TSTP Solution File: SEU180+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU180+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 : n019.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 12:07:42 EDT 2022
% Result : Theorem 231.00s 231.33s
% Output : CNFRefutation 232.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 122
% Syntax : Number of formulae : 2543 (1001 unt; 68 typ; 0 def)
% Number of atoms : 20827 (7339 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 49358 (8884 ~;8155 |; 359 &;31786 @)
% ( 74 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 129 ( 129 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 7 con; 0-4 aty)
% Number of variables : 8562 ( 0 ^8542 !; 20 ?;8562 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_are_equipotent,type,
are_equipotent: $i > $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_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_in,type,
in: $i > $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_C,type,
sK10_C: $i > $i > $i ).
thf(tp_sK11_SY2046,type,
sK11_SY2046: $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK13_D,type,
sK13_D: $i > $i > $i > $i ).
thf(tp_sK14_C,type,
sK14_C: $i > $i > $i ).
thf(tp_sK15_SY2048,type,
sK15_SY2048: $i > $i > $i ).
thf(tp_sK16_D,type,
sK16_D: $i > $i > $i > $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_SY2050,type,
sK18_SY2050: $i > $i > $i ).
thf(tp_sK19_D,type,
sK19_D: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_C,type,
sK20_C: $i > $i > $i ).
thf(tp_sK21_E,type,
sK21_E: $i > $i > $i > $i > $i ).
thf(tp_sK22_SY2051,type,
sK22_SY2051: $i > $i > $i > $i > $i ).
thf(tp_sK23_D,type,
sK23_D: $i > $i > $i > $i ).
thf(tp_sK24_SY2054,type,
sK24_SY2054: $i > $i > $i > $i ).
thf(tp_sK25_SY2056,type,
sK25_SY2056: $i > $i > $i > $i ).
thf(tp_sK26_D,type,
sK26_D: $i > $i > $i > $i ).
thf(tp_sK27_D,type,
sK27_D: $i > $i > $i > $i ).
thf(tp_sK28_C,type,
sK28_C: $i > $i > $i ).
thf(tp_sK29_B,type,
sK29_B: $i > $i ).
thf(tp_sK2_SY2035,type,
sK2_SY2035: $i ).
thf(tp_sK30_C,type,
sK30_C: $i > $i > $i ).
thf(tp_sK31_D,type,
sK31_D: $i > $i > $i > $i ).
thf(tp_sK32_C,type,
sK32_C: $i > $i > $i ).
thf(tp_sK33_SY2057,type,
sK33_SY2057: $i > $i > $i ).
thf(tp_sK34_C,type,
sK34_C: $i > $i > $i ).
thf(tp_sK35_SY2059,type,
sK35_SY2059: $i > $i > $i ).
thf(tp_sK36_B,type,
sK36_B: $i > $i ).
thf(tp_sK37_C,type,
sK37_C: $i > $i > $i ).
thf(tp_sK38_C,type,
sK38_C: $i > $i > $i ).
thf(tp_sK39_B,type,
sK39_B: $i > $i ).
thf(tp_sK3_SY2037,type,
sK3_SY2037: $i ).
thf(tp_sK40_C,type,
sK40_C: $i > $i > $i ).
thf(tp_sK4_B,type,
sK4_B: $i > $i ).
thf(tp_sK5_SY2040,type,
sK5_SY2040: $i > $i > $i ).
thf(tp_sK6_C,type,
sK6_C: $i > $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_D,type,
sK8_D: $i > $i > $i > $i ).
thf(tp_sK9_D,type,
sK9_D: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_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(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(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(5,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(6,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(10,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(11,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,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(24,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(35,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(36,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(64,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(67,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(68,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(69,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(71,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(72,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(73,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(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(75,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(76,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(77,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(78,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(79,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(80,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(81,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(82,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(88,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(98,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(101,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(102,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(103,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(107,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(113,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(116,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(117,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(125,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(126,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(132,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(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(138,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(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(142,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(143,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(145,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(147,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(150,conjecture,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(151,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[150]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[151]) ).
thf(153,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(154,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(155,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(156,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(160,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(163,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(164,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(166,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(167,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)],[68]) ).
thf(168,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)],[69]) ).
thf(169,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(170,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)],[72]) ).
thf(171,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(172,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(173,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)],[75]) ).
thf(174,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)],[76]) ).
thf(175,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)],[77]) ).
thf(176,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(177,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(179,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)],[81]) ).
thf(180,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)],[82]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(184,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)],[101]) ).
thf(185,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)],[102]) ).
thf(186,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)],[103]) ).
thf(187,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(188,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)],[113]) ).
thf(189,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)],[116]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(191,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(192,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(193,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(194,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(195,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)],[132]) ).
thf(196,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(197,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(198,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(200,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)],[142]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(202,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(203,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(204,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(205,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(206,plain,
( ( ! [SY2035: $i,SY2036: $i] :
( ( relation @ SY2036 )
=> ( ( in @ ( ordered_pair @ sK1_A @ SY2035 ) @ SY2036 )
=> ( ( in @ sK1_A @ ( relation_field @ SY2036 ) )
& ( in @ SY2035 @ ( relation_field @ SY2036 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[152]) ).
thf(207,plain,
( ( ! [SY2037: $i] :
( ( relation @ SY2037 )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY2035 ) @ SY2037 )
=> ( ( in @ sK1_A @ ( relation_field @ SY2037 ) )
& ( in @ sK2_SY2035 @ ( relation_field @ SY2037 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(208,plain,
( ( ( relation @ sK3_SY2037 )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY2035 ) @ sK3_SY2037 )
=> ( ( in @ sK1_A @ ( relation_field @ sK3_SY2037 ) )
& ( in @ sK2_SY2035 @ ( relation_field @ sK3_SY2037 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[207]) ).
thf(209,plain,
( ( relation @ sK3_SY2037 )
= $true ),
inference(standard_cnf,[status(thm)],[208]) ).
thf(210,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY2035 ) @ sK3_SY2037 )
= $true ),
inference(standard_cnf,[status(thm)],[208]) ).
thf(211,plain,
( ( ( in @ sK1_A @ ( relation_field @ sK3_SY2037 ) )
& ( in @ sK2_SY2035 @ ( relation_field @ sK3_SY2037 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[208]) ).
thf(212,plain,
( ( in @ sK1_A @ ( relation_field @ sK3_SY2037 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[211]) ).
thf(213,plain,
( ( in @ sK2_SY2035 @ ( relation_field @ sK3_SY2037 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[211]) ).
thf(214,plain,
( ( ~ ( in @ sK1_A @ ( relation_field @ sK3_SY2037 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[212]) ).
thf(215,plain,
( ( ~ ( in @ sK2_SY2035 @ ( relation_field @ sK3_SY2037 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[213]) ).
thf(216,plain,
( ( ! [A: $i] :
( ! [SY2038: $i] :
( ~ ( subset @ SY2038 @ ( sK4_B @ A ) )
| ( are_equipotent @ SY2038 @ ( sK4_B @ A ) )
| ( in @ SY2038 @ ( sK4_B @ A ) ) )
& ! [SY2039: $i] :
( ( ! [SY2044: $i] :
( ~ ( subset @ SY2044 @ SY2039 )
| ( in @ SY2044 @ ( sK5_SY2040 @ SY2039 @ A ) ) )
& ( in @ ( sK5_SY2040 @ SY2039 @ A ) @ ( sK4_B @ A ) ) )
| ~ ( in @ SY2039 @ ( sK4_B @ A ) ) )
& ! [SY2042: $i,SY2043: $i] :
( ~ ( in @ SY2042 @ ( sK4_B @ A ) )
| ~ ( subset @ SY2043 @ SY2042 )
| ( in @ SY2043 @ ( sK4_B @ A ) ) )
& ( in @ A @ ( sK4_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(218,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(219,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(220,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)],[157]) ).
thf(221,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(223,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(225,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( ( element @ ( sK8_D @ C @ B @ A ) @ ( powerset @ A ) )
& ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ C )
| ~ ( in @ ( subset_complement @ A @ ( sK8_D @ C @ B @ A ) ) @ B ) )
& ( ( in @ ( sK8_D @ C @ B @ A ) @ C )
| ( in @ ( subset_complement @ A @ ( sK8_D @ C @ B @ A ) ) @ B ) ) )
| ( C
= ( complements_of_subsets @ A @ B ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( C
!= ( complements_of_subsets @ A @ B ) )
| ( ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ ( subset_complement @ A @ D ) @ B ) )
& ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ ( subset_complement @ A @ D ) @ B )
| ( in @ D @ C ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(226,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(227,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY2045: $i] :
~ ( in @ ( ordered_pair @ SY2045 @ ( sK10_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(228,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ( in @ ( sK12_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)],[167]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY2047: $i] :
( ~ ( in @ ( sK14_C @ B @ A ) @ SY2047 )
| ~ ( in @ SY2047 @ A ) )
| ~ ( in @ ( sK14_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK14_C @ B @ A ) @ ( sK15_SY2048 @ B @ A ) )
& ( in @ ( sK15_SY2048 @ B @ A ) @ A ) )
| ( in @ ( sK14_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 @ ( sK13_D @ C @ B @ A ) )
& ( in @ ( sK13_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(230,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY2049: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ SY2049 ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY2050 @ B @ A ) ) @ A )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK16_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(231,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ( in @ ( sK19_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ B )
| ( in @ ( sK19_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)],[170]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK20_C @ B @ A ) @ A )
& ~ ( in @ ( sK20_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)],[171]) ).
thf(233,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY2052: $i,SY2053: $i] :
( ~ ( in @ SY2052 @ A )
| ~ ( in @ SY2053 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY2052 @ SY2053 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY2054 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY2056 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY2054 @ C @ B @ A ) @ ( sK25_SY2056 @ C @ B @ A ) ) ) )
| ( in @ ( sK23_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK21_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK22_SY2051 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY2051 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(234,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ( in @ ( sK26_D @ C @ B @ A ) @ A )
| ( in @ ( sK26_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)],[173]) ).
thf(235,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
= A )
| ( ( sK27_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)],[174]) ).
thf(236,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)],[175]) ).
thf(237,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK28_C @ B @ A ) @ B )
| ~ ( subset @ ( sK28_C @ B @ A ) @ A ) )
& ( ( in @ ( sK28_C @ B @ A ) @ B )
| ( subset @ ( sK28_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)],[176]) ).
thf(238,plain,
( ( ! [A: $i] :
( ( in @ ( sK29_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(239,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK30_C @ B @ A )
!= A )
| ~ ( in @ ( sK30_C @ B @ A ) @ B ) )
& ( ( ( sK30_C @ B @ A )
= A )
| ( in @ ( sK30_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)],[178]) ).
thf(240,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK33_SY2057 @ B @ A ) @ A )
& ~ ( in @ ( sK32_C @ B @ A ) @ ( sK33_SY2057 @ B @ A ) ) )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ! [SY2058: $i] :
( ~ ( in @ SY2058 @ A )
| ( in @ ( sK32_C @ B @ A ) @ SY2058 ) )
| ( in @ ( sK32_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK31_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK31_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)],[179]) ).
thf(241,plain,
( ( ! [A: $i] :
( ( ! [SY2060: $i,SY2061: $i] :
( ( sK36_B @ A )
!= ( ordered_pair @ SY2060 @ SY2061 ) )
& ( in @ ( sK36_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK34_C @ B @ A ) @ ( sK35_SY2059 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(242,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(243,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(244,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)],[183]) ).
thf(245,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)],[184]) ).
thf(246,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)],[185]) ).
thf(247,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK37_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)],[186]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK38_C @ B @ A ) @ A )
& ( in @ ( sK38_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)],[188]) ).
thf(250,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)],[189]) ).
thf(251,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)],[190]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(253,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[192]) ).
thf(254,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[193]) ).
thf(255,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(256,plain,
( ( ! [A: $i] :
( ! [SY2062: $i] :
( ~ ( subset @ SY2062 @ ( sK39_B @ A ) )
| ( are_equipotent @ SY2062 @ ( sK39_B @ A ) )
| ( in @ SY2062 @ ( sK39_B @ A ) ) )
& ! [SY2063: $i] :
( ~ ( in @ SY2063 @ ( sK39_B @ A ) )
| ( in @ ( powerset @ SY2063 ) @ ( sK39_B @ A ) ) )
& ! [SY2064: $i,SY2065: $i] :
( ~ ( in @ SY2064 @ ( sK39_B @ A ) )
| ~ ( subset @ SY2065 @ SY2064 )
| ( in @ SY2065 @ ( sK39_B @ A ) ) )
& ( in @ A @ ( sK39_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[195]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[196]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK40_C @ B @ A ) @ A )
& ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[197]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(261,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)],[200]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[201]) ).
thf(263,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)],[202]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[203]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[204]) ).
thf(266,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(269,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(270,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)],[263]) ).
thf(271,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(272,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)],[261]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(274,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK40_C @ B @ A ) @ A )
& ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(276,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(277,plain,
( ( ! [A: $i] :
( ! [SY2062: $i] :
( ~ ( subset @ SY2062 @ ( sK39_B @ A ) )
| ( are_equipotent @ SY2062 @ ( sK39_B @ A ) )
| ( in @ SY2062 @ ( sK39_B @ A ) ) )
& ! [SY2063: $i] :
( ~ ( in @ SY2063 @ ( sK39_B @ A ) )
| ( in @ ( powerset @ SY2063 ) @ ( sK39_B @ A ) ) )
& ! [SY2064: $i,SY2065: $i] :
( ~ ( in @ SY2064 @ ( sK39_B @ A ) )
| ~ ( subset @ SY2065 @ SY2064 )
| ( in @ SY2065 @ ( sK39_B @ A ) ) )
& ( in @ A @ ( sK39_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(278,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(279,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(280,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(281,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(282,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)],[251]) ).
thf(283,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)],[250]) ).
thf(284,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK38_C @ B @ A ) @ A )
& ( in @ ( sK38_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK37_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)],[247]) ).
thf(287,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)],[246]) ).
thf(288,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)],[245]) ).
thf(289,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)],[244]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(291,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(292,plain,
( ( ! [A: $i] :
( ( ! [SY2060: $i,SY2061: $i] :
( ( sK36_B @ A )
!= ( ordered_pair @ SY2060 @ SY2061 ) )
& ( in @ ( sK36_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK34_C @ B @ A ) @ ( sK35_SY2059 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK33_SY2057 @ B @ A ) @ A )
& ~ ( in @ ( sK32_C @ B @ A ) @ ( sK33_SY2057 @ B @ A ) ) )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ! [SY2058: $i] :
( ~ ( in @ SY2058 @ A )
| ( in @ ( sK32_C @ B @ A ) @ SY2058 ) )
| ( in @ ( sK32_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK31_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK31_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)],[240]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK30_C @ B @ A )
!= A )
| ~ ( in @ ( sK30_C @ B @ A ) @ B ) )
& ( ( ( sK30_C @ B @ A )
= A )
| ( in @ ( sK30_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)],[239]) ).
thf(295,plain,
( ( ! [A: $i] :
( ( in @ ( sK29_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK28_C @ B @ A ) @ B )
| ~ ( subset @ ( sK28_C @ B @ A ) @ A ) )
& ( ( in @ ( sK28_C @ B @ A ) @ B )
| ( subset @ ( sK28_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)],[237]) ).
thf(297,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)],[236]) ).
thf(298,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
= A )
| ( ( sK27_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)],[235]) ).
thf(299,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ( in @ ( sK26_D @ C @ B @ A ) @ A )
| ( in @ ( sK26_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)],[234]) ).
thf(300,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY2052: $i,SY2053: $i] :
( ~ ( in @ SY2052 @ A )
| ~ ( in @ SY2053 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY2052 @ SY2053 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY2054 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY2056 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY2054 @ C @ B @ A ) @ ( sK25_SY2056 @ C @ B @ A ) ) ) )
| ( in @ ( sK23_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK21_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK22_SY2051 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY2051 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK20_C @ B @ A ) @ A )
& ~ ( in @ ( sK20_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)],[232]) ).
thf(302,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ( in @ ( sK19_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ B )
| ( in @ ( sK19_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)],[231]) ).
thf(303,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY2049: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ SY2049 ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY2050 @ B @ A ) ) @ A )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK16_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY2047: $i] :
( ~ ( in @ ( sK14_C @ B @ A ) @ SY2047 )
| ~ ( in @ SY2047 @ A ) )
| ~ ( in @ ( sK14_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK14_C @ B @ A ) @ ( sK15_SY2048 @ B @ A ) )
& ( in @ ( sK15_SY2048 @ B @ A ) @ A ) )
| ( in @ ( sK14_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 @ ( sK13_D @ C @ B @ A ) )
& ( in @ ( sK13_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(305,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ( in @ ( sK12_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)],[228]) ).
thf(306,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY2045: $i] :
~ ( in @ ( ordered_pair @ SY2045 @ ( sK10_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(307,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(308,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( ( element @ ( sK8_D @ C @ B @ A ) @ ( powerset @ A ) )
& ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ C )
| ~ ( in @ ( subset_complement @ A @ ( sK8_D @ C @ B @ A ) ) @ B ) )
& ( ( in @ ( sK8_D @ C @ B @ A ) @ C )
| ( in @ ( subset_complement @ A @ ( sK8_D @ C @ B @ A ) ) @ B ) ) )
| ( C
= ( complements_of_subsets @ A @ B ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( C
!= ( complements_of_subsets @ A @ B ) )
| ( ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ ( subset_complement @ A @ D ) @ B ) )
& ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ ( subset_complement @ A @ D ) @ B )
| ( in @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(310,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(311,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(312,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(314,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(315,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)],[220]) ).
thf(316,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(317,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(318,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(319,plain,
( ( ! [A: $i] :
( ! [SY2038: $i] :
( ~ ( subset @ SY2038 @ ( sK4_B @ A ) )
| ( are_equipotent @ SY2038 @ ( sK4_B @ A ) )
| ( in @ SY2038 @ ( sK4_B @ A ) ) )
& ! [SY2039: $i] :
( ( ! [SY2044: $i] :
( ~ ( subset @ SY2044 @ SY2039 )
| ( in @ SY2044 @ ( sK5_SY2040 @ SY2039 @ A ) ) )
& ( in @ ( sK5_SY2040 @ SY2039 @ A ) @ ( sK4_B @ A ) ) )
| ~ ( in @ SY2039 @ ( sK4_B @ A ) ) )
& ! [SY2042: $i,SY2043: $i] :
( ~ ( in @ SY2042 @ ( sK4_B @ A ) )
| ~ ( subset @ SY2043 @ SY2042 )
| ( in @ SY2043 @ ( sK4_B @ A ) ) )
& ( in @ A @ ( sK4_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(320,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY2035 ) @ sK3_SY2037 )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(321,plain,
( ( relation @ sK3_SY2037 )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(322,plain,
( ( ~ ( in @ sK1_A @ ( relation_field @ sK3_SY2037 ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(323,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)],[282]) ).
