 )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3121,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( ( sK19_E @ SV462 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3092]) ).
thf(3122,plain,
! [SV106: $i,SV181: $i,SV462: $i] :
( ( ( in @ SV462 @ ( sK20_SY404 @ SV462 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV462 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3093]) ).
thf(3123,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV480: $i,SV487: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SV487 )
| ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV480 != SV487 )
| ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3094]) ).
thf(3124,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3125,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV481: $i,SV488: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SV488 )
| ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV481 != SV488 )
| ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3126,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3127,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV482: $i,SV489: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SV489 )
| ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) ) )
= $true )
| ( ( ( SV482 != SV489 )
| ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3128,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) )
| ~ ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3129,plain,
! [SV106: $i,SV181: $i,SV464: $i,SV469: $i,SV455: $i] :
( ( ( in @ SV455 @ SV469 )
= $false )
| ( ( SV464 = SV469 )
= $false )
| ( ( in @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) @ SV469 )
= $true )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3130,plain,
! [SV106: $i,SV181: $i,SV455: $i,SV469: $i,SV464: $i] :
( ( ( SV464 = SV469 )
= $false )
| ( ( ~ ( in @ SV455 @ SV469 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3104]) ).
thf(3131,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV466: $i,SV470: $i,SV457: $i] :
( ( ( in @ SV457 @ SV470 )
= $false )
| ( ( SV466 = SV470 )
= $false )
| ( ( in @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) @ SV470 )
= $true )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3108]) ).
thf(3132,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV457: $i,SV470: $i,SV466: $i] :
( ( ( SV466 = SV470 )
= $false )
| ( ( ~ ( in @ SV457 @ SV470 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3133,plain,
! [SV106: $i,SV181: $i,SV467: $i,SV471: $i,SV459: $i] :
( ( ( in @ SV459 @ SV471 )
= $false )
| ( ( SV467 = SV471 )
= $false )
| ( ( in @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) @ SV471 )
= $true )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3134,plain,
! [SV106: $i,SV181: $i,SV459: $i,SV471: $i,SV467: $i] :
( ( ( SV467 = SV471 )
= $false )
| ( ( ~ ( in @ SV459 @ SV471 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3135,plain,
! [SV106: $i,SV181: $i,SV468: $i,SV472: $i,SV461: $i] :
( ( ( in @ SV461 @ SV472 )
= $false )
| ( ( SV468 = SV472 )
= $false )
| ( ( in @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) @ SV472 )
= $true )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3136,plain,
! [SV106: $i,SV181: $i,SV461: $i,SV472: $i,SV468: $i] :
( ( ( SV468 = SV472 )
= $false )
| ( ( ~ ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3119]) ).
thf(3137,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV480: $i,SV487: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SV487 )
| ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV480 != SV487 )
| ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3138,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3124]) ).
thf(3139,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3124]) ).
thf(3140,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV481: $i,SV488: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SV488 )
| ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV481 != SV488 )
| ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3125]) ).
thf(3141,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3142,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3143,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV482: $i,SV489: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SV489 )
| ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV482 != SV489 )
| ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3144,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3128]) ).
thf(3145,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3128]) ).
thf(3146,plain,
! [SV106: $i,SV181: $i,SV464: $i,SV469: $i,SV455: $i] :
( ( ( in @ SV455 @ SV469 )
= $false )
| ( ( SV464 = SV469 )
= $false )
| ( ( in @ ( ordered_pair @ SV455 @ ( sK21_K @ SV469 @ SV464 @ SV455 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV464 @ SV106 )
= $false )
| ( ( in @ SV455 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK22_C @ SV181 @ SV106 ) @ SV106 )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3147,plain,
! [SV437: $i,SV106: $i,SV181: $i,SV466: $i,SV470: $i,SV457: $i] :
( ( ( in @ SV457 @ SV470 )
= $false )
| ( ( SV466 = SV470 )
= $false )
| ( ( in @ ( ordered_pair @ SV457 @ ( sK21_K @ SV470 @ SV466 @ SV457 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV466 @ SV106 )
= $false )
| ( ( in @ SV457 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY413 @ SV181 @ SV106 ) @ SV437 ) @ SV181 )
= $true )
| ( ( in @ SV437 @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3148,plain,
! [SV106: $i,SV181: $i,SV467: $i,SV471: $i,SV459: $i] :
( ( ( in @ SV459 @ SV471 )
= $false )
| ( ( SV467 = SV471 )
= $false )
| ( ( in @ ( ordered_pair @ SV459 @ ( sK21_K @ SV471 @ SV467 @ SV459 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV467 @ SV106 )
= $false )
| ( ( in @ SV459 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3149,plain,
! [SV106: $i,SV181: $i,SV468: $i,SV472: $i,SV461: $i] :
( ( ( in @ SV461 @ SV472 )
= $false )
| ( ( SV468 = SV472 )
= $false )
| ( ( in @ ( ordered_pair @ SV461 @ ( sK21_K @ SV472 @ SV468 @ SV461 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV468 @ SV106 )
= $false )
| ( ( in @ SV461 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK24_SY413 @ SV181 @ SV106 ) @ ( sK25_SY420 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3150,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV480: $i,SV487: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SV487 ) )
= $false )
| ( ( ( SV480 != SV487 )
| ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3137]) ).