thf(324,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(325,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_SY2056 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK24_SY2054 @ SX2 @ SX1 @ SX0 ) @ ( sK25_SY2056 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK22_SY2051 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY2051 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(326,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY2048 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK15_SY2048 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK14_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 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(327,plain,
( ( ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(328,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK26_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)],[299]) ).
thf(329,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_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)],[284]) ).
thf(330,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( subset_complement @ SX0 @ ( sK8_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( subset_complement @ SX0 @ ( sK8_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX2
= ( complements_of_subsets @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( SX2
!= ( complements_of_subsets @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( in @ SX3 @ SX2 )
| ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(331,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK27_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)],[298]) ).
thf(332,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(333,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(334,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK4_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK4_B @ SX0 ) )
| ( in @ SX1 @ ( sK4_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK5_SY2040 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SX1 @ SX0 ) @ ( sK4_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK4_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK4_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK4_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK4_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(335,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_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)],[296]) ).
thf(336,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SX1 @ SX0 ) @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(337,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(338,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK20_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)],[301]) ).
thf(339,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)],[283]) ).
thf(340,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[293]) ).
thf(341,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY2050 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(342,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)],[270]) ).
thf(343,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK39_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK39_B @ SX0 ) )
| ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK39_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK39_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK39_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK39_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(344,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_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)],[294]) ).
thf(345,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)],[315]) ).
thf(346,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(347,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK36_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK36_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY2059 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(348,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(349,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK37_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)],[286]) ).
thf(350,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)],[289]) ).
thf(351,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(352,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)],[297]) ).
thf(353,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK12_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)],[305]) ).
thf(354,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK19_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)],[302]) ).
thf(355,plain,
! [SV1: $i] :
( ( ! [SY2066: $i] :
( ~ ( in @ SV1 @ SY2066 )
| ( ( set_union2 @ ( singleton @ SV1 ) @ SY2066 )
= SY2066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(356,plain,
! [SV2: $i] :
( ( ! [SY2067: $i] :
( ~ ( disjoint @ ( singleton @ SV2 ) @ SY2067 )
| ~ ( in @ SV2 @ SY2067 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(357,plain,
! [SV3: $i] :
( ( ! [SY2068: $i] :
( ( in @ SV3 @ SY2068 )
| ( disjoint @ ( singleton @ SV3 ) @ SY2068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(358,plain,
! [SV4: $i] :
( ( ! [SY2069: $i] :
( ~ ( element @ SY2069 @ ( powerset @ SV4 ) )
| ! [SY2070: $i] :
( ~ ( in @ SY2070 @ SY2069 )
| ( in @ SY2070 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(359,plain,
! [SV5: $i] :
( ( ! [SY2071: $i] :
( ~ ( subset @ SV5 @ SY2071 )
| ! [SY2072: $i] :
( ( in @ SY2072 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SY2071 @ ( singleton @ SY2072 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(360,plain,
! [SV6: $i] :
( ( ! [SY2073: $i] :
( ~ ( in @ SV6 @ SY2073 )
| ( subset @ SV6 @ ( union @ SY2073 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(361,plain,
! [SV7: $i] :
( ( ~ ( relation @ SV7 )
| ( subset @ SV7 @ ( cartesian_product2 @ ( relation_dom @ SV7 ) @ ( relation_rng @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(362,plain,
! [SV8: $i] :
( ( ! [SY2074: $i] :
( ~ ( in @ SV8 @ SY2074 )
| ( ( set_union2 @ ( singleton @ SV8 ) @ SY2074 )
= SY2074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(363,plain,
! [SV9: $i] :
( ( ( SV9 = empty_set )
| ! [SY2075: $i] :
( ~ ( element @ SY2075 @ ( powerset @ SV9 ) )
| ! [SY2076: $i] :
( ~ ( element @ SY2076 @ SV9 )
| ( in @ SY2076 @ SY2075 )
| ( in @ SY2076 @ ( subset_complement @ SV9 @ SY2075 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(364,plain,
! [SV10: $i] :
( ( ! [SY2077: $i,SY2078: $i] :
( ~ ( element @ SY2078 @ ( powerset @ SV10 ) )
| ~ ( in @ SY2077 @ ( subset_complement @ SV10 @ SY2078 ) )
| ~ ( in @ SY2077 @ SY2078 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(365,plain,
! [SV11: $i] :
( ( ! [SY2079: $i] :
( ~ ( in @ SV11 @ SY2079 )
| ( subset @ SV11 @ ( union @ SY2079 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(366,plain,
! [SV12: $i] :
( ( ! [SY2080: $i] :
( ~ ( in @ SV12 @ SY2080 )
| ~ ( in @ SY2080 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(367,plain,
! [SV13: $i] :
( ( ! [SY2081: $i] :
( ( ordered_pair @ SV13 @ SY2081 )
= ( unordered_pair @ ( unordered_pair @ SV13 @ SY2081 ) @ ( singleton @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(368,plain,
! [SV14: $i] :
( ( ~ ( relation @ SV14 )
| ( ( relation_field @ SV14 )
= ( set_union2 @ ( relation_dom @ SV14 ) @ ( relation_rng @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(369,plain,
! [SV15: $i] :
( ( ! [SY2082: $i] :
~ ( empty @ ( ordered_pair @ SV15 @ SY2082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(370,plain,
! [SV16: $i] :
( ( ! [SY2083: $i] :
( ~ ( relation @ SV16 )
| ~ ( relation @ SY2083 )
| ( relation @ ( set_union2 @ SV16 @ SY2083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(371,plain,
! [SV17: $i] :
( ( ! [SY2084: $i] :
( ~ ( in @ SV17 @ SY2084 )
| ( element @ SV17 @ SY2084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(372,plain,
! [SV18: $i] :
( ( ! [SY2085: $i] :
( ~ ( element @ SV18 @ SY2085 )
| ( empty @ SY2085 )
| ( in @ SV18 @ SY2085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(373,plain,
! [SV19: $i] :
( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( element @ SY2086 @ ( powerset @ SY2087 ) )
| ~ ( in @ SV19 @ SY2086 )
| ( element @ SV19 @ SY2087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(374,plain,
! [SV20: $i] :
( ( ! [SY2088: $i,SY2089: $i] :
( ~ ( element @ SY2088 @ ( powerset @ SY2089 ) )
| ~ ( in @ SV20 @ SY2088 )
| ~ ( empty @ SY2089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(375,plain,
! [SV21: $i] :
( ( ! [SY2090: $i] :
( ~ ( empty @ SY2090 )
| ~ ( in @ SV21 @ SY2090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(376,plain,
( ( in @ sK1_A @ ( relation_field @ sK3_SY2037 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(377,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)],[323]) ).
thf(378,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY2091: $i,SY2092: $i] :
( ~ ( relation @ SY2092 )
| ~ ( in @ ( ordered_pair @ SV22 @ SY2091 ) @ SY2092 )
| ( in @ SV22 @ ( relation_dom @ SY2092 ) ) )
| ~ ! [SY2093: $i,SY2094: $i] :
( ~ ( relation @ SY2094 )
| ~ ( in @ ( ordered_pair @ SV22 @ SY2093 ) @ SY2094 )
| ( in @ SY2093 @ ( relation_rng @ SY2094 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(379,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY2095: $i,SY2096: $i] :
( ~ ( ~ ( ! [SY2097: $i,SY2098: $i] :
( ~ ( in @ SY2097 @ SV23 )
| ~ ( in @ SY2098 @ SY2095 )
| ( ( sK23_D @ SY2096 @ SY2095 @ SV23 )
!= ( ordered_pair @ SY2097 @ SY2098 ) ) )
| ~ ( in @ ( sK23_D @ SY2096 @ SY2095 @ SV23 ) @ SY2096 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2096 @ SY2095 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SY2096 @ SY2095 @ SV23 ) @ SY2095 ) )
| ( ( sK23_D @ SY2096 @ SY2095 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2096 @ SY2095 @ SV23 ) @ ( sK25_SY2056 @ SY2096 @ SY2095 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SY2096 @ SY2095 @ SV23 ) @ SY2096 ) ) )
| ( SY2096
= ( cartesian_product2 @ SV23 @ SY2095 ) ) )
| ~ ! [SY2099: $i,SY2100: $i] :
( ( SY2100
!= ( cartesian_product2 @ SV23 @ SY2099 ) )
| ~ ( ~ ! [SY2101: $i] :
( ! [SY2102: $i,SY2103: $i] :
( ~ ( in @ SY2102 @ SV23 )
| ~ ( in @ SY2103 @ SY2099 )
| ( SY2101
!= ( ordered_pair @ SY2102 @ SY2103 ) ) )
| ( in @ SY2101 @ SY2100 ) )
| ~ ! [SY2104: $i] :
( ~ ( in @ SY2104 @ SY2100 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ SY2099 ) )
| ( SY2104
!= ( ordered_pair @ ( sK21_E @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ ( sK22_SY2051 @ SY2104 @ SY2100 @ SY2099 @ SV23 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(380,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY2048 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK15_SY2048 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK14_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 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(381,plain,
( ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(382,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY2105: $i,SY2106: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2105 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2105 ) ) )
| ( SY2106
= ( set_union2 @ SV24 @ SY2105 ) ) )
| ~ ! [SY2107: $i,SY2108: $i] :
( ( SY2108
!= ( set_union2 @ SV24 @ SY2107 ) )
| ~ ( ~ ! [SY2109: $i] :
( ~ ( in @ SY2109 @ SY2108 )
| ( in @ SY2109 @ SV24 )
| ( in @ SY2109 @ SY2107 ) )
| ~ ~ ( ~ ! [SY2110: $i] :
( ~ ( in @ SY2110 @ SV24 )
| ( in @ SY2110 @ SY2108 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2107 )
| ( in @ SX3 @ SY2108 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(383,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_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)],[329]) ).
thf(384,plain,
! [SV25: $i] :
( ( ! [SY2112: $i] :
( ~ ( element @ SY2112 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ! [SY2113: $i] :
( ~ ( element @ SY2113 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2113 @ SY2112 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2113 @ SY2112 @ SV25 ) @ SY2113 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2113 @ SY2112 @ SV25 ) ) @ SY2112 ) )
| ~ ( ( in @ ( sK8_D @ SY2113 @ SY2112 @ SV25 ) @ SY2113 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2113 @ SY2112 @ SV25 ) ) @ SY2112 ) ) ) )
| ( SY2113
= ( complements_of_subsets @ SV25 @ SY2112 ) ) )
| ~ ! [SY2114: $i] :
( ~ ( element @ SY2114 @ ( powerset @ ( powerset @ SV25 ) ) )
| ( SY2114
!= ( complements_of_subsets @ SV25 @ SY2112 ) )
| ~ ( ~ ! [SY2115: $i] :
( ~ ( element @ SY2115 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2115 @ SY2114 )
| ( in @ ( subset_complement @ SV25 @ SY2115 ) @ SY2112 ) )
| ~ ! [SY2116: $i] :
( ~ ( element @ SY2116 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2116 ) @ SY2112 )
| ( in @ SY2116 @ SY2114 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(385,plain,
! [SV26: $i] :
( ( ~ ( ~ ! [SY2117: $i,SY2118: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
!= SY2117 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
= SV26 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
= SY2117 ) ) )
| ( SY2118
= ( unordered_pair @ SV26 @ SY2117 ) ) )
| ~ ! [SY2119: $i,SY2120: $i] :
( ( SY2120
!= ( unordered_pair @ SV26 @ SY2119 ) )
| ~ ( ~ ! [SY2121: $i] :
( ~ ( in @ SY2121 @ SY2120 )
| ( SY2121 = SV26 )
| ( SY2121 = SY2119 ) )
| ~ ~ ( ~ ! [SY2122: $i] :
( ( SY2122 != SV26 )
| ( in @ SY2122 @ SY2120 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY2119 )
| ( in @ SX3 @ SY2120 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(386,plain,
! [SV27: $i] :
( ( ! [SY2124: $i] :
~ ( ~ ! [SY2125: $i] :
( ! [SY2126: $i] :
( ( ordered_pair @ SV27 @ SY2124 )
!= ( ordered_pair @ SY2125 @ SY2126 ) )
| ( SV27 = SY2125 ) )
| ~ ! [SY2127: $i,SY2128: $i] :
( ( ( ordered_pair @ SV27 @ SY2124 )
!= ( ordered_pair @ SY2127 @ SY2128 ) )
| ( SY2124 = SY2128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(387,plain,
! [SV28: $i] :
( ( ! [SY2129: $i] :
~ ( ~ ! [SY2130: $i,SY2131: $i] :
( ~ ( in @ SV28 @ SY2130 )
| ~ ( in @ SY2129 @ SY2131 )
| ( in @ ( ordered_pair @ SV28 @ SY2129 ) @ ( cartesian_product2 @ SY2130 @ SY2131 ) ) )
| ~ ~ ( ~ ! [SY2132: $i] :
( ! [SY2133: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SY2129 ) @ ( cartesian_product2 @ SY2132 @ SY2133 ) )
| ( in @ SV28 @ SY2132 ) )
| ~ ! [SY2134: $i,SY2135: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SY2129 ) @ ( cartesian_product2 @ SY2134 @ SY2135 ) )
| ( in @ SY2129 @ SY2135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(388,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY2136: $i] :
( ~ ( subset @ SY2136 @ ( sK4_B @ SV29 ) )
| ( are_equipotent @ SY2136 @ ( sK4_B @ SV29 ) )
| ( in @ SY2136 @ ( sK4_B @ SV29 ) ) )
| ~ ~ ( ~ ! [SY2137: $i] :
( ~ ( ~ ! [SY2138: $i] :
( ~ ( subset @ SY2138 @ SY2137 )
| ( in @ SY2138 @ ( sK5_SY2040 @ SY2137 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2137 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SY2137 @ ( sK4_B @ SV29 ) ) )
| ~ ~ ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(389,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_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)],[335]) ).
thf(390,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ~ ( ~ ! [SY2141: $i] :
( ~ ( ~ ( ! [SY2142: $i] :
~ ( in @ ( ordered_pair @ SY2142 @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2141 @ SV30 ) @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) ) )
| ( SY2141
= ( relation_rng @ SV30 ) ) )
| ~ ! [SY2143: $i] :
( ( SY2143
!= ( relation_rng @ SV30 ) )
| ~ ( ~ ! [SY2144: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2144 ) @ SV30 )
| ( in @ SY2144 @ SY2143 ) )
| ~ ! [SY2146: $i] :
( ~ ( in @ SY2146 @ SY2143 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2146 @ SY2143 @ SV30 ) @ SY2146 ) @ SV30 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(391,plain,
! [SV31: $i] :
( ( ! [SY2147: $i] :
( ~ ( ~ ( in @ ( sK40_C @ SY2147 @ SV31 ) @ SV31 )
| ~ ~ ( in @ ( sK40_C @ SY2147 @ SV31 ) @ SY2147 ) )
| ( element @ SV31 @ ( powerset @ SY2147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(392,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK20_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)],[338]) ).
thf(393,plain,
! [SV32: $i] :
( ( ~ ( ~ ! [SY2148: $i,SY2149: $i] :
( ~ ( in @ SV32 @ SY2149 )
| ~ ( in @ SY2148 @ SY2149 )
| ( subset @ ( unordered_pair @ SV32 @ SY2148 ) @ SY2149 ) )
| ~ ~ ( ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2150 ) @ SY2151 )
| ( in @ SV32 @ SY2151 ) )
| ~ ! [SY2152: $i,SY2153: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2152 ) @ SY2153 )
| ( in @ SY2152 @ SY2153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(394,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[340]) ).
thf(395,plain,
! [SV33: $i] :
( ( ~ ( relation @ SV33 )
| ~ ( ~ ! [SY2154: $i] :
( ~ ( ~ ( ! [SY2155: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ SY2155 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ ( sK18_SY2050 @ SY2154 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) ) )
| ( SY2154
= ( relation_dom @ SV33 ) ) )
| ~ ! [SY2156: $i] :
( ( SY2156
!= ( relation_dom @ SV33 ) )
| ~ ( ~ ! [SY2157: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2157 @ SY2158 ) @ SV33 )
| ( in @ SY2157 @ SY2156 ) )
| ~ ! [SY2159: $i] :
( ~ ( in @ SY2159 @ SY2156 )
| ( in @ ( ordered_pair @ SY2159 @ ( sK16_D @ SY2159 @ SY2156 @ SV33 ) ) @ SV33 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(396,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)],[342]) ).
thf(397,plain,
! [SV34: $i] :
( ( ~ ( ~ ! [SY2160: $i] :
( ~ ( subset @ SY2160 @ ( sK39_B @ SV34 ) )
| ( are_equipotent @ SY2160 @ ( sK39_B @ SV34 ) )
| ( in @ SY2160 @ ( sK39_B @ SV34 ) ) )
| ~ ~ ( ~ ! [SY2161: $i] :
( ~ ( in @ SY2161 @ ( sK39_B @ SV34 ) )
| ( in @ ( powerset @ SY2161 ) @ ( sK39_B @ SV34 ) ) )
| ~ ~ ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) )
| ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(398,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_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)],[344]) ).
thf(399,plain,
! [SV35: $i] :
( ( ! [SY2164: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SY2164 @ SV35 ) @ SV35 )
| ~ ( in @ ( sK6_C @ SY2164 @ SV35 ) @ SY2164 ) )
| ~ ( ( in @ ( sK6_C @ SY2164 @ SV35 ) @ SV35 )
| ( in @ ( sK6_C @ SY2164 @ SV35 ) @ SY2164 ) ) )
| ( SV35 = SY2164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(400,plain,
! [SV36: $i] :
( ( ! [SY2165: $i] :
~ ( ~ ! [SY2166: $i,SY2167: $i] :
( ~ ( in @ SV36 @ SY2166 )
| ~ ( in @ SY2165 @ SY2167 )
| ( in @ ( ordered_pair @ SV36 @ SY2165 ) @ ( cartesian_product2 @ SY2166 @ SY2167 ) ) )
| ~ ~ ( ~ ! [SY2168: $i] :
( ! [SY2169: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SY2165 ) @ ( cartesian_product2 @ SY2168 @ SY2169 ) )
| ( in @ SV36 @ SY2168 ) )
| ~ ! [SY2170: $i,SY2171: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SY2165 ) @ ( cartesian_product2 @ SY2170 @ SY2171 ) )
| ( in @ SY2165 @ SY2171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(401,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK36_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK36_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY2059 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(402,plain,
! [SV37: $i] :
( ( ~ ( relation @ SV37 )
| ~ ( ~ ! [SY2172: $i] :
( ~ ( relation @ SY2172 )
| ~ ( subset @ SV37 @ SY2172 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SY2172 ) ) )
| ~ ! [SY2173: $i] :
( ~ ( relation @ SY2173 )
| ~ ( subset @ SV37 @ SY2173 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SY2173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(403,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK37_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)],[349]) ).
thf(404,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)],[350]) ).
thf(405,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(406,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)],[352]) ).
thf(407,plain,
! [SV38: $i] :
( ( ~ ( ~ ! [SY2174: $i,SY2175: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2174 )
| ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2174 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) ) ) )
| ( SY2175
= ( set_difference @ SV38 @ SY2174 ) ) )
| ~ ! [SY2176: $i,SY2177: $i] :
( ( SY2177
!= ( set_difference @ SV38 @ SY2176 ) )
| ~ ( ~ ! [SY2178: $i] :
( ~ ( in @ SY2178 @ SV38 )
| ( in @ SY2178 @ SY2176 )
| ( in @ SY2178 @ SY2177 ) )
| ~ ~ ( ~ ! [SY2179: $i] :
( ~ ( in @ SY2179 @ SY2177 )
| ( in @ SY2179 @ SV38 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2177 )
| ~ ( in @ SX3 @ SY2176 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(408,plain,
! [SV39: $i] :
( ( ~ ( ~ ! [SY2181: $i,SY2182: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2181 )
| ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) )
| ~ ( ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2181 )
| ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) ) ) )
| ( SY2182
= ( set_intersection2 @ SV39 @ SY2181 ) ) )
| ~ ! [SY2183: $i,SY2184: $i] :
( ( SY2184
!= ( set_intersection2 @ SV39 @ SY2183 ) )
| ~ ( ~ ! [SY2185: $i] :
( ~ ( in @ SY2185 @ SV39 )
| ~ ( in @ SY2185 @ SY2183 )
| ( in @ SY2185 @ SY2184 ) )
| ~ ~ ( ~ ! [SY2186: $i] :
( ~ ( in @ SY2186 @ SY2184 )
| ( in @ SY2186 @ SV39 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2184 )
| ( in @ SX3 @ SY2183 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(409,plain,
! [SV40: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV40 )
| ( ( set_union2 @ ( singleton @ SV1 ) @ SV40 )
= SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(410,plain,
! [SV41: $i,SV2: $i] :
( ( ~ ( disjoint @ ( singleton @ SV2 ) @ SV41 )
| ~ ( in @ SV2 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(411,plain,
! [SV42: $i,SV3: $i] :
( ( ( in @ SV3 @ SV42 )
| ( disjoint @ ( singleton @ SV3 ) @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(412,plain,
! [SV4: $i,SV43: $i] :
( ( ~ ( element @ SV43 @ ( powerset @ SV4 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SV43 )
| ( in @ SY2188 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(413,plain,
! [SV44: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV44 )
| ! [SY2189: $i] :
( ( in @ SY2189 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV44 @ ( singleton @ SY2189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(414,plain,
! [SV45: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV45 )
| ( subset @ SV6 @ ( union @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(415,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( subset @ SV7 @ ( cartesian_product2 @ ( relation_dom @ SV7 ) @ ( relation_rng @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(416,plain,
! [SV46: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV46 )
| ( ( set_union2 @ ( singleton @ SV8 ) @ SV46 )
= SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(417,plain,
! [SV9: $i] :
( ( ( SV9 = empty_set )
= $true )
| ( ( ! [SY2075: $i] :
( ~ ( element @ SY2075 @ ( powerset @ SV9 ) )
| ! [SY2076: $i] :
( ~ ( element @ SY2076 @ SV9 )
| ( in @ SY2076 @ SY2075 )
| ( in @ SY2076 @ ( subset_complement @ SV9 @ SY2075 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(418,plain,
! [SV47: $i,SV10: $i] :
( ( ! [SY2190: $i] :
( ~ ( element @ SY2190 @ ( powerset @ SV10 ) )
| ~ ( in @ SV47 @ ( subset_complement @ SV10 @ SY2190 ) )
| ~ ( in @ SV47 @ SY2190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(419,plain,
! [SV48: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV48 )
| ( subset @ SV11 @ ( union @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(420,plain,
! [SV49: $i,SV12: $i] :
( ( ~ ( in @ SV12 @ SV49 )
| ~ ( in @ SV49 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(421,plain,
! [SV50: $i,SV13: $i] :
( ( ( ordered_pair @ SV13 @ SV50 )
= ( unordered_pair @ ( unordered_pair @ SV13 @ SV50 ) @ ( singleton @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(422,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ( relation_field @ SV14 )
= ( set_union2 @ ( relation_dom @ SV14 ) @ ( relation_rng @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(423,plain,
! [SV51: $i,SV15: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV15 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(424,plain,
! [SV52: $i,SV16: $i] :
( ( ~ ( relation @ SV16 )
| ~ ( relation @ SV52 )
| ( relation @ ( set_union2 @ SV16 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(425,plain,
! [SV53: $i,SV17: $i] :
( ( ~ ( in @ SV17 @ SV53 )
| ( element @ SV17 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(426,plain,
! [SV54: $i,SV18: $i] :
( ( ~ ( element @ SV18 @ SV54 )
| ( empty @ SV54 )
| ( in @ SV18 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(427,plain,
! [SV19: $i,SV55: $i] :
( ( ! [SY2191: $i] :
( ~ ( element @ SV55 @ ( powerset @ SY2191 ) )
| ~ ( in @ SV19 @ SV55 )
| ( element @ SV19 @ SY2191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(428,plain,
! [SV20: $i,SV56: $i] :
( ( ! [SY2192: $i] :
( ~ ( element @ SV56 @ ( powerset @ SY2192 ) )
| ~ ( in @ SV20 @ SV56 )
| ~ ( empty @ SY2192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(429,plain,
! [SV21: $i,SV57: $i] :
( ( ~ ( empty @ SV57 )
| ~ ( in @ SV21 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(430,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(431,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(432,plain,
! [SV22: $i] :
( ( ~ ! [SY2091: $i,SY2092: $i] :
( ~ ( relation @ SY2092 )
| ~ ( in @ ( ordered_pair @ SV22 @ SY2091 ) @ SY2092 )
| ( in @ SV22 @ ( relation_dom @ SY2092 ) ) )
| ~ ! [SY2093: $i,SY2094: $i] :
( ~ ( relation @ SY2094 )
| ~ ( in @ ( ordered_pair @ SV22 @ SY2093 ) @ SY2094 )
| ( in @ SY2093 @ ( relation_rng @ SY2094 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(433,plain,
! [SV23: $i] :
( ( ~ ! [SY2095: $i,SY2096: $i] :
( ~ ( ~ ( ! [SY2097: $i,SY2098: $i] :
( ~ ( in @ SY2097 @ SV23 )
| ~ ( in @ SY2098 @ SY2095 )
| ( ( sK23_D @ SY2096 @ SY2095 @ SV23 )
!= ( ordered_pair @ SY2097 @ SY2098 ) ) )
| ~ ( in @ ( sK23_D @ SY2096 @ SY2095 @ SV23 ) @ SY2096 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2096 @ SY2095 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SY2096 @ SY2095 @ SV23 ) @ SY2095 ) )
| ( ( sK23_D @ SY2096 @ SY2095 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2096 @ SY2095 @ SV23 ) @ ( sK25_SY2056 @ SY2096 @ SY2095 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SY2096 @ SY2095 @ SV23 ) @ SY2096 ) ) )
| ( SY2096
= ( cartesian_product2 @ SV23 @ SY2095 ) ) )
| ~ ! [SY2099: $i,SY2100: $i] :
( ( SY2100
!= ( cartesian_product2 @ SV23 @ SY2099 ) )
| ~ ( ~ ! [SY2101: $i] :
( ! [SY2102: $i,SY2103: $i] :
( ~ ( in @ SY2102 @ SV23 )
| ~ ( in @ SY2103 @ SY2099 )
| ( SY2101
!= ( ordered_pair @ SY2102 @ SY2103 ) ) )
| ( in @ SY2101 @ SY2100 ) )
| ~ ! [SY2104: $i] :
( ~ ( in @ SY2104 @ SY2100 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ SY2099 ) )
| ( SY2104
!= ( ordered_pair @ ( sK21_E @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ ( sK22_SY2051 @ SY2104 @ SY2100 @ SY2099 @ SV23 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(434,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY2048 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK15_SY2048 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(435,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 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(436,plain,
( ( ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(437,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(438,plain,
! [SV24: $i] :
( ( ~ ! [SY2105: $i,SY2106: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2105 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2105 ) ) )
| ( SY2106
= ( set_union2 @ SV24 @ SY2105 ) ) )
| ~ ! [SY2107: $i,SY2108: $i] :
( ( SY2108
!= ( set_union2 @ SV24 @ SY2107 ) )
| ~ ( ~ ! [SY2109: $i] :
( ~ ( in @ SY2109 @ SY2108 )
| ( in @ SY2109 @ SV24 )
| ( in @ SY2109 @ SY2107 ) )
| ~ ~ ( ~ ! [SY2110: $i] :
( ~ ( in @ SY2110 @ SV24 )
| ( in @ SY2110 @ SY2108 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2107 )
| ( in @ SX3 @ SY2108 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(439,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(440,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(441,plain,
! [SV25: $i,SV58: $i] :
( ( ~ ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ! [SY2193: $i] :
( ~ ( element @ SY2193 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SY2193
= ( complements_of_subsets @ SV25 @ SV58 ) ) )
| ~ ! [SY2194: $i] :
( ~ ( element @ SY2194 @ ( powerset @ ( powerset @ SV25 ) ) )
| ( SY2194
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2195: $i] :
( ~ ( element @ SY2195 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2195 @ SY2194 )
| ( in @ ( subset_complement @ SV25 @ SY2195 ) @ SV58 ) )
| ~ ! [SY2196: $i] :
( ~ ( element @ SY2196 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2196 ) @ SV58 )
| ( in @ SY2196 @ SY2194 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(442,plain,
! [SV26: $i] :
( ( ~ ! [SY2117: $i,SY2118: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
!= SY2117 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
= SV26 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
= SY2117 ) ) )
| ( SY2118
= ( unordered_pair @ SV26 @ SY2117 ) ) )
| ~ ! [SY2119: $i,SY2120: $i] :
( ( SY2120
!= ( unordered_pair @ SV26 @ SY2119 ) )
| ~ ( ~ ! [SY2121: $i] :
( ~ ( in @ SY2121 @ SY2120 )
| ( SY2121 = SV26 )
| ( SY2121 = SY2119 ) )
| ~ ~ ( ~ ! [SY2122: $i] :
( ( SY2122 != SV26 )
| ( in @ SY2122 @ SY2120 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY2119 )
| ( in @ SX3 @ SY2120 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(443,plain,
! [SV59: $i,SV27: $i] :
( ( ~ ( ~ ! [SY2197: $i] :
( ! [SY2198: $i] :
( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SY2197 @ SY2198 ) )
| ( SV27 = SY2197 ) )
| ~ ! [SY2199: $i,SY2200: $i] :
( ( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SY2199 @ SY2200 ) )
| ( SV59 = SY2200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(444,plain,
! [SV60: $i,SV28: $i] :
( ( ~ ( ~ ! [SY2201: $i,SY2202: $i] :
( ~ ( in @ SV28 @ SY2201 )
| ~ ( in @ SV60 @ SY2202 )
| ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2201 @ SY2202 ) ) )
| ~ ~ ( ~ ! [SY2203: $i] :
( ! [SY2204: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2203 @ SY2204 ) )
| ( in @ SV28 @ SY2203 ) )
| ~ ! [SY2205: $i,SY2206: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2205 @ SY2206 ) )
| ( in @ SV60 @ SY2206 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(445,plain,
! [SV29: $i] :
( ( ~ ! [SY2136: $i] :
( ~ ( subset @ SY2136 @ ( sK4_B @ SV29 ) )
| ( are_equipotent @ SY2136 @ ( sK4_B @ SV29 ) )
| ( in @ SY2136 @ ( sK4_B @ SV29 ) ) )
| ~ ~ ( ~ ! [SY2137: $i] :
( ~ ( ~ ! [SY2138: $i] :
( ~ ( subset @ SY2138 @ SY2137 )
| ( in @ SY2138 @ ( sK5_SY2040 @ SY2137 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2137 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SY2137 @ ( sK4_B @ SV29 ) ) )
| ~ ~ ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(446,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(447,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)],[389]) ).
thf(448,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ~ ( ~ ! [SY2141: $i] :
( ~ ( ~ ( ! [SY2142: $i] :
~ ( in @ ( ordered_pair @ SY2142 @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2141 @ SV30 ) @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) ) )
| ( SY2141
= ( relation_rng @ SV30 ) ) )
| ~ ! [SY2143: $i] :
( ( SY2143
!= ( relation_rng @ SV30 ) )
| ~ ( ~ ! [SY2144: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2144 ) @ SV30 )
| ( in @ SY2144 @ SY2143 ) )
| ~ ! [SY2146: $i] :
( ~ ( in @ SY2146 @ SY2143 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2146 @ SY2143 @ SV30 ) @ SY2146 ) @ SV30 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(449,plain,
! [SV31: $i,SV61: $i] :
( ( ~ ( ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV31 )
| ~ ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV61 ) )
| ( element @ SV31 @ ( powerset @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(450,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(451,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(452,plain,
! [SV32: $i] :
( ( ~ ! [SY2148: $i,SY2149: $i] :
( ~ ( in @ SV32 @ SY2149 )
| ~ ( in @ SY2148 @ SY2149 )
| ( subset @ ( unordered_pair @ SV32 @ SY2148 ) @ SY2149 ) )
| ~ ~ ( ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2150 ) @ SY2151 )
| ( in @ SV32 @ SY2151 ) )
| ~ ! [SY2152: $i,SY2153: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2152 ) @ SY2153 )
| ( in @ SY2152 @ SY2153 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(453,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[394]) ).
thf(454,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)],[394]) ).
thf(455,plain,
! [SV33: $i] :
( ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ~ ( ~ ! [SY2154: $i] :
( ~ ( ~ ( ! [SY2155: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ SY2155 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ ( sK18_SY2050 @ SY2154 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) ) )
| ( SY2154
= ( relation_dom @ SV33 ) ) )
| ~ ! [SY2156: $i] :
( ( SY2156
!= ( relation_dom @ SV33 ) )
| ~ ( ~ ! [SY2157: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2157 @ SY2158 ) @ SV33 )
| ( in @ SY2157 @ SY2156 ) )
| ~ ! [SY2159: $i] :
( ~ ( in @ SY2159 @ SY2156 )
| ( in @ ( ordered_pair @ SY2159 @ ( sK16_D @ SY2159 @ SY2156 @ SV33 ) ) @ SV33 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(456,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(457,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(458,plain,
! [SV34: $i] :
( ( ~ ! [SY2160: $i] :
( ~ ( subset @ SY2160 @ ( sK39_B @ SV34 ) )
| ( are_equipotent @ SY2160 @ ( sK39_B @ SV34 ) )
| ( in @ SY2160 @ ( sK39_B @ SV34 ) ) )
| ~ ~ ( ~ ! [SY2161: $i] :
( ~ ( in @ SY2161 @ ( sK39_B @ SV34 ) )
| ( in @ ( powerset @ SY2161 ) @ ( sK39_B @ SV34 ) ) )
| ~ ~ ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) )
| ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(459,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(460,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)],[398]) ).
thf(461,plain,
! [SV35: $i,SV62: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) )
| ~ ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) ) )
| ( SV35 = SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(462,plain,
! [SV63: $i,SV36: $i] :
( ( ~ ( ~ ! [SY2207: $i,SY2208: $i] :
( ~ ( in @ SV36 @ SY2207 )
| ~ ( in @ SV63 @ SY2208 )
| ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2207 @ SY2208 ) ) )
| ~ ~ ( ~ ! [SY2209: $i] :
( ! [SY2210: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2209 @ SY2210 ) )
| ( in @ SV36 @ SY2209 ) )
| ~ ! [SY2211: $i,SY2212: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2211 @ SY2212 ) )
| ( in @ SV63 @ SY2212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(463,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK36_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK36_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(464,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY2059 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(465,plain,
! [SV37: $i] :
( ( ( ~ ( relation @ SV37 ) )
= $true )
| ( ( ~ ( ~ ! [SY2172: $i] :
( ~ ( relation @ SY2172 )
| ~ ( subset @ SV37 @ SY2172 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SY2172 ) ) )
| ~ ! [SY2173: $i] :
( ~ ( relation @ SY2173 )
| ~ ( subset @ SV37 @ SY2173 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SY2173 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(466,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK37_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(467,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(468,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(469,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(470,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(471,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(472,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)],[406]) ).
thf(473,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)],[406]) ).