thf(3151,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV480: $i,SV487: $i,SV473: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV480 != SV487 )
| ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3137]) ).
thf(3152,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ! [SY847: $i] :
( ~ ( in @ SY847 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SY847 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3138]) ).
thf(3153,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3139]) ).
thf(3154,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV481: $i,SV488: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SV488 ) )
= $false )
| ( ( ( SV481 != SV488 )
| ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3140]) ).
thf(3155,plain,
! [SV106: $i,SV181: $i,SV481: $i,SV488: $i,SV475: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV481 != SV488 )
| ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3140]) ).
thf(3156,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SY850 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3141]) ).
thf(3157,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3142]) ).
thf(3158,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV482: $i,SV489: $i] :
( ( ( ~ ( in @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SV489 ) )
= $false )
| ( ( ( SV482 != SV489 )
| ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3143]) ).
thf(3159,plain,
! [SV106: $i,SV181: $i,SV482: $i,SV489: $i,SV477: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
= $false )
| ( ( ( SV482 != SV489 )
| ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3143]) ).
thf(3160,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ! [SY853: $i] :
( ~ ( in @ SY853 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SY853 ) @ SV181 ) ) )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3144]) ).
thf(3161,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) ) )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3145]) ).
thf(3162,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV480: $i,SV487: $i] :
( ( ( in @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SV487 )
= $true )
| ( ( ( SV480 != SV487 )
| ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3150]) ).
thf(3163,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV480: $i,SV487: $i,SV473: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV480 != SV487 )
| ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3151]) ).
thf(3164,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV474 @ SV490 ) @ SV181 ) )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3165,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
| ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3166,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV481: $i,SV488: $i] :
( ( ( in @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SV488 )
= $true )
| ( ( ( SV481 != SV488 )
| ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3154]) ).
thf(3167,plain,
! [SV106: $i,SV181: $i,SV481: $i,SV488: $i,SV475: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV481 != SV488 )
| ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3155]) ).
thf(3168,plain,
! [SV106: $i,SV181: $i,SV476: $i,SV491: $i] :
( ( ( ~ ( in @ SV491 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV476 @ SV491 ) @ SV181 ) )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3169,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
| ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3157]) ).
thf(3170,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV482: $i,SV489: $i] :
( ( ( in @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SV489 )
= $true )
| ( ( ( SV482 != SV489 )
| ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3158]) ).
thf(3171,plain,
! [SV106: $i,SV181: $i,SV482: $i,SV489: $i,SV477: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 ) )
= $true )
| ( ( ( SV482 != SV489 )
| ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3159]) ).
thf(3172,plain,
! [SV106: $i,SV181: $i,SV478: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ( in @ ( ordered_pair @ SV478 @ SV492 ) @ SV181 ) )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3173,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
| ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3174,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV487: $i,SV480: $i] :
( ( ( ( SV480 != SV487 ) )
= $true )
| ( ( ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SV487 )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3175,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV480: $i,SV487: $i,SV473: $i] :
( ( ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV480 != SV487 )
| ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3176,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV474 @ SV490 ) @ SV181 )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3177,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3165]) ).
thf(3178,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3165]) ).
thf(3179,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV488: $i,SV481: $i] :
( ( ( ( SV481 != SV488 ) )
= $true )
| ( ( ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SV488 )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3180,plain,
! [SV106: $i,SV181: $i,SV481: $i,SV488: $i,SV475: $i] :
( ( ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV481 != SV488 )
| ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3181,plain,
! [SV106: $i,SV181: $i,SV476: $i,SV491: $i] :
( ( ( ~ ( in @ SV491 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV476 @ SV491 ) @ SV181 )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3182,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3169]) ).
thf(3183,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3169]) ).
thf(3184,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV489: $i,SV482: $i] :
( ( ( ( SV482 != SV489 ) )
= $true )
| ( ( ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SV489 )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3185,plain,
! [SV106: $i,SV181: $i,SV482: $i,SV489: $i,SV477: $i] :
( ( ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( ( SV482 != SV489 )
| ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3171]) ).