thf(474,plain,
! [SV38: $i] :
( ( ~ ! [SY2174: $i,SY2175: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2174 )
| ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2174 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) ) ) )
| ( SY2175
= ( set_difference @ SV38 @ SY2174 ) ) )
| ~ ! [SY2176: $i,SY2177: $i] :
( ( SY2177
!= ( set_difference @ SV38 @ SY2176 ) )
| ~ ( ~ ! [SY2178: $i] :
( ~ ( in @ SY2178 @ SV38 )
| ( in @ SY2178 @ SY2176 )
| ( in @ SY2178 @ SY2177 ) )
| ~ ~ ( ~ ! [SY2179: $i] :
( ~ ( in @ SY2179 @ SY2177 )
| ( in @ SY2179 @ SV38 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2177 )
| ~ ( in @ SX3 @ SY2176 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(475,plain,
! [SV39: $i] :
( ( ~ ! [SY2181: $i,SY2182: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2181 )
| ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) )
| ~ ( ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2181 )
| ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) ) ) )
| ( SY2182
= ( set_intersection2 @ SV39 @ SY2181 ) ) )
| ~ ! [SY2183: $i,SY2184: $i] :
( ( SY2184
!= ( set_intersection2 @ SV39 @ SY2183 ) )
| ~ ( ~ ! [SY2185: $i] :
( ~ ( in @ SY2185 @ SV39 )
| ~ ( in @ SY2185 @ SY2183 )
| ( in @ SY2185 @ SY2184 ) )
| ~ ~ ( ~ ! [SY2186: $i] :
( ~ ( in @ SY2186 @ SY2184 )
| ( in @ SY2186 @ SV39 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2184 )
| ( in @ SX3 @ SY2183 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(476,plain,
! [SV40: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV40 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV1 ) @ SV40 )
= SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(477,plain,
! [SV41: $i,SV2: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV2 ) @ SV41 ) )
= $true )
| ( ( ~ ( in @ SV2 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(478,plain,
! [SV42: $i,SV3: $i] :
( ( ( in @ SV3 @ SV42 )
= $true )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(479,plain,
! [SV4: $i,SV43: $i] :
( ( ( ~ ( element @ SV43 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SV43 )
| ( in @ SY2188 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(480,plain,
! [SV44: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV44 ) )
= $true )
| ( ( ! [SY2189: $i] :
( ( in @ SY2189 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV44 @ ( singleton @ SY2189 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(481,plain,
! [SV45: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV45 ) )
= $true )
| ( ( subset @ SV6 @ ( union @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(482,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( subset @ SV7 @ ( cartesian_product2 @ ( relation_dom @ SV7 ) @ ( relation_rng @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(483,plain,
! [SV46: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV46 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV8 ) @ SV46 )
= SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(484,plain,
! [SV9: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ ( powerset @ SV9 ) )
| ! [SY2213: $i] :
( ~ ( element @ SY2213 @ SV9 )
| ( in @ SY2213 @ SV64 )
| ( in @ SY2213 @ ( subset_complement @ SV9 @ SV64 ) ) ) )
= $true )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(485,plain,
! [SV47: $i,SV10: $i,SV65: $i] :
( ( ~ ( element @ SV65 @ ( powerset @ SV10 ) )
| ~ ( in @ SV47 @ ( subset_complement @ SV10 @ SV65 ) )
| ~ ( in @ SV47 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(486,plain,
! [SV48: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV48 ) )
= $true )
| ( ( subset @ SV11 @ ( union @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(487,plain,
! [SV49: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV49 ) )
= $true )
| ( ( ~ ( in @ SV49 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(488,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ( relation_field @ SV14 )
= ( set_union2 @ ( relation_dom @ SV14 ) @ ( relation_rng @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(489,plain,
! [SV51: $i,SV15: $i] :
( ( empty @ ( ordered_pair @ SV15 @ SV51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(490,plain,
! [SV52: $i,SV16: $i] :
( ( ( ~ ( relation @ SV16 )
| ~ ( relation @ SV52 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV16 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(491,plain,
! [SV53: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV53 ) )
= $true )
| ( ( element @ SV17 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(492,plain,
! [SV54: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ SV54 ) )
= $true )
| ( ( ( empty @ SV54 )
| ( in @ SV18 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(493,plain,
! [SV19: $i,SV66: $i,SV55: $i] :
( ( ~ ( element @ SV55 @ ( powerset @ SV66 ) )
| ~ ( in @ SV19 @ SV55 )
| ( element @ SV19 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(494,plain,
! [SV20: $i,SV67: $i,SV56: $i] :
( ( ~ ( element @ SV56 @ ( powerset @ SV67 ) )
| ~ ( in @ SV20 @ SV56 )
| ~ ( empty @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(495,plain,
! [SV21: $i,SV57: $i] :
( ( ( ~ ( empty @ SV57 ) )
= $true )
| ( ( ~ ( in @ SV21 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(496,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(497,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(498,plain,
! [SV22: $i] :
( ( ~ ! [SY2091: $i,SY2092: $i] :
( ~ ( relation @ SY2092 )
| ~ ( in @ ( ordered_pair @ SV22 @ SY2091 ) @ SY2092 )
| ( in @ SV22 @ ( relation_dom @ SY2092 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(499,plain,
! [SV22: $i] :
( ( ~ ! [SY2093: $i,SY2094: $i] :
( ~ ( relation @ SY2094 )
| ~ ( in @ ( ordered_pair @ SV22 @ SY2093 ) @ SY2094 )
| ( in @ SY2093 @ ( relation_rng @ SY2094 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(500,plain,
! [SV23: $i] :
( ( ~ ! [SY2095: $i,SY2096: $i] :
( ~ ( ~ ( ! [SY2097: $i,SY2098: $i] :
( ~ ( in @ SY2097 @ SV23 )
| ~ ( in @ SY2098 @ SY2095 )
| ( ( sK23_D @ SY2096 @ SY2095 @ SV23 )
!= ( ordered_pair @ SY2097 @ SY2098 ) ) )
| ~ ( in @ ( sK23_D @ SY2096 @ SY2095 @ SV23 ) @ SY2096 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2096 @ SY2095 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SY2096 @ SY2095 @ SV23 ) @ SY2095 ) )
| ( ( sK23_D @ SY2096 @ SY2095 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2096 @ SY2095 @ SV23 ) @ ( sK25_SY2056 @ SY2096 @ SY2095 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SY2096 @ SY2095 @ SV23 ) @ SY2096 ) ) )
| ( SY2096
= ( cartesian_product2 @ SV23 @ SY2095 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(501,plain,
! [SV23: $i] :
( ( ~ ! [SY2099: $i,SY2100: $i] :
( ( SY2100
!= ( cartesian_product2 @ SV23 @ SY2099 ) )
| ~ ( ~ ! [SY2101: $i] :
( ! [SY2102: $i,SY2103: $i] :
( ~ ( in @ SY2102 @ SV23 )
| ~ ( in @ SY2103 @ SY2099 )
| ( SY2101
!= ( ordered_pair @ SY2102 @ SY2103 ) ) )
| ( in @ SY2101 @ SY2100 ) )
| ~ ! [SY2104: $i] :
( ~ ( in @ SY2104 @ SY2100 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ SY2099 ) )
| ( SY2104
!= ( ordered_pair @ ( sK21_E @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ ( sK22_SY2051 @ SY2104 @ SY2100 @ SY2099 @ SV23 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(502,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY2048 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK15_SY2048 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(503,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 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(504,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(505,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(506,plain,
! [SV24: $i] :
( ( ~ ! [SY2105: $i,SY2106: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2105 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2105 ) ) )
| ( SY2106
= ( set_union2 @ SV24 @ SY2105 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(507,plain,
! [SV24: $i] :
( ( ~ ! [SY2107: $i,SY2108: $i] :
( ( SY2108
!= ( set_union2 @ SV24 @ SY2107 ) )
| ~ ( ~ ! [SY2109: $i] :
( ~ ( in @ SY2109 @ SY2108 )
| ( in @ SY2109 @ SV24 )
| ( in @ SY2109 @ SY2107 ) )
| ~ ~ ( ~ ! [SY2110: $i] :
( ~ ( in @ SY2110 @ SV24 )
| ( in @ SY2110 @ SY2108 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2107 )
| ( in @ SX3 @ SY2108 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(508,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(509,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(510,plain,
! [SV25: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2193: $i] :
( ~ ( element @ SY2193 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SY2193
= ( complements_of_subsets @ SV25 @ SV58 ) ) )
| ~ ! [SY2194: $i] :
( ~ ( element @ SY2194 @ ( powerset @ ( powerset @ SV25 ) ) )
| ( SY2194
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2195: $i] :
( ~ ( element @ SY2195 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2195 @ SY2194 )
| ( in @ ( subset_complement @ SV25 @ SY2195 ) @ SV58 ) )
| ~ ! [SY2196: $i] :
( ~ ( element @ SY2196 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2196 ) @ SV58 )
| ( in @ SY2196 @ SY2194 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(511,plain,
! [SV26: $i] :
( ( ~ ! [SY2117: $i,SY2118: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
!= SY2117 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
= SV26 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
= SY2117 ) ) )
| ( SY2118
= ( unordered_pair @ SV26 @ SY2117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(512,plain,
! [SV26: $i] :
( ( ~ ! [SY2119: $i,SY2120: $i] :
( ( SY2120
!= ( unordered_pair @ SV26 @ SY2119 ) )
| ~ ( ~ ! [SY2121: $i] :
( ~ ( in @ SY2121 @ SY2120 )
| ( SY2121 = SV26 )
| ( SY2121 = SY2119 ) )
| ~ ~ ( ~ ! [SY2122: $i] :
( ( SY2122 != SV26 )
| ( in @ SY2122 @ SY2120 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY2119 )
| ( in @ SX3 @ SY2120 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(513,plain,
! [SV59: $i,SV27: $i] :
( ( ~ ! [SY2197: $i] :
( ! [SY2198: $i] :
( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SY2197 @ SY2198 ) )
| ( SV27 = SY2197 ) )
| ~ ! [SY2199: $i,SY2200: $i] :
( ( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SY2199 @ SY2200 ) )
| ( SV59 = SY2200 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(514,plain,
! [SV60: $i,SV28: $i] :
( ( ~ ! [SY2201: $i,SY2202: $i] :
( ~ ( in @ SV28 @ SY2201 )
| ~ ( in @ SV60 @ SY2202 )
| ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2201 @ SY2202 ) ) )
| ~ ~ ( ~ ! [SY2203: $i] :
( ! [SY2204: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2203 @ SY2204 ) )
| ( in @ SV28 @ SY2203 ) )
| ~ ! [SY2205: $i,SY2206: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2205 @ SY2206 ) )
| ( in @ SV60 @ SY2206 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(515,plain,
! [SV29: $i] :
( ( ~ ! [SY2136: $i] :
( ~ ( subset @ SY2136 @ ( sK4_B @ SV29 ) )
| ( are_equipotent @ SY2136 @ ( sK4_B @ SV29 ) )
| ( in @ SY2136 @ ( sK4_B @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(516,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY2137: $i] :
( ~ ( ~ ! [SY2138: $i] :
( ~ ( subset @ SY2138 @ SY2137 )
| ( in @ SY2138 @ ( sK5_SY2040 @ SY2137 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2137 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SY2137 @ ( sK4_B @ SV29 ) ) )
| ~ ~ ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(517,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(518,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)],[447]) ).
thf(519,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ~ ( ~ ! [SY2141: $i] :
( ~ ( ~ ( ! [SY2142: $i] :
~ ( in @ ( ordered_pair @ SY2142 @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2141 @ SV30 ) @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) ) )
| ( SY2141
= ( relation_rng @ SV30 ) ) )
| ~ ! [SY2143: $i] :
( ( SY2143
!= ( relation_rng @ SV30 ) )
| ~ ( ~ ! [SY2144: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2144 ) @ SV30 )
| ( in @ SY2144 @ SY2143 ) )
| ~ ! [SY2146: $i] :
( ~ ( in @ SY2146 @ SY2143 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2146 @ SY2143 @ SV30 ) @ SY2146 ) @ SV30 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(520,plain,
! [SV31: $i,SV61: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV31 )
| ~ ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV61 ) ) )
= $true )
| ( ( element @ SV31 @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(521,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(522,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(523,plain,
! [SV32: $i] :
( ( ~ ! [SY2148: $i,SY2149: $i] :
( ~ ( in @ SV32 @ SY2149 )
| ~ ( in @ SY2148 @ SY2149 )
| ( subset @ ( unordered_pair @ SV32 @ SY2148 ) @ SY2149 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(524,plain,
! [SV32: $i] :
( ( ~ ~ ( ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2150 ) @ SY2151 )
| ( in @ SV32 @ SY2151 ) )
| ~ ! [SY2152: $i,SY2153: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2152 ) @ SY2153 )
| ( in @ SY2152 @ SY2153 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(525,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[453]) ).
thf(526,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)],[454]) ).
thf(527,plain,
! [SV33: $i] :
( ( ( relation @ SV33 )
= $false )
| ( ( ~ ( ~ ! [SY2154: $i] :
( ~ ( ~ ( ! [SY2155: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ SY2155 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ ( sK18_SY2050 @ SY2154 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) ) )
| ( SY2154
= ( relation_dom @ SV33 ) ) )
| ~ ! [SY2156: $i] :
( ( SY2156
!= ( relation_dom @ SV33 ) )
| ~ ( ~ ! [SY2157: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2157 @ SY2158 ) @ SV33 )
| ( in @ SY2157 @ SY2156 ) )
| ~ ! [SY2159: $i] :
( ~ ( in @ SY2159 @ SY2156 )
| ( in @ ( ordered_pair @ SY2159 @ ( sK16_D @ SY2159 @ SY2156 @ SV33 ) ) @ SV33 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(528,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(529,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(530,plain,
! [SV34: $i] :
( ( ~ ! [SY2160: $i] :
( ~ ( subset @ SY2160 @ ( sK39_B @ SV34 ) )
| ( are_equipotent @ SY2160 @ ( sK39_B @ SV34 ) )
| ( in @ SY2160 @ ( sK39_B @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(531,plain,
! [SV34: $i] :
( ( ~ ~ ( ~ ! [SY2161: $i] :
( ~ ( in @ SY2161 @ ( sK39_B @ SV34 ) )
| ( in @ ( powerset @ SY2161 ) @ ( sK39_B @ SV34 ) ) )
| ~ ~ ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) )
| ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(532,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(533,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)],[460]) ).
thf(534,plain,
! [SV35: $i,SV62: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) )
| ~ ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) ) ) )
= $true )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(535,plain,
! [SV63: $i,SV36: $i] :
( ( ~ ! [SY2207: $i,SY2208: $i] :
( ~ ( in @ SV36 @ SY2207 )
| ~ ( in @ SV63 @ SY2208 )
| ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2207 @ SY2208 ) ) )
| ~ ~ ( ~ ! [SY2209: $i] :
( ! [SY2210: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2209 @ SY2210 ) )
| ( in @ SV36 @ SY2209 ) )
| ~ ! [SY2211: $i,SY2212: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2211 @ SY2212 ) )
| ( in @ SV63 @ SY2212 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(536,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK36_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK36_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(537,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY2059 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(538,plain,
! [SV37: $i] :
( ( ( relation @ SV37 )
= $false )
| ( ( ~ ( ~ ! [SY2172: $i] :
( ~ ( relation @ SY2172 )
| ~ ( subset @ SV37 @ SY2172 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SY2172 ) ) )
| ~ ! [SY2173: $i] :
( ~ ( relation @ SY2173 )
| ~ ( subset @ SV37 @ SY2173 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SY2173 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(539,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK37_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(540,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(541,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(543,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(544,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(545,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)],[472]) ).
thf(546,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)],[473]) ).
thf(547,plain,
! [SV38: $i] :
( ( ~ ! [SY2174: $i,SY2175: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2174 )
| ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2174 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) ) ) )
| ( SY2175
= ( set_difference @ SV38 @ SY2174 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(548,plain,
! [SV38: $i] :
( ( ~ ! [SY2176: $i,SY2177: $i] :
( ( SY2177
!= ( set_difference @ SV38 @ SY2176 ) )
| ~ ( ~ ! [SY2178: $i] :
( ~ ( in @ SY2178 @ SV38 )
| ( in @ SY2178 @ SY2176 )
| ( in @ SY2178 @ SY2177 ) )
| ~ ~ ( ~ ! [SY2179: $i] :
( ~ ( in @ SY2179 @ SY2177 )
| ( in @ SY2179 @ SV38 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2177 )
| ~ ( in @ SX3 @ SY2176 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(549,plain,
! [SV39: $i] :
( ( ~ ! [SY2181: $i,SY2182: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2181 )
| ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) )
| ~ ( ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2181 )
| ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) ) ) )
| ( SY2182
= ( set_intersection2 @ SV39 @ SY2181 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(550,plain,
! [SV39: $i] :
( ( ~ ! [SY2183: $i,SY2184: $i] :
( ( SY2184
!= ( set_intersection2 @ SV39 @ SY2183 ) )
| ~ ( ~ ! [SY2185: $i] :
( ~ ( in @ SY2185 @ SV39 )
| ~ ( in @ SY2185 @ SY2183 )
| ( in @ SY2185 @ SY2184 ) )
| ~ ~ ( ~ ! [SY2186: $i] :
( ~ ( in @ SY2186 @ SY2184 )
| ( in @ SY2186 @ SV39 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2184 )
| ( in @ SX3 @ SY2183 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(551,plain,
! [SV40: $i,SV1: $i] :
( ( ( in @ SV1 @ SV40 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV1 ) @ SV40 )
= SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(552,plain,
! [SV41: $i,SV2: $i] :
( ( ( disjoint @ ( singleton @ SV2 ) @ SV41 )
= $false )
| ( ( ~ ( in @ SV2 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(553,plain,
! [SV4: $i,SV43: $i] :
( ( ( element @ SV43 @ ( powerset @ SV4 ) )
= $false )
| ( ( ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SV43 )
| ( in @ SY2188 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(554,plain,
! [SV44: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV44 )
= $false )
| ( ( ! [SY2189: $i] :
( ( in @ SY2189 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV44 @ ( singleton @ SY2189 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(555,plain,
! [SV45: $i,SV6: $i] :
( ( ( in @ SV6 @ SV45 )
= $false )
| ( ( subset @ SV6 @ ( union @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(556,plain,
! [SV46: $i,SV8: $i] :
( ( ( in @ SV8 @ SV46 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV8 ) @ SV46 )
= SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(557,plain,
! [SV9: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( ! [SY2213: $i] :
( ~ ( element @ SY2213 @ SV9 )
| ( in @ SY2213 @ SV64 )
| ( in @ SY2213 @ ( subset_complement @ SV9 @ SV64 ) ) ) )
= $true )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(558,plain,
! [SV47: $i,SV10: $i,SV65: $i] :
( ( ( ~ ( element @ SV65 @ ( powerset @ SV10 ) ) )
= $true )
| ( ( ~ ( in @ SV47 @ ( subset_complement @ SV10 @ SV65 ) )
| ~ ( in @ SV47 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(559,plain,
! [SV48: $i,SV11: $i] :
( ( ( in @ SV11 @ SV48 )
= $false )
| ( ( subset @ SV11 @ ( union @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(560,plain,
! [SV49: $i,SV12: $i] :
( ( ( in @ SV12 @ SV49 )
= $false )
| ( ( ~ ( in @ SV49 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(561,plain,
! [SV52: $i,SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV16 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(562,plain,
! [SV53: $i,SV17: $i] :
( ( ( in @ SV17 @ SV53 )
= $false )
| ( ( element @ SV17 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(563,plain,
! [SV54: $i,SV18: $i] :
( ( ( element @ SV18 @ SV54 )
= $false )
| ( ( ( empty @ SV54 )
| ( in @ SV18 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(564,plain,
! [SV19: $i,SV66: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( powerset @ SV66 ) )
| ~ ( in @ SV19 @ SV55 ) )
= $true )
| ( ( element @ SV19 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(565,plain,
! [SV20: $i,SV67: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( powerset @ SV67 ) )
| ~ ( in @ SV20 @ SV56 ) )
= $true )
| ( ( ~ ( empty @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(566,plain,
! [SV21: $i,SV57: $i] :
( ( ( empty @ SV57 )
= $false )
| ( ( ~ ( in @ SV21 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(567,plain,
! [SV68: $i] :
( ( ! [SY2214: $i] :
( ~ ( in @ SV68 @ SY2214 )
| ( subset @ ( singleton @ SV68 ) @ SY2214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(568,plain,
! [SV69: $i] :
( ( ! [SY2215: $i] :
( ~ ( subset @ ( singleton @ SV69 ) @ SY2215 )
| ( in @ SV69 @ SY2215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(569,plain,
! [SV22: $i] :
( ( ! [SY2091: $i,SY2092: $i] :
( ~ ( relation @ SY2092 )
| ~ ( in @ ( ordered_pair @ SV22 @ SY2091 ) @ SY2092 )
| ( in @ SV22 @ ( relation_dom @ SY2092 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(570,plain,
! [SV22: $i] :
( ( ! [SY2093: $i,SY2094: $i] :
( ~ ( relation @ SY2094 )
| ~ ( in @ ( ordered_pair @ SV22 @ SY2093 ) @ SY2094 )
| ( in @ SY2093 @ ( relation_rng @ SY2094 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(571,plain,
! [SV23: $i] :
( ( ! [SY2095: $i,SY2096: $i] :
( ~ ( ~ ( ! [SY2097: $i,SY2098: $i] :
( ~ ( in @ SY2097 @ SV23 )
| ~ ( in @ SY2098 @ SY2095 )
| ( ( sK23_D @ SY2096 @ SY2095 @ SV23 )
!= ( ordered_pair @ SY2097 @ SY2098 ) ) )
| ~ ( in @ ( sK23_D @ SY2096 @ SY2095 @ SV23 ) @ SY2096 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2096 @ SY2095 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SY2096 @ SY2095 @ SV23 ) @ SY2095 ) )
| ( ( sK23_D @ SY2096 @ SY2095 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2096 @ SY2095 @ SV23 ) @ ( sK25_SY2056 @ SY2096 @ SY2095 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SY2096 @ SY2095 @ SV23 ) @ SY2096 ) ) )
| ( SY2096
= ( cartesian_product2 @ SV23 @ SY2095 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(572,plain,
! [SV23: $i] :
( ( ! [SY2099: $i,SY2100: $i] :
( ( SY2100
!= ( cartesian_product2 @ SV23 @ SY2099 ) )
| ~ ( ~ ! [SY2101: $i] :
( ! [SY2102: $i,SY2103: $i] :
( ~ ( in @ SY2102 @ SV23 )
| ~ ( in @ SY2103 @ SY2099 )
| ( SY2101
!= ( ordered_pair @ SY2102 @ SY2103 ) ) )
| ( in @ SY2101 @ SY2100 ) )
| ~ ! [SY2104: $i] :
( ~ ( in @ SY2104 @ SY2100 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ SY2099 ) )
| ( SY2104
!= ( ordered_pair @ ( sK21_E @ SY2104 @ SY2100 @ SY2099 @ SV23 ) @ ( sK22_SY2051 @ SY2104 @ SY2100 @ SY2099 @ SV23 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(573,plain,
! [SV70: $i] :
( ( ! [SY2216: $i] :
( ~ ( ~ ( ! [SY2217: $i] :
( ~ ( in @ ( sK14_C @ SY2216 @ SV70 ) @ SY2217 )
| ~ ( in @ SY2217 @ SV70 ) )
| ~ ( in @ ( sK14_C @ SY2216 @ SV70 ) @ SY2216 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SY2216 @ SV70 ) @ ( sK15_SY2048 @ SY2216 @ SV70 ) )
| ~ ( in @ ( sK15_SY2048 @ SY2216 @ SV70 ) @ SV70 ) )
| ( in @ ( sK14_C @ SY2216 @ SV70 ) @ SY2216 ) ) )
| ( SY2216
= ( union @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(574,plain,
! [SV71: $i] :
( ( ! [SY2218: $i] :
( ( SY2218
!= ( union @ SV71 ) )
| ~ ( ~ ! [SY2219: $i] :
( ! [SY2220: $i] :
( ~ ( in @ SY2219 @ SY2220 )
| ~ ( in @ SY2220 @ SV71 ) )
| ( in @ SY2219 @ SY2218 ) )
| ~ ! [SY2221: $i] :
( ~ ( in @ SY2221 @ SY2218 )
| ~ ( ~ ( in @ SY2221 @ ( sK13_D @ SY2221 @ SY2218 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SY2221 @ SY2218 @ SV71 ) @ SV71 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(575,plain,
! [SV24: $i] :
( ( ! [SY2105: $i,SY2106: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ~ ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2105 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2106 )
| ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SY2106 @ SY2105 @ SV24 ) @ SY2105 ) ) )
| ( SY2106
= ( set_union2 @ SV24 @ SY2105 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(576,plain,
! [SV24: $i] :
( ( ! [SY2107: $i,SY2108: $i] :
( ( SY2108
!= ( set_union2 @ SV24 @ SY2107 ) )
| ~ ( ~ ! [SY2109: $i] :
( ~ ( in @ SY2109 @ SY2108 )
| ( in @ SY2109 @ SV24 )
| ( in @ SY2109 @ SY2107 ) )
| ~ ~ ( ~ ! [SY2110: $i] :
( ~ ( in @ SY2110 @ SV24 )
| ( in @ SY2110 @ SY2108 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2107 )
| ( in @ SX3 @ SY2108 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(577,plain,
! [SV72: $i] :
( ( ! [SY2222: $i] :
( ( disjoint @ SV72 @ SY2222 )
| ~ ( ~ ( in @ ( sK38_C @ SY2222 @ SV72 ) @ SV72 )
| ~ ( in @ ( sK38_C @ SY2222 @ SV72 ) @ SY2222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(578,plain,
! [SV73: $i] :
( ( ! [SY2223: $i] :
( ! [SY2224: $i] :
( ~ ( in @ SY2224 @ SV73 )
| ~ ( in @ SY2224 @ SY2223 ) )
| ~ ( disjoint @ SV73 @ SY2223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(579,plain,
! [SV25: $i,SV58: $i] :
( ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2193: $i] :
( ~ ( element @ SY2193 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SY2193
= ( complements_of_subsets @ SV25 @ SV58 ) ) )
| ~ ! [SY2194: $i] :
( ~ ( element @ SY2194 @ ( powerset @ ( powerset @ SV25 ) ) )
| ( SY2194
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2195: $i] :
( ~ ( element @ SY2195 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2195 @ SY2194 )
| ( in @ ( subset_complement @ SV25 @ SY2195 ) @ SV58 ) )
| ~ ! [SY2196: $i] :
( ~ ( element @ SY2196 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2196 ) @ SV58 )
| ( in @ SY2196 @ SY2194 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(580,plain,
! [SV26: $i] :
( ( ! [SY2117: $i,SY2118: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
!= SY2117 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2118 @ SY2117 @ SV26 ) @ SY2118 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
= SV26 )
| ( ( sK27_D @ SY2118 @ SY2117 @ SV26 )
= SY2117 ) ) )
| ( SY2118
= ( unordered_pair @ SV26 @ SY2117 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(581,plain,
! [SV26: $i] :
( ( ! [SY2119: $i,SY2120: $i] :
( ( SY2120
!= ( unordered_pair @ SV26 @ SY2119 ) )
| ~ ( ~ ! [SY2121: $i] :
( ~ ( in @ SY2121 @ SY2120 )
| ( SY2121 = SV26 )
| ( SY2121 = SY2119 ) )
| ~ ~ ( ~ ! [SY2122: $i] :
( ( SY2122 != SV26 )
| ( in @ SY2122 @ SY2120 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY2119 )
| ( in @ SX3 @ SY2120 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(582,plain,
! [SV59: $i,SV27: $i] :
( ( ~ ! [SY2197: $i] :
( ! [SY2198: $i] :
( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SY2197 @ SY2198 ) )
| ( SV27 = SY2197 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(583,plain,
! [SV59: $i,SV27: $i] :
( ( ~ ! [SY2199: $i,SY2200: $i] :
( ( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SY2199 @ SY2200 ) )
| ( SV59 = SY2200 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(584,plain,
! [SV60: $i,SV28: $i] :
( ( ~ ! [SY2201: $i,SY2202: $i] :
( ~ ( in @ SV28 @ SY2201 )
| ~ ( in @ SV60 @ SY2202 )
| ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2201 @ SY2202 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(585,plain,
! [SV60: $i,SV28: $i] :
( ( ~ ~ ( ~ ! [SY2203: $i] :
( ! [SY2204: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2203 @ SY2204 ) )
| ( in @ SV28 @ SY2203 ) )
| ~ ! [SY2205: $i,SY2206: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2205 @ SY2206 ) )
| ( in @ SV60 @ SY2206 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(586,plain,
! [SV29: $i] :
( ( ! [SY2136: $i] :
( ~ ( subset @ SY2136 @ ( sK4_B @ SV29 ) )
| ( are_equipotent @ SY2136 @ ( sK4_B @ SV29 ) )
| ( in @ SY2136 @ ( sK4_B @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(587,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY2137: $i] :
( ~ ( ~ ! [SY2138: $i] :
( ~ ( subset @ SY2138 @ SY2137 )
| ( in @ SY2138 @ ( sK5_SY2040 @ SY2137 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2137 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SY2137 @ ( sK4_B @ SV29 ) ) )
| ~ ~ ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(588,plain,
! [SV74: $i] :
( ( ! [SY2225: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SY2225 @ SV74 ) @ SY2225 )
| ~ ( subset @ ( sK28_C @ SY2225 @ SV74 ) @ SV74 ) )
| ~ ( ( in @ ( sK28_C @ SY2225 @ SV74 ) @ SY2225 )
| ( subset @ ( sK28_C @ SY2225 @ SV74 ) @ SV74 ) ) )
| ( SY2225
= ( powerset @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(589,plain,
! [SV75: $i] :
( ( ! [SY2226: $i] :
( ( SY2226
!= ( powerset @ SV75 ) )
| ~ ( ~ ! [SY2227: $i] :
( ~ ( in @ SY2227 @ SY2226 )
| ( subset @ SY2227 @ SV75 ) )
| ~ ! [SY2228: $i] :
( ~ ( subset @ SY2228 @ SV75 )
| ( in @ SY2228 @ SY2226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(590,plain,
! [SV30: $i] :
( ( ( ~ ! [SY2141: $i] :
( ~ ( ~ ( ! [SY2142: $i] :
~ ( in @ ( ordered_pair @ SY2142 @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2141 @ SV30 ) @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) ) )
| ( SY2141
= ( relation_rng @ SV30 ) ) )
| ~ ! [SY2143: $i] :
( ( SY2143
!= ( relation_rng @ SV30 ) )
| ~ ( ~ ! [SY2144: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2144 ) @ SV30 )
| ( in @ SY2144 @ SY2143 ) )
| ~ ! [SY2146: $i] :
( ~ ( in @ SY2146 @ SY2143 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2146 @ SY2143 @ SV30 ) @ SY2146 ) @ SV30 ) ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(591,plain,
! [SV31: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV31 )
| ~ ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV61 ) )
= $false )
| ( ( element @ SV31 @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(592,plain,
! [SV76: $i] :
( ( ! [SY2229: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SY2229 @ SV76 ) @ SV76 )
| ~ ~ ( in @ ( sK20_C @ SY2229 @ SV76 ) @ SY2229 ) )
| ( subset @ SV76 @ SY2229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(593,plain,
! [SV77: $i] :
( ( ! [SY2230: $i] :
( ~ ( subset @ SV77 @ SY2230 )
| ! [SY2231: $i] :
( ~ ( in @ SY2231 @ SV77 )
| ( in @ SY2231 @ SY2230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(594,plain,
! [SV32: $i] :
( ( ! [SY2148: $i,SY2149: $i] :
( ~ ( in @ SV32 @ SY2149 )
| ~ ( in @ SY2148 @ SY2149 )
| ( subset @ ( unordered_pair @ SV32 @ SY2148 ) @ SY2149 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(595,plain,
! [SV32: $i] :
( ( ~ ( ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2150 ) @ SY2151 )
| ( in @ SV32 @ SY2151 ) )
| ~ ! [SY2152: $i,SY2153: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2152 ) @ SY2153 )
| ( in @ SY2152 @ SY2153 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(596,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[525]) ).
thf(597,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)],[526]) ).
thf(598,plain,
! [SV33: $i] :
( ( ( ~ ! [SY2154: $i] :
( ~ ( ~ ( ! [SY2155: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ SY2155 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ ( sK18_SY2050 @ SY2154 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) ) )
| ( SY2154
= ( relation_dom @ SV33 ) ) )
| ~ ! [SY2156: $i] :
( ( SY2156
!= ( relation_dom @ SV33 ) )
| ~ ( ~ ! [SY2157: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2157 @ SY2158 ) @ SV33 )
| ( in @ SY2157 @ SY2156 ) )
| ~ ! [SY2159: $i] :
( ~ ( in @ SY2159 @ SY2156 )
| ( in @ ( ordered_pair @ SY2159 @ ( sK16_D @ SY2159 @ SY2156 @ SV33 ) ) @ SV33 ) ) ) ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(599,plain,
! [SV78: $i] :
( ( ! [SY2232: $i] :
( ~ ( in @ SV78 @ SY2232 )
| ( subset @ ( singleton @ SV78 ) @ SY2232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(600,plain,
! [SV79: $i] :
( ( ! [SY2233: $i] :
( ~ ( subset @ ( singleton @ SV79 ) @ SY2233 )
| ( in @ SV79 @ SY2233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(601,plain,
! [SV34: $i] :
( ( ! [SY2160: $i] :
( ~ ( subset @ SY2160 @ ( sK39_B @ SV34 ) )
| ( are_equipotent @ SY2160 @ ( sK39_B @ SV34 ) )
| ( in @ SY2160 @ ( sK39_B @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(602,plain,
! [SV34: $i] :
( ( ~ ( ~ ! [SY2161: $i] :
( ~ ( in @ SY2161 @ ( sK39_B @ SV34 ) )
| ( in @ ( powerset @ SY2161 ) @ ( sK39_B @ SV34 ) ) )
| ~ ~ ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) )
| ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(603,plain,
! [SV80: $i] :
( ( ! [SY2234: $i] :
( ~ ( ~ ( ( ( sK30_C @ SY2234 @ SV80 )
!= SV80 )
| ~ ( in @ ( sK30_C @ SY2234 @ SV80 ) @ SY2234 ) )
| ~ ( ( ( sK30_C @ SY2234 @ SV80 )
= SV80 )
| ( in @ ( sK30_C @ SY2234 @ SV80 ) @ SY2234 ) ) )
| ( SY2234
= ( singleton @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(604,plain,
! [SV81: $i] :
( ( ! [SY2235: $i] :
( ( SY2235
!= ( singleton @ SV81 ) )
| ~ ( ~ ! [SY2236: $i] :
( ( SY2236 != SV81 )
| ( in @ SY2236 @ SY2235 ) )
| ~ ! [SY2237: $i] :
( ~ ( in @ SY2237 @ SY2235 )
| ( SY2237 = SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(605,plain,
! [SV35: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) )
| ~ ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) ) )
= $false )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(606,plain,
! [SV63: $i,SV36: $i] :
( ( ~ ! [SY2207: $i,SY2208: $i] :
( ~ ( in @ SV36 @ SY2207 )
| ~ ( in @ SV63 @ SY2208 )
| ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2207 @ SY2208 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(607,plain,
! [SV63: $i,SV36: $i] :
( ( ~ ~ ( ~ ! [SY2209: $i] :
( ! [SY2210: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2209 @ SY2210 ) )
| ( in @ SV36 @ SY2209 ) )
| ~ ! [SY2211: $i,SY2212: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2211 @ SY2212 ) )
| ( in @ SV63 @ SY2212 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(608,plain,
! [SV82: $i] :
( ( ~ ( ~ ! [SY2238: $i,SY2239: $i] :
( ( sK36_B @ SV82 )
!= ( ordered_pair @ SY2238 @ SY2239 ) )
| ~ ( in @ ( sK36_B @ SV82 ) @ SV82 ) )
| ( relation @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(609,plain,
! [SV83: $i] :
( ( ~ ( relation @ SV83 )
| ! [SY2240: $i] :
( ( SY2240
= ( ordered_pair @ ( sK34_C @ SY2240 @ SV83 ) @ ( sK35_SY2059 @ SY2240 @ SV83 ) ) )
| ~ ( in @ SY2240 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(610,plain,
! [SV37: $i] :
( ( ( ~ ! [SY2172: $i] :
( ~ ( relation @ SY2172 )
| ~ ( subset @ SV37 @ SY2172 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SY2172 ) ) )
| ~ ! [SY2173: $i] :
( ~ ( relation @ SY2173 )
| ~ ( subset @ SV37 @ SY2173 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SY2173 ) ) ) )
= $false )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(611,plain,
! [SV84: $i] :
( ( ! [SY2241: $i] :
( ( disjoint @ SV84 @ SY2241 )
| ( in @ ( sK37_C @ SY2241 @ SV84 ) @ ( set_intersection2 @ SV84 @ SY2241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(612,plain,
! [SV85: $i] :
( ( ! [SY2242: $i] :
( ! [SY2243: $i] :
~ ( in @ SY2243 @ ( set_intersection2 @ SV85 @ SY2242 ) )
| ~ ( disjoint @ SV85 @ SY2242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(613,plain,
! [SV86: $i] :
( ( ! [SY2244: $i] :
( ( ( set_difference @ SV86 @ ( singleton @ SY2244 ) )
!= SV86 )
| ~ ( in @ SY2244 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(614,plain,
! [SV87: $i] :
( ( ! [SY2245: $i] :
( ( in @ SY2245 @ SV87 )
| ( ( set_difference @ SV87 @ ( singleton @ SY2245 ) )
= SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(615,plain,
! [SV88: $i] :
( ( ( in @ ( sK29_B @ SV88 ) @ SV88 )
| ( SV88 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(616,plain,
! [SV89: $i] :
( ( ( SV89 != empty_set )
| ! [SY2246: $i] :
~ ( in @ SY2246 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(617,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)],[545]) ).
thf(618,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)],[546]) ).