thf(3186,plain,
! [SV106: $i,SV181: $i,SV478: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV478 @ SV492 ) @ SV181 )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3187,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
!= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3188,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) ) )
= $false )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3189,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV487: $i,SV480: $i] :
( ( ( SV480 = SV487 )
= $false )
| ( ( ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SV487 )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3190,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV487: $i,SV480: $i] :
( ( ( ( SV480 != SV487 ) )
= $true )
| ( ( ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3191,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i,SV490: $i] :
( ( ( in @ SV490 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV474 @ SV490 ) @ SV181 )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3192,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( ( sK19_E @ SV474 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3177]) ).
thf(3193,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV474: $i] :
( ( ( in @ SV474 @ ( sK20_SY404 @ SV474 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV474 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3178]) ).
thf(3194,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV488: $i,SV481: $i] :
( ( ( SV481 = SV488 )
= $false )
| ( ( ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SV488 )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3179]) ).
thf(3195,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV488: $i,SV481: $i] :
( ( ( ( SV481 != SV488 ) )
= $true )
| ( ( ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3180]) ).
thf(3196,plain,
! [SV106: $i,SV181: $i,SV476: $i,SV491: $i] :
( ( ( in @ SV491 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV476 @ SV491 ) @ SV181 )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3197,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( ( sK19_E @ SV476 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3182]) ).
thf(3198,plain,
! [SV106: $i,SV181: $i,SV476: $i] :
( ( ( in @ SV476 @ ( sK20_SY404 @ SV476 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV476 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3183]) ).
thf(3199,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV489: $i,SV482: $i] :
( ( ( SV482 = SV489 )
= $false )
| ( ( ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SV489 )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3200,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV489: $i,SV482: $i] :
( ( ( ( SV482 != SV489 ) )
= $true )
| ( ( ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3185]) ).
thf(3201,plain,
! [SV106: $i,SV181: $i,SV478: $i,SV492: $i] :
( ( ( in @ SV492 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV478 @ SV492 ) @ SV181 )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3202,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( ( sK19_E @ SV478 @ SV181 @ SV106 )
= ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3187]) ).
thf(3203,plain,
! [SV106: $i,SV181: $i,SV478: $i] :
( ( ( in @ SV478 @ ( sK20_SY404 @ SV478 @ SV181 @ SV106 ) )
= $true )
| ( ( in @ SV478 @ ( sK18_C @ SV181 @ SV106 ) )
= $false )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3188]) ).
thf(3204,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV480: $i,SV487: $i,SV473: $i] :
( ( ( in @ SV473 @ SV487 )
= $false )
| ( ( SV480 = SV487 )
= $false )
| ( ( in @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) @ SV487 )
= $true )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3189]) ).
thf(3205,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV473: $i,SV487: $i,SV480: $i] :
( ( ( SV480 = SV487 )
= $false )
| ( ( ~ ( in @ SV473 @ SV487 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3190]) ).
thf(3206,plain,
! [SV106: $i,SV181: $i,SV481: $i,SV488: $i,SV475: $i] :
( ( ( in @ SV475 @ SV488 )
= $false )
| ( ( SV481 = SV488 )
= $false )
| ( ( in @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) @ SV488 )
= $true )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3194]) ).
thf(3207,plain,
! [SV106: $i,SV181: $i,SV475: $i,SV488: $i,SV481: $i] :
( ( ( SV481 = SV488 )
= $false )
| ( ( ~ ( in @ SV475 @ SV488 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3208,plain,
! [SV106: $i,SV181: $i,SV482: $i,SV489: $i,SV477: $i] :
( ( ( in @ SV477 @ SV489 )
= $false )
| ( ( SV482 = SV489 )
= $false )
| ( ( in @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) @ SV489 )
= $true )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3209,plain,
! [SV106: $i,SV181: $i,SV477: $i,SV489: $i,SV482: $i] :
( ( ( SV482 = SV489 )
= $false )
| ( ( ~ ( in @ SV477 @ SV489 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3210,plain,
! [SV454: $i,SV106: $i,SV181: $i,SV480: $i,SV487: $i,SV473: $i] :
( ( ( in @ SV473 @ SV487 )
= $false )
| ( ( SV480 = SV487 )
= $false )
| ( ( in @ ( ordered_pair @ SV473 @ ( sK21_K @ SV487 @ SV480 @ SV473 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV480 @ SV106 )
= $false )
| ( ( in @ SV473 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY407 @ SV181 @ SV106 ) @ SV454 ) @ SV181 )
= $true )
| ( ( in @ SV454 @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $false )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3211,plain,
! [SV106: $i,SV181: $i,SV481: $i,SV488: $i,SV475: $i] :
( ( ( in @ SV475 @ SV488 )
= $false )
| ( ( SV481 = SV488 )
= $false )
| ( ( in @ ( ordered_pair @ SV475 @ ( sK21_K @ SV488 @ SV481 @ SV475 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV481 @ SV106 )
= $false )
| ( ( in @ SV475 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( ( sK22_C @ SV181 @ SV106 )
= ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3212,plain,
! [SV106: $i,SV181: $i,SV482: $i,SV489: $i,SV477: $i] :
( ( ( in @ SV477 @ SV489 )
= $false )
| ( ( SV482 = SV489 )
= $false )
| ( ( in @ ( ordered_pair @ SV477 @ ( sK21_K @ SV489 @ SV482 @ SV477 @ SV181 @ SV106 ) ) @ SV181 )
= $false )
| ( ( in @ SV482 @ SV106 )
= $false )
| ( ( in @ SV477 @ ( sK18_C @ SV181 @ SV106 ) )
= $true )
| ( ( in @ ( sK23_SY407 @ SV181 @ SV106 ) @ ( sK26_SY414 @ SV181 @ SV106 ) )
= $true )
| ( ( empty @ SV106 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3209]) ).
thf(3213,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[740,3212,3211,3210,3208,3206,3204,3203,3202,3201,3198,3197,3196,3193,3192,3191,3149,3148,3147,3146,3135,3133,3131,3129,3122,3121,3120,3117,3116,3115,3112,3111,3110,3107,3106,3105,3101,3098,3095,3078,3050,3027,3026,3025,2971,2969,2966,2963,2956,2947,2925,2924,2923,2895,2888,2887,2886,2885,2884,2883,2838,2837,2821,2820,2819,2818,2817,2810,2809,2792,2791,2778,2765,2758,2755,2742,2741,2738,2735,2734,2733,2732,2731,2723,2719,2716,2715,2714,2702,2701,2700,2699,2698,2697,2696,2695,2687,2686,2676,2675,2664,2663,2662,2653,2650,2649,2646,2645,2640,2633,2630,2629,2628,2627,2616,2615,2609,2604,2591,2587,2571,2555,2554,2550,2547,2533,2528,2527,2519,2517,2510,2509,2501,2491,2473,2472,2462,2461,2443,2442,2436,2433,2418,2417,2405,2404,2403,2388,2379,2336,2335,2330,2317,2316,2315,2313,2312,2307,2299,2298,2295,2281,2280,2279,2278,2277,2265,2264,2251,2250,2243,2235,2233,2231,2230,2213,2205,2204,2195,2194,2191,2190,2181,2176,2174,2163,2162,2159,2156,2143,2135,2131,2127,2104,2099,2098,2095,2092,2091,2090,2060,2048,2046,2043,2042,2039,2030,2029,2027,2026,2025,2024,2003,1993,1992,1982,1981,1980,1978,1977,1942,1941,1940,1939,1938,1937,1928,1927,1926,1916,1915,1914,1913,1912,1907,1906,1903,1902,1881,1878,1877,1876,1872,1855,1854,1842,1841,1829,1828,1803,1802,1793,1788,1784,1783,1781,1776,1773,1768,1766,1765,1763,1738,1689,1670,1666,1649,1646,1644,1643,1642,1637,1636,1633,1628,1619,1616,1576,1571,1570,1522,1521,1513,1505,1504,1502,1501,1497,1495,1493,1492,1491,1489,1488,1486,1485,1484,1481,1479,1478,1475,1471,1463,1461,1460,1455,1454,1452,1448,1447,1422,1421,1418,1417,1407,1391,1381,1374,1373,1342,1336,1328,1322,1318,1310,1305,1304,1291,1277,1271,1148,1145,1144,1125,1116,1113,1112,1097,1093,1090,1086,1023,1017,1016,1013,1011,1009,993,987,981,980,974,955,946,939,938,863,836,815]) ).
thf(3214,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU295+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 19 04:18:03 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.35/0.53 ............
% 0.59/0.78
% 0.59/0.78 No.of.Axioms: 397
% 0.59/0.78
% 0.59/0.78 Length.of.Defs: 0
% 0.59/0.78
% 0.59/0.78 Contains.Choice.Funs: false
% 0.66/0.89 .......................
% 0.76/0.95 (rf:2,axioms:161,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:399,loop_count:0,foatp_calls:0,translation:fof_full)........................................................................................................................................................................................................
% 1.56/1.98
% 1.56/1.98 ********************************
% 1.56/1.98 * All subproblems solved! *
% 1.56/1.98 ********************************
% 1.56/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:162,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3213,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.47/4.68
% 4.47/4.68 %**** Beginning of derivation protocol ****
% 4.47/4.68 % SZS output start CNFRefutation
% See solution above
% 4.47/4.69
% 4.47/4.69 %**** End of derivation protocol ****
% 4.47/4.69 %**** no. of clauses in derivation: 2978 ****
% 4.47/4.69 %**** clause counter: 3213 ****
% 4.47/4.69
% 4.47/4.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:162,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3213,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------