thf(619,plain,
! [SV38: $i] :
( ( ! [SY2174: $i,SY2175: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2174 )
| ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2174 )
| ( in @ ( sK12_D @ SY2175 @ SY2174 @ SV38 ) @ SY2175 ) ) ) )
| ( SY2175
= ( set_difference @ SV38 @ SY2174 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(620,plain,
! [SV38: $i] :
( ( ! [SY2176: $i,SY2177: $i] :
( ( SY2177
!= ( set_difference @ SV38 @ SY2176 ) )
| ~ ( ~ ! [SY2178: $i] :
( ~ ( in @ SY2178 @ SV38 )
| ( in @ SY2178 @ SY2176 )
| ( in @ SY2178 @ SY2177 ) )
| ~ ~ ( ~ ! [SY2179: $i] :
( ~ ( in @ SY2179 @ SY2177 )
| ( in @ SY2179 @ SV38 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2177 )
| ~ ( in @ SX3 @ SY2176 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(621,plain,
! [SV39: $i] :
( ( ! [SY2181: $i,SY2182: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2181 )
| ~ ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) )
| ~ ( ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2181 )
| ( in @ ( sK19_D @ SY2182 @ SY2181 @ SV39 ) @ SY2182 ) ) ) )
| ( SY2182
= ( set_intersection2 @ SV39 @ SY2181 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(622,plain,
! [SV39: $i] :
( ( ! [SY2183: $i,SY2184: $i] :
( ( SY2184
!= ( set_intersection2 @ SV39 @ SY2183 ) )
| ~ ( ~ ! [SY2185: $i] :
( ~ ( in @ SY2185 @ SV39 )
| ~ ( in @ SY2185 @ SY2183 )
| ( in @ SY2185 @ SY2184 ) )
| ~ ~ ( ~ ! [SY2186: $i] :
( ~ ( in @ SY2186 @ SY2184 )
| ( in @ SY2186 @ SV39 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2184 )
| ( in @ SX3 @ SY2183 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(623,plain,
! [SV41: $i,SV2: $i] :
( ( ( in @ SV2 @ SV41 )
= $false )
| ( ( disjoint @ ( singleton @ SV2 ) @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(624,plain,
! [SV4: $i,SV43: $i,SV90: $i] :
( ( ( ~ ( in @ SV90 @ SV43 )
| ( in @ SV90 @ SV4 ) )
= $true )
| ( ( element @ SV43 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(625,plain,
! [SV44: $i,SV5: $i,SV91: $i] :
( ( ( ( in @ SV91 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV44 @ ( singleton @ SV91 ) ) ) )
= $true )
| ( ( subset @ SV5 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(626,plain,
! [SV9: $i,SV64: $i] :
( ( ( element @ SV64 @ ( powerset @ SV9 ) )
= $false )
| ( ( ! [SY2213: $i] :
( ~ ( element @ SY2213 @ SV9 )
| ( in @ SY2213 @ SV64 )
| ( in @ SY2213 @ ( subset_complement @ SV9 @ SV64 ) ) ) )
= $true )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(627,plain,
! [SV47: $i,SV10: $i,SV65: $i] :
( ( ( element @ SV65 @ ( powerset @ SV10 ) )
= $false )
| ( ( ~ ( in @ SV47 @ ( subset_complement @ SV10 @ SV65 ) )
| ~ ( in @ SV47 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(628,plain,
! [SV12: $i,SV49: $i] :
( ( ( in @ SV49 @ SV12 )
= $false )
| ( ( in @ SV12 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(629,plain,
! [SV52: $i,SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV16 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(630,plain,
! [SV18: $i,SV54: $i] :
( ( ( empty @ SV54 )
= $true )
| ( ( in @ SV18 @ SV54 )
= $true )
| ( ( element @ SV18 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(631,plain,
! [SV19: $i,SV66: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( ~ ( in @ SV19 @ SV55 ) )
= $true )
| ( ( element @ SV19 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(632,plain,
! [SV20: $i,SV67: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( powerset @ SV67 ) ) )
= $true )
| ( ( ~ ( in @ SV20 @ SV56 ) )
= $true )
| ( ( ~ ( empty @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(633,plain,
! [SV57: $i,SV21: $i] :
( ( ( in @ SV21 @ SV57 )
= $false )
| ( ( empty @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(634,plain,
! [SV92: $i,SV68: $i] :
( ( ~ ( in @ SV68 @ SV92 )
| ( subset @ ( singleton @ SV68 ) @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(635,plain,
! [SV93: $i,SV69: $i] :
( ( ~ ( subset @ ( singleton @ SV69 ) @ SV93 )
| ( in @ SV69 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(636,plain,
! [SV94: $i,SV22: $i] :
( ( ! [SY2247: $i] :
( ~ ( relation @ SY2247 )
| ~ ( in @ ( ordered_pair @ SV22 @ SV94 ) @ SY2247 )
| ( in @ SV22 @ ( relation_dom @ SY2247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(637,plain,
! [SV95: $i,SV22: $i] :
( ( ! [SY2248: $i] :
( ~ ( relation @ SY2248 )
| ~ ( in @ ( ordered_pair @ SV22 @ SV95 ) @ SY2248 )
| ( in @ SV95 @ ( relation_rng @ SY2248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(638,plain,
! [SV96: $i,SV23: $i] :
( ( ! [SY2249: $i] :
( ~ ( ~ ( ! [SY2250: $i,SY2251: $i] :
( ~ ( in @ SY2250 @ SV23 )
| ~ ( in @ SY2251 @ SV96 )
| ( ( sK23_D @ SY2249 @ SV96 @ SV23 )
!= ( ordered_pair @ SY2250 @ SY2251 ) ) )
| ~ ( in @ ( sK23_D @ SY2249 @ SV96 @ SV23 ) @ SY2249 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2249 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SY2249 @ SV96 @ SV23 ) @ SV96 ) )
| ( ( sK23_D @ SY2249 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2249 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SY2249 @ SV96 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SY2249 @ SV96 @ SV23 ) @ SY2249 ) ) )
| ( SY2249
= ( cartesian_product2 @ SV23 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(639,plain,
! [SV97: $i,SV23: $i] :
( ( ! [SY2252: $i] :
( ( SY2252
!= ( cartesian_product2 @ SV23 @ SV97 ) )
| ~ ( ~ ! [SY2253: $i] :
( ! [SY2254: $i,SY2255: $i] :
( ~ ( in @ SY2254 @ SV23 )
| ~ ( in @ SY2255 @ SV97 )
| ( SY2253
!= ( ordered_pair @ SY2254 @ SY2255 ) ) )
| ( in @ SY2253 @ SY2252 ) )
| ~ ! [SY2256: $i] :
( ~ ( in @ SY2256 @ SY2252 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2256 @ SY2252 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2256 @ SY2252 @ SV97 @ SV23 ) @ SV97 ) )
| ( SY2256
!= ( ordered_pair @ ( sK21_E @ SY2256 @ SY2252 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SY2256 @ SY2252 @ SV97 @ SV23 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(640,plain,
! [SV70: $i,SV98: $i] :
( ( ~ ( ~ ( ! [SY2257: $i] :
( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SY2257 )
| ~ ( in @ SY2257 @ SV70 ) )
| ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) )
| ~ ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 ) )
| ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) ) )
| ( SV98
= ( union @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(641,plain,
! [SV71: $i,SV99: $i] :
( ( ( SV99
!= ( union @ SV71 ) )
| ~ ( ~ ! [SY2258: $i] :
( ! [SY2220: $i] :
( ~ ( in @ SY2258 @ SY2220 )
| ~ ( in @ SY2220 @ SV71 ) )
| ( in @ SY2258 @ SV99 ) )
| ~ ! [SY2260: $i] :
( ~ ( in @ SY2260 @ SV99 )
| ~ ( ~ ( in @ SY2260 @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(642,plain,
! [SV24: $i,SV100: $i] :
( ( ! [SY2261: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2261 @ SV100 @ SV24 ) @ SY2261 )
| ~ ( in @ ( sK26_D @ SY2261 @ SV100 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2261 @ SV100 @ SV24 ) @ SY2261 )
| ~ ( in @ ( sK26_D @ SY2261 @ SV100 @ SV24 ) @ SV100 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2261 @ SV100 @ SV24 ) @ SY2261 )
| ( in @ ( sK26_D @ SY2261 @ SV100 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SY2261 @ SV100 @ SV24 ) @ SV100 ) ) )
| ( SY2261
= ( set_union2 @ SV24 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(643,plain,
! [SV101: $i,SV24: $i] :
( ( ! [SY2262: $i] :
( ( SY2262
!= ( set_union2 @ SV24 @ SV101 ) )
| ~ ( ~ ! [SY2263: $i] :
( ~ ( in @ SY2263 @ SY2262 )
| ( in @ SY2263 @ SV24 )
| ( in @ SY2263 @ SV101 ) )
| ~ ~ ( ~ ! [SY2110: $i] :
( ~ ( in @ SY2110 @ SV24 )
| ( in @ SY2110 @ SY2262 ) )
| ~ ! [SY2265: $i] :
( ~ ( in @ SY2265 @ SV101 )
| ( in @ SY2265 @ SY2262 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(644,plain,
! [SV102: $i,SV72: $i] :
( ( ( disjoint @ SV72 @ SV102 )
| ~ ( ~ ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV72 )
| ~ ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(645,plain,
! [SV103: $i,SV73: $i] :
( ( ! [SY2266: $i] :
( ~ ( in @ SY2266 @ SV73 )
| ~ ( in @ SY2266 @ SV103 ) )
| ~ ( disjoint @ SV73 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(646,plain,
! [SV58: $i,SV25: $i] :
( ( ( ~ ! [SY2193: $i] :
( ~ ( element @ SY2193 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SY2193
= ( complements_of_subsets @ SV25 @ SV58 ) ) )
| ~ ! [SY2194: $i] :
( ~ ( element @ SY2194 @ ( powerset @ ( powerset @ SV25 ) ) )
| ( SY2194
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2195: $i] :
( ~ ( element @ SY2195 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2195 @ SY2194 )
| ( in @ ( subset_complement @ SV25 @ SY2195 ) @ SV58 ) )
| ~ ! [SY2196: $i] :
( ~ ( element @ SY2196 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2196 ) @ SV58 )
| ( in @ SY2196 @ SY2194 ) ) ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(647,plain,
! [SV26: $i,SV104: $i] :
( ( ! [SY2267: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2267 @ SV104 @ SV26 ) @ SY2267 )
| ( ( sK27_D @ SY2267 @ SV104 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2267 @ SV104 @ SV26 ) @ SY2267 )
| ( ( sK27_D @ SY2267 @ SV104 @ SV26 )
!= SV104 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2267 @ SV104 @ SV26 ) @ SY2267 )
| ( ( sK27_D @ SY2267 @ SV104 @ SV26 )
= SV26 )
| ( ( sK27_D @ SY2267 @ SV104 @ SV26 )
= SV104 ) ) )
| ( SY2267
= ( unordered_pair @ SV26 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(648,plain,
! [SV105: $i,SV26: $i] :
( ( ! [SY2268: $i] :
( ( SY2268
!= ( unordered_pair @ SV26 @ SV105 ) )
| ~ ( ~ ! [SY2269: $i] :
( ~ ( in @ SY2269 @ SY2268 )
| ( SY2269 = SV26 )
| ( SY2269 = SV105 ) )
| ~ ~ ( ~ ! [SY2122: $i] :
( ( SY2122 != SV26 )
| ( in @ SY2122 @ SY2268 ) )
| ~ ! [SY2271: $i] :
( ( SY2271 != SV105 )
| ( in @ SY2271 @ SY2268 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(649,plain,
! [SV59: $i,SV27: $i] :
( ( ! [SY2197: $i] :
( ! [SY2198: $i] :
( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SY2197 @ SY2198 ) )
| ( SV27 = SY2197 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(650,plain,
! [SV59: $i,SV27: $i] :
( ( ! [SY2199: $i,SY2200: $i] :
( ( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SY2199 @ SY2200 ) )
| ( SV59 = SY2200 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(651,plain,
! [SV60: $i,SV28: $i] :
( ( ! [SY2201: $i,SY2202: $i] :
( ~ ( in @ SV28 @ SY2201 )
| ~ ( in @ SV60 @ SY2202 )
| ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2201 @ SY2202 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(652,plain,
! [SV60: $i,SV28: $i] :
( ( ~ ( ~ ! [SY2203: $i] :
( ! [SY2204: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2203 @ SY2204 ) )
| ( in @ SV28 @ SY2203 ) )
| ~ ! [SY2205: $i,SY2206: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2205 @ SY2206 ) )
| ( in @ SV60 @ SY2206 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(653,plain,
! [SV29: $i,SV106: $i] :
( ( ~ ( subset @ SV106 @ ( sK4_B @ SV29 ) )
| ( are_equipotent @ SV106 @ ( sK4_B @ SV29 ) )
| ( in @ SV106 @ ( sK4_B @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(654,plain,
! [SV29: $i] :
( ( ~ ! [SY2137: $i] :
( ~ ( ~ ! [SY2138: $i] :
( ~ ( subset @ SY2138 @ SY2137 )
| ( in @ SY2138 @ ( sK5_SY2040 @ SY2137 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2137 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SY2137 @ ( sK4_B @ SV29 ) ) )
| ~ ~ ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(655,plain,
! [SV74: $i,SV107: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ~ ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) )
| ~ ( ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) ) )
| ( SV107
= ( powerset @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(656,plain,
! [SV75: $i,SV108: $i] :
( ( ( SV108
!= ( powerset @ SV75 ) )
| ~ ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ SV108 )
| ( subset @ SY2272 @ SV75 ) )
| ~ ! [SY2273: $i] :
( ~ ( subset @ SY2273 @ SV75 )
| ( in @ SY2273 @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(657,plain,
! [SV30: $i] :
( ( ( ~ ! [SY2141: $i] :
( ~ ( ~ ( ! [SY2142: $i] :
~ ( in @ ( ordered_pair @ SY2142 @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2141 @ SV30 ) @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) ) )
| ( SY2141
= ( relation_rng @ SV30 ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[590]) ).
thf(658,plain,
! [SV30: $i] :
( ( ( ~ ! [SY2143: $i] :
( ( SY2143
!= ( relation_rng @ SV30 ) )
| ~ ( ~ ! [SY2144: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2144 ) @ SV30 )
| ( in @ SY2144 @ SY2143 ) )
| ~ ! [SY2146: $i] :
( ~ ( in @ SY2146 @ SY2143 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2146 @ SY2143 @ SV30 ) @ SY2146 ) @ SV30 ) ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[590]) ).
thf(659,plain,
! [SV31: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV31 ) )
= $false )
| ( ( element @ SV31 @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(660,plain,
! [SV31: $i,SV61: $i] :
( ( ( ~ ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV61 ) )
= $false )
| ( ( element @ SV31 @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(661,plain,
! [SV76: $i,SV109: $i] :
( ( ~ ( ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV76 )
| ~ ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV109 ) )
| ( subset @ SV76 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(662,plain,
! [SV110: $i,SV77: $i] :
( ( ~ ( subset @ SV77 @ SV110 )
| ! [SY2274: $i] :
( ~ ( in @ SY2274 @ SV77 )
| ( in @ SY2274 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(663,plain,
! [SV111: $i,SV32: $i] :
( ( ! [SY2275: $i] :
( ~ ( in @ SV32 @ SY2275 )
| ~ ( in @ SV111 @ SY2275 )
| ( subset @ ( unordered_pair @ SV32 @ SV111 ) @ SY2275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(664,plain,
! [SV32: $i] :
( ( ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2150 ) @ SY2151 )
| ( in @ SV32 @ SY2151 ) )
| ~ ! [SY2152: $i,SY2153: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2152 ) @ SY2153 )
| ( in @ SY2152 @ SY2153 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(665,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(666,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[596]) ).
thf(667,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(668,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(669,plain,
! [SV33: $i] :
( ( ( ~ ! [SY2154: $i] :
( ~ ( ~ ( ! [SY2155: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ SY2155 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ ( sK18_SY2050 @ SY2154 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) ) )
| ( SY2154
= ( relation_dom @ SV33 ) ) ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(670,plain,
! [SV33: $i] :
( ( ( ~ ! [SY2156: $i] :
( ( SY2156
!= ( relation_dom @ SV33 ) )
| ~ ( ~ ! [SY2157: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2157 @ SY2158 ) @ SV33 )
| ( in @ SY2157 @ SY2156 ) )
| ~ ! [SY2159: $i] :
( ~ ( in @ SY2159 @ SY2156 )
| ( in @ ( ordered_pair @ SY2159 @ ( sK16_D @ SY2159 @ SY2156 @ SV33 ) ) @ SV33 ) ) ) ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(671,plain,
! [SV112: $i,SV78: $i] :
( ( ~ ( in @ SV78 @ SV112 )
| ( subset @ ( singleton @ SV78 ) @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(672,plain,
! [SV113: $i,SV79: $i] :
( ( ~ ( subset @ ( singleton @ SV79 ) @ SV113 )
| ( in @ SV79 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(673,plain,
! [SV34: $i,SV114: $i] :
( ( ~ ( subset @ SV114 @ ( sK39_B @ SV34 ) )
| ( are_equipotent @ SV114 @ ( sK39_B @ SV34 ) )
| ( in @ SV114 @ ( sK39_B @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(674,plain,
! [SV34: $i] :
( ( ~ ! [SY2161: $i] :
( ~ ( in @ SY2161 @ ( sK39_B @ SV34 ) )
| ( in @ ( powerset @ SY2161 ) @ ( sK39_B @ SV34 ) ) )
| ~ ~ ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) )
| ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(675,plain,
! [SV80: $i,SV115: $i] :
( ( ~ ( ~ ( ( ( sK30_C @ SV115 @ SV80 )
!= SV80 )
| ~ ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) )
| ~ ( ( ( sK30_C @ SV115 @ SV80 )
= SV80 )
| ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) ) )
| ( SV115
= ( singleton @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(676,plain,
! [SV81: $i,SV116: $i] :
( ( ( SV116
!= ( singleton @ SV81 ) )
| ~ ( ~ ! [SY2276: $i] :
( ( SY2276 != SV81 )
| ( in @ SY2276 @ SV116 ) )
| ~ ! [SY2277: $i] :
( ~ ( in @ SY2277 @ SV116 )
| ( SY2277 = SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(677,plain,
! [SV35: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) ) )
= $false )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(678,plain,
! [SV35: $i,SV62: $i] :
( ( ( ~ ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) ) )
= $false )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(679,plain,
! [SV63: $i,SV36: $i] :
( ( ! [SY2207: $i,SY2208: $i] :
( ~ ( in @ SV36 @ SY2207 )
| ~ ( in @ SV63 @ SY2208 )
| ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2207 @ SY2208 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(680,plain,
! [SV63: $i,SV36: $i] :
( ( ~ ( ~ ! [SY2209: $i] :
( ! [SY2210: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2209 @ SY2210 ) )
| ( in @ SV36 @ SY2209 ) )
| ~ ! [SY2211: $i,SY2212: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2211 @ SY2212 ) )
| ( in @ SV63 @ SY2212 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(681,plain,
! [SV82: $i] :
( ( ( ~ ( ~ ! [SY2238: $i,SY2239: $i] :
( ( sK36_B @ SV82 )
!= ( ordered_pair @ SY2238 @ SY2239 ) )
| ~ ( in @ ( sK36_B @ SV82 ) @ SV82 ) ) )
= $true )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(682,plain,
! [SV83: $i] :
( ( ( ~ ( relation @ SV83 ) )
= $true )
| ( ( ! [SY2240: $i] :
( ( SY2240
= ( ordered_pair @ ( sK34_C @ SY2240 @ SV83 ) @ ( sK35_SY2059 @ SY2240 @ SV83 ) ) )
| ~ ( in @ SY2240 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(683,plain,
! [SV37: $i] :
( ( ( ~ ! [SY2172: $i] :
( ~ ( relation @ SY2172 )
| ~ ( subset @ SV37 @ SY2172 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SY2172 ) ) ) )
= $false )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(684,plain,
! [SV37: $i] :
( ( ( ~ ! [SY2173: $i] :
( ~ ( relation @ SY2173 )
| ~ ( subset @ SV37 @ SY2173 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SY2173 ) ) ) )
= $false )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(685,plain,
! [SV117: $i,SV84: $i] :
( ( ( disjoint @ SV84 @ SV117 )
| ( in @ ( sK37_C @ SV117 @ SV84 ) @ ( set_intersection2 @ SV84 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(686,plain,
! [SV118: $i,SV85: $i] :
( ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( set_intersection2 @ SV85 @ SV118 ) )
| ~ ( disjoint @ SV85 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(687,plain,
! [SV119: $i,SV86: $i] :
( ( ( ( set_difference @ SV86 @ ( singleton @ SV119 ) )
!= SV86 )
| ~ ( in @ SV119 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(688,plain,
! [SV87: $i,SV120: $i] :
( ( ( in @ SV120 @ SV87 )
| ( ( set_difference @ SV87 @ ( singleton @ SV120 ) )
= SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(689,plain,
! [SV88: $i] :
( ( ( in @ ( sK29_B @ SV88 ) @ SV88 )
= $true )
| ( ( SV88 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(690,plain,
! [SV89: $i] :
( ( ( ( SV89 != empty_set ) )
= $true )
| ( ( ! [SY2246: $i] :
~ ( in @ SY2246 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(691,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(692,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(693,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(694,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(695,plain,
! [SV38: $i,SV121: $i] :
( ( ! [SY2279: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2279 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2279 @ SV121 @ SV38 ) @ SV121 )
| ~ ( in @ ( sK12_D @ SY2279 @ SV121 @ SV38 ) @ SY2279 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2279 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SY2279 @ SV121 @ SV38 ) @ SY2279 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2279 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SY2279 @ SV121 @ SV38 ) @ SY2279 ) ) ) )
| ( SY2279
= ( set_difference @ SV38 @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(696,plain,
! [SV122: $i,SV38: $i] :
( ( ! [SY2280: $i] :
( ( SY2280
!= ( set_difference @ SV38 @ SV122 ) )
| ~ ( ~ ! [SY2281: $i] :
( ~ ( in @ SY2281 @ SV38 )
| ( in @ SY2281 @ SV122 )
| ( in @ SY2281 @ SY2280 ) )
| ~ ~ ( ~ ! [SY2179: $i] :
( ~ ( in @ SY2179 @ SY2280 )
| ( in @ SY2179 @ SV38 ) )
| ~ ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SY2280 )
| ~ ( in @ SY2283 @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(697,plain,
! [SV39: $i,SV123: $i] :
( ( ! [SY2284: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2284 @ SV123 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SY2284 @ SV123 @ SV39 ) @ SV123 )
| ~ ( in @ ( sK19_D @ SY2284 @ SV123 @ SV39 ) @ SY2284 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2284 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SY2284 @ SV123 @ SV39 ) @ SY2284 ) )
| ~ ( ( in @ ( sK19_D @ SY2284 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SY2284 @ SV123 @ SV39 ) @ SY2284 ) ) ) )
| ( SY2284
= ( set_intersection2 @ SV39 @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(698,plain,
! [SV124: $i,SV39: $i] :
( ( ! [SY2285: $i] :
( ( SY2285
!= ( set_intersection2 @ SV39 @ SV124 ) )
| ~ ( ~ ! [SY2286: $i] :
( ~ ( in @ SY2286 @ SV39 )
| ~ ( in @ SY2286 @ SV124 )
| ( in @ SY2286 @ SY2285 ) )
| ~ ~ ( ~ ! [SY2186: $i] :
( ~ ( in @ SY2186 @ SY2285 )
| ( in @ SY2186 @ SV39 ) )
| ~ ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SY2285 )
| ( in @ SY2288 @ SV124 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(699,plain,
! [SV4: $i,SV43: $i,SV90: $i] :
( ( ( ~ ( in @ SV90 @ SV43 ) )
= $true )
| ( ( in @ SV90 @ SV4 )
= $true )
| ( ( element @ SV43 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(700,plain,
! [SV44: $i,SV5: $i,SV91: $i] :
( ( ( in @ SV91 @ SV5 )
= $true )
| ( ( subset @ SV5 @ ( set_difference @ SV44 @ ( singleton @ SV91 ) ) )
= $true )
| ( ( subset @ SV5 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(701,plain,
! [SV64: $i,SV9: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ SV9 )
| ( in @ SV125 @ SV64 )
| ( in @ SV125 @ ( subset_complement @ SV9 @ SV64 ) ) )
= $true )
| ( ( element @ SV64 @ ( powerset @ SV9 ) )
= $false )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(702,plain,
! [SV65: $i,SV10: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ ( subset_complement @ SV10 @ SV65 ) ) )
= $true )
| ( ( ~ ( in @ SV47 @ SV65 ) )
= $true )
| ( ( element @ SV65 @ ( powerset @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(703,plain,
! [SV16: $i,SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ ( set_union2 @ SV16 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(704,plain,
! [SV19: $i,SV66: $i,SV55: $i] :
( ( ( element @ SV55 @ ( powerset @ SV66 ) )
= $false )
| ( ( ~ ( in @ SV19 @ SV55 ) )
= $true )
| ( ( element @ SV19 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(705,plain,
! [SV20: $i,SV67: $i,SV56: $i] :
( ( ( element @ SV56 @ ( powerset @ SV67 ) )
= $false )
| ( ( ~ ( in @ SV20 @ SV56 ) )
= $true )
| ( ( ~ ( empty @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(706,plain,
! [SV92: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ SV92 ) )
= $true )
| ( ( subset @ ( singleton @ SV68 ) @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(707,plain,
! [SV93: $i,SV69: $i] :
( ( ( ~ ( subset @ ( singleton @ SV69 ) @ SV93 ) )
= $true )
| ( ( in @ SV69 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(708,plain,
! [SV94: $i,SV22: $i,SV126: $i] :
( ( ~ ( relation @ SV126 )
| ~ ( in @ ( ordered_pair @ SV22 @ SV94 ) @ SV126 )
| ( in @ SV22 @ ( relation_dom @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(709,plain,
! [SV95: $i,SV22: $i,SV127: $i] :
( ( ~ ( relation @ SV127 )
| ~ ( in @ ( ordered_pair @ SV22 @ SV95 ) @ SV127 )
| ( in @ SV95 @ ( relation_rng @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(710,plain,
! [SV128: $i,SV96: $i,SV23: $i] :
( ( ~ ( ~ ( ! [SY2289: $i,SY2290: $i] :
( ~ ( in @ SY2289 @ SV23 )
| ~ ( in @ SY2290 @ SV96 )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SY2289 @ SY2290 ) ) )
| ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) ) )
| ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(711,plain,
! [SV97: $i,SV23: $i,SV129: $i] :
( ( ( SV129
!= ( cartesian_product2 @ SV23 @ SV97 ) )
| ~ ( ~ ! [SY2291: $i] :
( ! [SY2254: $i,SY2255: $i] :
( ~ ( in @ SY2254 @ SV23 )
| ~ ( in @ SY2255 @ SV97 )
| ( SY2291
!= ( ordered_pair @ SY2254 @ SY2255 ) ) )
| ( in @ SY2291 @ SV129 ) )
| ~ ! [SY2294: $i] :
( ~ ( in @ SY2294 @ SV129 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SY2294
!= ( ordered_pair @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(712,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( ~ ( ! [SY2257: $i] :
( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SY2257 )
| ~ ( in @ SY2257 @ SV70 ) )
| ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) )
| ~ ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 ) )
| ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) ) ) )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(713,plain,
! [SV71: $i,SV99: $i] :
( ( ( ( SV99
!= ( union @ SV71 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2258: $i] :
( ! [SY2220: $i] :
( ~ ( in @ SY2258 @ SY2220 )
| ~ ( in @ SY2220 @ SV71 ) )
| ( in @ SY2258 @ SV99 ) )
| ~ ! [SY2260: $i] :
( ~ ( in @ SY2260 @ SV99 )
| ~ ( ~ ( in @ SY2260 @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(714,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) )
| ~ ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) )
| ( SV130
= ( set_union2 @ SV24 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(715,plain,
! [SV101: $i,SV24: $i,SV131: $i] :
( ( ( SV131
!= ( set_union2 @ SV24 @ SV101 ) )
| ~ ( ~ ! [SY2295: $i] :
( ~ ( in @ SY2295 @ SV131 )
| ( in @ SY2295 @ SV24 )
| ( in @ SY2295 @ SV101 ) )
| ~ ~ ( ~ ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) )
| ~ ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(716,plain,
! [SV102: $i,SV72: $i] :
( ( ( disjoint @ SV72 @ SV102 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV72 )
| ~ ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(717,plain,
! [SV103: $i,SV73: $i] :
( ( ( ! [SY2266: $i] :
( ~ ( in @ SY2266 @ SV73 )
| ~ ( in @ SY2266 @ SV103 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV73 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(718,plain,
! [SV58: $i,SV25: $i] :
( ( ( ~ ! [SY2193: $i] :
( ~ ( element @ SY2193 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SY2193
= ( complements_of_subsets @ SV25 @ SV58 ) ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(719,plain,
! [SV58: $i,SV25: $i] :
( ( ( ~ ! [SY2194: $i] :
( ~ ( element @ SY2194 @ ( powerset @ ( powerset @ SV25 ) ) )
| ( SY2194
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2195: $i] :
( ~ ( element @ SY2195 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2195 @ SY2194 )
| ( in @ ( subset_complement @ SV25 @ SY2195 ) @ SV58 ) )
| ~ ! [SY2196: $i] :
( ~ ( element @ SY2196 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2196 ) @ SV58 )
| ( in @ SY2196 @ SY2194 ) ) ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(720,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) ) )
| ~ ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV26 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV104 ) ) )
| ( SV132
= ( unordered_pair @ SV26 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(721,plain,
! [SV105: $i,SV26: $i,SV133: $i] :
( ( ( SV133
!= ( unordered_pair @ SV26 @ SV105 ) )
| ~ ( ~ ! [SY2298: $i] :
( ~ ( in @ SY2298 @ SV133 )
| ( SY2298 = SV26 )
| ( SY2298 = SV105 ) )
| ~ ~ ( ~ ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) )
| ~ ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(722,plain,
! [SV134: $i,SV59: $i,SV27: $i] :
( ( ! [SY2301: $i] :
( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SV134 @ SY2301 ) )
| ( SV27 = SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(723,plain,
! [SV135: $i,SV59: $i,SV27: $i] :
( ( ! [SY2302: $i] :
( ( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SV135 @ SY2302 ) )
| ( SV59 = SY2302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(724,plain,
! [SV60: $i,SV136: $i,SV28: $i] :
( ( ! [SY2303: $i] :
( ~ ( in @ SV28 @ SV136 )
| ~ ( in @ SV60 @ SY2303 )
| ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV136 @ SY2303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(725,plain,
! [SV60: $i,SV28: $i] :
( ( ~ ! [SY2203: $i] :
( ! [SY2204: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2203 @ SY2204 ) )
| ( in @ SV28 @ SY2203 ) )
| ~ ! [SY2205: $i,SY2206: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2205 @ SY2206 ) )
| ( in @ SV60 @ SY2206 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(726,plain,
! [SV29: $i,SV106: $i] :
( ( ( ~ ( subset @ SV106 @ ( sK4_B @ SV29 ) )
| ( are_equipotent @ SV106 @ ( sK4_B @ SV29 ) ) )
= $true )
| ( ( in @ SV106 @ ( sK4_B @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(727,plain,
! [SV29: $i] :
( ( ~ ! [SY2137: $i] :
( ~ ( ~ ! [SY2138: $i] :
( ~ ( subset @ SY2138 @ SY2137 )
| ( in @ SY2138 @ ( sK5_SY2040 @ SY2137 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2137 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SY2137 @ ( sK4_B @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(728,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(729,plain,
! [SV74: $i,SV107: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ~ ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) )
| ~ ( ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) ) ) )
= $true )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(730,plain,
! [SV75: $i,SV108: $i] :
( ( ( ( SV108
!= ( powerset @ SV75 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ SV108 )
| ( subset @ SY2272 @ SV75 ) )
| ~ ! [SY2273: $i] :
( ~ ( subset @ SY2273 @ SV75 )
| ( in @ SY2273 @ SV108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(731,plain,
! [SV30: $i] :
( ( ( ! [SY2141: $i] :
( ~ ( ~ ( ! [SY2142: $i] :
~ ( in @ ( ordered_pair @ SY2142 @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2141 @ SV30 ) @ ( sK10_C @ SY2141 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SY2141 @ SV30 ) @ SY2141 ) ) )
| ( SY2141
= ( relation_rng @ SV30 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(732,plain,
! [SV30: $i] :
( ( ( ! [SY2143: $i] :
( ( SY2143
!= ( relation_rng @ SV30 ) )
| ~ ( ~ ! [SY2144: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2144 ) @ SV30 )
| ( in @ SY2144 @ SY2143 ) )
| ~ ! [SY2146: $i] :
( ~ ( in @ SY2146 @ SY2143 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2146 @ SY2143 @ SV30 ) @ SY2146 ) @ SV30 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[658]) ).
thf(733,plain,
! [SV31: $i,SV61: $i] :
( ( ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV31 )
= $true )
| ( ( element @ SV31 @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(734,plain,
! [SV31: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV61 ) )
= $true )
| ( ( element @ SV31 @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(735,plain,
! [SV76: $i,SV109: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV76 )
| ~ ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV109 ) ) )
= $true )
| ( ( subset @ SV76 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(736,plain,
! [SV110: $i,SV77: $i] :
( ( ( ~ ( subset @ SV77 @ SV110 ) )
= $true )
| ( ( ! [SY2274: $i] :
( ~ ( in @ SY2274 @ SV77 )
| ( in @ SY2274 @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(737,plain,
! [SV111: $i,SV137: $i,SV32: $i] :
( ( ~ ( in @ SV32 @ SV137 )
| ~ ( in @ SV111 @ SV137 )
| ( subset @ ( unordered_pair @ SV32 @ SV111 ) @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(738,plain,
! [SV32: $i] :
( ( ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2150 ) @ SY2151 )
| ( in @ SV32 @ SY2151 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(739,plain,
! [SV32: $i] :
( ( ~ ! [SY2152: $i,SY2153: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2152 ) @ SY2153 )
| ( in @ SY2152 @ SY2153 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(740,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[665]) ).
thf(741,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[666]) ).
thf(742,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(743,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(744,plain,
! [SV33: $i] :
( ( ( ! [SY2154: $i] :
( ~ ( ~ ( ! [SY2155: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ SY2155 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2154 @ SV33 ) @ ( sK18_SY2050 @ SY2154 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SY2154 @ SV33 ) @ SY2154 ) ) )
| ( SY2154
= ( relation_dom @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(745,plain,
! [SV33: $i] :
( ( ( ! [SY2156: $i] :
( ( SY2156
!= ( relation_dom @ SV33 ) )
| ~ ( ~ ! [SY2157: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2157 @ SY2158 ) @ SV33 )
| ( in @ SY2157 @ SY2156 ) )
| ~ ! [SY2159: $i] :
( ~ ( in @ SY2159 @ SY2156 )
| ( in @ ( ordered_pair @ SY2159 @ ( sK16_D @ SY2159 @ SY2156 @ SV33 ) ) @ SV33 ) ) ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(746,plain,
! [SV112: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ SV112 ) )
= $true )
| ( ( subset @ ( singleton @ SV78 ) @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(747,plain,
! [SV113: $i,SV79: $i] :
( ( ( ~ ( subset @ ( singleton @ SV79 ) @ SV113 ) )
= $true )
| ( ( in @ SV79 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(748,plain,
! [SV34: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ ( sK39_B @ SV34 ) )
| ( are_equipotent @ SV114 @ ( sK39_B @ SV34 ) ) )
= $true )
| ( ( in @ SV114 @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(749,plain,
! [SV34: $i] :
( ( ~ ! [SY2161: $i] :
( ~ ( in @ SY2161 @ ( sK39_B @ SV34 ) )
| ( in @ ( powerset @ SY2161 ) @ ( sK39_B @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(750,plain,
! [SV34: $i] :
( ( ~ ~ ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) )
| ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(751,plain,
! [SV80: $i,SV115: $i] :
( ( ( ~ ( ~ ( ( ( sK30_C @ SV115 @ SV80 )
!= SV80 )
| ~ ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) )
| ~ ( ( ( sK30_C @ SV115 @ SV80 )
= SV80 )
| ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) ) ) )
= $true )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(752,plain,
! [SV81: $i,SV116: $i] :
( ( ( ( SV116
!= ( singleton @ SV81 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2276: $i] :
( ( SY2276 != SV81 )
| ( in @ SY2276 @ SV116 ) )
| ~ ! [SY2277: $i] :
( ~ ( in @ SY2277 @ SV116 )
| ( SY2277 = SV81 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(753,plain,
! [SV35: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) )
= $true )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(754,plain,
! [SV35: $i,SV62: $i] :
( ( ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
| ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) )
= $true )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(755,plain,
! [SV63: $i,SV138: $i,SV36: $i] :
( ( ! [SY2304: $i] :
( ~ ( in @ SV36 @ SV138 )
| ~ ( in @ SV63 @ SY2304 )
| ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV138 @ SY2304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(756,plain,
! [SV63: $i,SV36: $i] :
( ( ~ ! [SY2209: $i] :
( ! [SY2210: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2209 @ SY2210 ) )
| ( in @ SV36 @ SY2209 ) )
| ~ ! [SY2211: $i,SY2212: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2211 @ SY2212 ) )
| ( in @ SV63 @ SY2212 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(757,plain,
! [SV82: $i] :
( ( ( ~ ! [SY2238: $i,SY2239: $i] :
( ( sK36_B @ SV82 )
!= ( ordered_pair @ SY2238 @ SY2239 ) )
| ~ ( in @ ( sK36_B @ SV82 ) @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(758,plain,
! [SV83: $i] :
( ( ( relation @ SV83 )
= $false )
| ( ( ! [SY2240: $i] :
( ( SY2240
= ( ordered_pair @ ( sK34_C @ SY2240 @ SV83 ) @ ( sK35_SY2059 @ SY2240 @ SV83 ) ) )
| ~ ( in @ SY2240 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(759,plain,
! [SV37: $i] :
( ( ( ! [SY2172: $i] :
( ~ ( relation @ SY2172 )
| ~ ( subset @ SV37 @ SY2172 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SY2172 ) ) ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(760,plain,
! [SV37: $i] :
( ( ( ! [SY2173: $i] :
( ~ ( relation @ SY2173 )
| ~ ( subset @ SV37 @ SY2173 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SY2173 ) ) ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[684]) ).
thf(761,plain,
! [SV117: $i,SV84: $i] :
( ( ( disjoint @ SV84 @ SV117 )
= $true )
| ( ( in @ ( sK37_C @ SV117 @ SV84 ) @ ( set_intersection2 @ SV84 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(762,plain,
! [SV118: $i,SV85: $i] :
( ( ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( set_intersection2 @ SV85 @ SV118 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV85 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(763,plain,
! [SV119: $i,SV86: $i] :
( ( ( ( ( set_difference @ SV86 @ ( singleton @ SV119 ) )
!= SV86 ) )
= $true )
| ( ( ~ ( in @ SV119 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(764,plain,
! [SV87: $i,SV120: $i] :
( ( ( in @ SV120 @ SV87 )
= $true )
| ( ( ( set_difference @ SV87 @ ( singleton @ SV120 ) )
= SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(765,plain,
! [SV89: $i] :
( ( ( SV89 = empty_set )
= $false )
| ( ( ! [SY2246: $i] :
~ ( in @ SY2246 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(766,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(767,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(768,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(769,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(770,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) ) )
| ( SV139
= ( set_difference @ SV38 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(771,plain,
! [SV122: $i,SV38: $i,SV140: $i] :
( ( ( SV140
!= ( set_difference @ SV38 @ SV122 ) )
| ~ ( ~ ! [SY2305: $i] :
( ~ ( in @ SY2305 @ SV38 )
| ( in @ SY2305 @ SV122 )
| ( in @ SY2305 @ SV140 ) )
| ~ ~ ( ~ ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) )
| ~ ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(772,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) ) )
| ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(773,plain,
! [SV124: $i,SV39: $i,SV142: $i] :
( ( ( SV142
!= ( set_intersection2 @ SV39 @ SV124 ) )
| ~ ( ~ ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV39 )
| ~ ( in @ SY2308 @ SV124 )
| ( in @ SY2308 @ SV142 ) )
| ~ ~ ( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) )
| ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(774,plain,
! [SV4: $i,SV43: $i,SV90: $i] :
( ( ( in @ SV90 @ SV43 )
= $false )
| ( ( in @ SV90 @ SV4 )
= $true )
| ( ( element @ SV43 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(775,plain,
! [SV64: $i,SV9: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ SV9 ) )
= $true )
| ( ( ( in @ SV125 @ SV64 )
| ( in @ SV125 @ ( subset_complement @ SV9 @ SV64 ) ) )
= $true )
| ( ( element @ SV64 @ ( powerset @ SV9 ) )
= $false )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(776,plain,
! [SV65: $i,SV10: $i,SV47: $i] :
( ( ( in @ SV47 @ ( subset_complement @ SV10 @ SV65 ) )
= $false )
| ( ( ~ ( in @ SV47 @ SV65 ) )
= $true )
| ( ( element @ SV65 @ ( powerset @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(777,plain,
! [SV66: $i,SV55: $i,SV19: $i] :
( ( ( in @ SV19 @ SV55 )
= $false )
| ( ( element @ SV55 @ ( powerset @ SV66 ) )
= $false )
| ( ( element @ SV19 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(778,plain,
! [SV67: $i,SV56: $i,SV20: $i] :
( ( ( in @ SV20 @ SV56 )
= $false )
| ( ( element @ SV56 @ ( powerset @ SV67 ) )
= $false )
| ( ( ~ ( empty @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(779,plain,
! [SV92: $i,SV68: $i] :
( ( ( in @ SV68 @ SV92 )
= $false )
| ( ( subset @ ( singleton @ SV68 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(780,plain,
! [SV93: $i,SV69: $i] :
( ( ( subset @ ( singleton @ SV69 ) @ SV93 )
= $false )
| ( ( in @ SV69 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(781,plain,
! [SV94: $i,SV22: $i,SV126: $i] :
( ( ( ~ ( relation @ SV126 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV22 @ SV94 ) @ SV126 )
| ( in @ SV22 @ ( relation_dom @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(782,plain,
! [SV95: $i,SV22: $i,SV127: $i] :
( ( ( ~ ( relation @ SV127 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV22 @ SV95 ) @ SV127 )
| ( in @ SV95 @ ( relation_rng @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(783,plain,
! [SV128: $i,SV96: $i,SV23: $i] :
( ( ( ~ ( ~ ( ! [SY2289: $i,SY2290: $i] :
( ~ ( in @ SY2289 @ SV23 )
| ~ ( in @ SY2290 @ SV96 )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SY2289 @ SY2290 ) ) )
| ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) ) ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(784,plain,
! [SV97: $i,SV23: $i,SV129: $i] :
( ( ( ( SV129
!= ( cartesian_product2 @ SV23 @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2291: $i] :
( ! [SY2254: $i,SY2255: $i] :
( ~ ( in @ SY2254 @ SV23 )
| ~ ( in @ SY2255 @ SV97 )
| ( SY2291
!= ( ordered_pair @ SY2254 @ SY2255 ) ) )
| ( in @ SY2291 @ SV129 ) )
| ~ ! [SY2294: $i] :
( ~ ( in @ SY2294 @ SV129 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SY2294
!= ( ordered_pair @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(785,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( ! [SY2257: $i] :
( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SY2257 )
| ~ ( in @ SY2257 @ SV70 ) )
| ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) )
| ~ ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 ) )
| ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) ) )
= $false )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(786,plain,
! [SV71: $i,SV99: $i] :
( ( ( SV99
= ( union @ SV71 ) )
= $false )
| ( ( ~ ( ~ ! [SY2258: $i] :
( ! [SY2220: $i] :
( ~ ( in @ SY2258 @ SY2220 )
| ~ ( in @ SY2220 @ SV71 ) )
| ( in @ SY2258 @ SV99 ) )
| ~ ! [SY2260: $i] :
( ~ ( in @ SY2260 @ SV99 )
| ~ ( ~ ( in @ SY2260 @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(787,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) )
| ~ ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(788,plain,
! [SV101: $i,SV24: $i,SV131: $i] :
( ( ( ( SV131
!= ( set_union2 @ SV24 @ SV101 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2295: $i] :
( ~ ( in @ SY2295 @ SV131 )
| ( in @ SY2295 @ SV24 )
| ( in @ SY2295 @ SV101 ) )
| ~ ~ ( ~ ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) )
| ~ ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(789,plain,
! [SV72: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV72 )
| ~ ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV102 ) )
= $false )
| ( ( disjoint @ SV72 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(790,plain,
! [SV103: $i,SV73: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV73 )
| ~ ( in @ SV143 @ SV103 ) )
= $true )
| ( ( ~ ( disjoint @ SV73 @ SV103 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(791,plain,
! [SV58: $i,SV25: $i] :
( ( ( ! [SY2193: $i] :
( ~ ( element @ SY2193 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) @ SY2193 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SY2193 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SY2193
= ( complements_of_subsets @ SV25 @ SV58 ) ) ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(792,plain,
! [SV58: $i,SV25: $i] :
( ( ( ! [SY2194: $i] :
( ~ ( element @ SY2194 @ ( powerset @ ( powerset @ SV25 ) ) )
| ( SY2194
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2195: $i] :
( ~ ( element @ SY2195 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2195 @ SY2194 )
| ( in @ ( subset_complement @ SV25 @ SY2195 ) @ SV58 ) )
| ~ ! [SY2196: $i] :
( ~ ( element @ SY2196 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2196 ) @ SV58 )
| ( in @ SY2196 @ SY2194 ) ) ) ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(793,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) ) )
| ~ ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV26 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV104 ) ) ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(794,plain,
! [SV105: $i,SV26: $i,SV133: $i] :
( ( ( ( SV133
!= ( unordered_pair @ SV26 @ SV105 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2298: $i] :
( ~ ( in @ SY2298 @ SV133 )
| ( SY2298 = SV26 )
| ( SY2298 = SV105 ) )
| ~ ~ ( ~ ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) )
| ~ ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(795,plain,
! [SV134: $i,SV59: $i,SV27: $i] :
( ( ( ! [SY2301: $i] :
( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SV134 @ SY2301 ) ) )
= $true )
| ( ( SV27 = SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(796,plain,
! [SV144: $i,SV135: $i,SV59: $i,SV27: $i] :
( ( ( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SV135 @ SV144 ) )
| ( SV59 = SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(797,plain,
! [SV145: $i,SV60: $i,SV136: $i,SV28: $i] :
( ( ~ ( in @ SV28 @ SV136 )
| ~ ( in @ SV60 @ SV145 )
| ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV136 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(798,plain,
! [SV60: $i,SV28: $i] :
( ( ~ ! [SY2203: $i] :
( ! [SY2204: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2203 @ SY2204 ) )
| ( in @ SV28 @ SY2203 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(799,plain,
! [SV60: $i,SV28: $i] :
( ( ~ ! [SY2205: $i,SY2206: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2205 @ SY2206 ) )
| ( in @ SV60 @ SY2206 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(800,plain,
! [SV29: $i,SV106: $i] :
( ( ( ~ ( subset @ SV106 @ ( sK4_B @ SV29 ) ) )
= $true )
| ( ( are_equipotent @ SV106 @ ( sK4_B @ SV29 ) )
= $true )
| ( ( in @ SV106 @ ( sK4_B @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(801,plain,
! [SV29: $i] :
( ( ! [SY2137: $i] :
( ~ ( ~ ! [SY2138: $i] :
( ~ ( subset @ SY2138 @ SY2137 )
| ( in @ SY2138 @ ( sK5_SY2040 @ SY2137 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2137 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SY2137 @ ( sK4_B @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(802,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(803,plain,
! [SV74: $i,SV107: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ~ ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) )
| ~ ( ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) ) )
= $false )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(804,plain,
! [SV75: $i,SV108: $i] :
( ( ( SV108
= ( powerset @ SV75 ) )
= $false )
| ( ( ~ ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ SV108 )
| ( subset @ SY2272 @ SV75 ) )
| ~ ! [SY2273: $i] :
( ~ ( subset @ SY2273 @ SV75 )
| ( in @ SY2273 @ SV108 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(805,plain,
! [SV30: $i,SV146: $i] :
( ( ( ~ ( ~ ( ! [SY2311: $i] :
~ ( in @ ( ordered_pair @ SY2311 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV146 @ SV30 ) @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) ) )
| ( SV146
= ( relation_rng @ SV30 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(806,plain,
! [SV30: $i,SV147: $i] :
( ( ( ( SV147
!= ( relation_rng @ SV30 ) )
| ~ ( ~ ! [SY2312: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2312 ) @ SV30 )
| ( in @ SY2312 @ SV147 ) )
| ~ ! [SY2314: $i] :
( ~ ( in @ SY2314 @ SV147 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2314 @ SV147 @ SV30 ) @ SY2314 ) @ SV30 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(807,plain,
! [SV31: $i,SV61: $i] :
( ( ( in @ ( sK40_C @ SV61 @ SV31 ) @ SV61 )
= $false )
| ( ( element @ SV31 @ ( powerset @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(808,plain,
! [SV76: $i,SV109: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV76 )
| ~ ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV109 ) )
= $false )
| ( ( subset @ SV76 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(809,plain,
! [SV110: $i,SV77: $i] :
( ( ( subset @ SV77 @ SV110 )
= $false )
| ( ( ! [SY2274: $i] :
( ~ ( in @ SY2274 @ SV77 )
| ( in @ SY2274 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(810,plain,
! [SV111: $i,SV137: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV137 )
| ~ ( in @ SV111 @ SV137 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV32 @ SV111 ) @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(811,plain,
! [SV32: $i] :
( ( ! [SY2150: $i,SY2151: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2150 ) @ SY2151 )
| ( in @ SV32 @ SY2151 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(812,plain,
! [SV32: $i] :
( ( ! [SY2152: $i,SY2153: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SY2152 ) @ SY2153 )
| ( in @ SY2152 @ SY2153 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(813,plain,
! [SV148: $i] :
( ( ( SV148 = empty_set )
| ! [SY2315: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SY2315 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SY2315 @ SV148 ) @ ( sK33_SY2057 @ SY2315 @ SV148 ) ) )
| ~ ( in @ ( sK32_C @ SY2315 @ SV148 ) @ SY2315 ) )
| ~ ( ! [SY2316: $i] :
( ~ ( in @ SY2316 @ SV148 )
| ( in @ ( sK32_C @ SY2315 @ SV148 ) @ SY2316 ) )
| ( in @ ( sK32_C @ SY2315 @ SV148 ) @ SY2315 ) ) )
| ( SY2315
= ( set_meet @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(814,plain,
! [SV149: $i] :
( ( ( SV149 = empty_set )
| ! [SY2317: $i] :
( ( SY2317
!= ( set_meet @ SV149 ) )
| ~ ( ~ ! [SY2318: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2318 @ SY2317 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SY2318 @ ( sK31_D @ SY2318 @ SY2317 @ SV149 ) ) )
| ( in @ SY2318 @ SY2317 ) )
| ~ ! [SY2319: $i] :
( ~ ( in @ SY2319 @ SY2317 )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV149 )
| ( in @ SY2319 @ SY2320 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(815,plain,
! [SV150: $i] :
( ( ( SV150 != empty_set )
| ! [SY2321: $i] :
( ( SY2321
!= ( set_meet @ SV150 ) )
| ( SY2321 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(816,plain,
! [SV151: $i] :
( ( ( SV151 != empty_set )
| ! [SY2322: $i] :
( ( SY2322 != empty_set )
| ( SY2322
= ( set_meet @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(817,plain,
! [SV33: $i,SV152: $i] :
( ( ( ~ ( ~ ( ! [SY2323: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SY2323 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ ( sK18_SY2050 @ SV152 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) ) )
| ( SV152
= ( relation_dom @ SV33 ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(818,plain,
! [SV33: $i,SV153: $i] :
( ( ( ( SV153
!= ( relation_dom @ SV33 ) )
| ~ ( ~ ! [SY2324: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2324 @ SY2158 ) @ SV33 )
| ( in @ SY2324 @ SV153 ) )
| ~ ! [SY2326: $i] :
( ~ ( in @ SY2326 @ SV153 )
| ( in @ ( ordered_pair @ SY2326 @ ( sK16_D @ SY2326 @ SV153 @ SV33 ) ) @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(819,plain,
! [SV112: $i,SV78: $i] :
( ( ( in @ SV78 @ SV112 )
= $false )
| ( ( subset @ ( singleton @ SV78 ) @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(820,plain,
! [SV113: $i,SV79: $i] :
( ( ( subset @ ( singleton @ SV79 ) @ SV113 )
= $false )
| ( ( in @ SV79 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(821,plain,
! [SV34: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ ( sK39_B @ SV34 ) ) )
= $true )
| ( ( are_equipotent @ SV114 @ ( sK39_B @ SV34 ) )
= $true )
| ( ( in @ SV114 @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(822,plain,
! [SV34: $i] :
( ( ! [SY2161: $i] :
( ~ ( in @ SY2161 @ ( sK39_B @ SV34 ) )
| ( in @ ( powerset @ SY2161 ) @ ( sK39_B @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(823,plain,
! [SV34: $i] :
( ( ~ ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) )
| ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(824,plain,
! [SV80: $i,SV115: $i] :
( ( ( ~ ( ( ( sK30_C @ SV115 @ SV80 )
!= SV80 )
| ~ ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) )
| ~ ( ( ( sK30_C @ SV115 @ SV80 )
= SV80 )
| ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) ) )
= $false )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(825,plain,
! [SV81: $i,SV116: $i] :
( ( ( SV116
= ( singleton @ SV81 ) )
= $false )
| ( ( ~ ( ~ ! [SY2276: $i] :
( ( SY2276 != SV81 )
| ( in @ SY2276 @ SV116 ) )
| ~ ! [SY2277: $i] :
( ~ ( in @ SY2277 @ SV116 )
| ( SY2277 = SV81 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(826,plain,
! [SV35: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 ) )
= $true )
| ( ( ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) )
= $true )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(827,plain,
! [SV35: $i,SV62: $i] :
( ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
= $true )
| ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 )
= $true )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(828,plain,
! [SV154: $i,SV63: $i,SV138: $i,SV36: $i] :
( ( ~ ( in @ SV36 @ SV138 )
| ~ ( in @ SV63 @ SV154 )
| ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV138 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(829,plain,
! [SV63: $i,SV36: $i] :
( ( ~ ! [SY2209: $i] :
( ! [SY2210: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2209 @ SY2210 ) )
| ( in @ SV36 @ SY2209 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(830,plain,
! [SV63: $i,SV36: $i] :
( ( ~ ! [SY2211: $i,SY2212: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2211 @ SY2212 ) )
| ( in @ SV63 @ SY2212 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(831,plain,
! [SV82: $i] :
( ( ( ~ ! [SY2238: $i,SY2239: $i] :
( ( sK36_B @ SV82 )
!= ( ordered_pair @ SY2238 @ SY2239 ) ) )
= $false )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(832,plain,
! [SV82: $i] :
( ( ( ~ ( in @ ( sK36_B @ SV82 ) @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(833,plain,
! [SV83: $i,SV155: $i] :
( ( ( ( SV155
= ( ordered_pair @ ( sK34_C @ SV155 @ SV83 ) @ ( sK35_SY2059 @ SV155 @ SV83 ) ) )
| ~ ( in @ SV155 @ SV83 ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(834,plain,
! [SV37: $i,SV156: $i] :
( ( ( ~ ( relation @ SV156 )
| ~ ( subset @ SV37 @ SV156 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SV156 ) ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(835,plain,
! [SV37: $i,SV157: $i] :
( ( ( ~ ( relation @ SV157 )
| ~ ( subset @ SV37 @ SV157 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(836,plain,
! [SV118: $i,SV85: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ ( set_intersection2 @ SV85 @ SV118 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV85 @ SV118 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(837,plain,
! [SV119: $i,SV86: $i] :
( ( ( ( set_difference @ SV86 @ ( singleton @ SV119 ) )
= SV86 )
= $false )
| ( ( ~ ( in @ SV119 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(838,plain,
! [SV89: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV89 ) )
= $true )
| ( ( SV89 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(839,plain,
! [SV160: $i] :
( ( ( empty @ SV160 )
| ! [SY2327: $i] :
( ~ ( element @ SY2327 @ SV160 )
| ( in @ SY2327 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(840,plain,
! [SV161: $i] :
( ( ( empty @ SV161 )
| ! [SY2328: $i] :
( ~ ( in @ SY2328 @ SV161 )
| ( element @ SY2328 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(841,plain,
! [SV162: $i] :
( ( ~ ( empty @ SV162 )
| ! [SY2329: $i] :
( ~ ( element @ SY2329 @ SV162 )
| ( empty @ SY2329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(842,plain,
! [SV163: $i] :
( ( ~ ( empty @ SV163 )
| ! [SY2330: $i] :
( ~ ( empty @ SY2330 )
| ( element @ SY2330 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(843,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) ) ) )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(844,plain,
! [SV122: $i,SV38: $i,SV140: $i] :
( ( ( ( SV140
!= ( set_difference @ SV38 @ SV122 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2305: $i] :
( ~ ( in @ SY2305 @ SV38 )
| ( in @ SY2305 @ SV122 )
| ( in @ SY2305 @ SV140 ) )
| ~ ~ ( ~ ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) )
| ~ ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(845,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) ) ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(846,plain,
! [SV124: $i,SV39: $i,SV142: $i] :
( ( ( ( SV142
!= ( set_intersection2 @ SV39 @ SV124 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV39 )
| ~ ( in @ SY2308 @ SV124 )
| ( in @ SY2308 @ SV142 ) )
| ~ ~ ( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) )
| ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(847,plain,
! [SV64: $i,SV9: $i,SV125: $i] :
( ( ( element @ SV125 @ SV9 )
= $false )
| ( ( ( in @ SV125 @ SV64 )
| ( in @ SV125 @ ( subset_complement @ SV9 @ SV64 ) ) )
= $true )
| ( ( element @ SV64 @ ( powerset @ SV9 ) )
= $false )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(848,plain,
! [SV10: $i,SV65: $i,SV47: $i] :
( ( ( in @ SV47 @ SV65 )
= $false )
| ( ( in @ SV47 @ ( subset_complement @ SV10 @ SV65 ) )
= $false )
| ( ( element @ SV65 @ ( powerset @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(849,plain,
! [SV20: $i,SV56: $i,SV67: $i] :
( ( ( empty @ SV67 )
= $false )
| ( ( element @ SV56 @ ( powerset @ SV67 ) )
= $false )
| ( ( in @ SV20 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(850,plain,
! [SV94: $i,SV22: $i,SV126: $i] :
( ( ( relation @ SV126 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV22 @ SV94 ) @ SV126 )
| ( in @ SV22 @ ( relation_dom @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(851,plain,
! [SV95: $i,SV22: $i,SV127: $i] :
( ( ( relation @ SV127 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV22 @ SV95 ) @ SV127 )
| ( in @ SV95 @ ( relation_rng @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(852,plain,
! [SV128: $i,SV96: $i,SV23: $i] :
( ( ( ~ ( ! [SY2289: $i,SY2290: $i] :
( ~ ( in @ SY2289 @ SV23 )
| ~ ( in @ SY2290 @ SV96 )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SY2289 @ SY2290 ) ) )
| ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) ) )
= $false )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(853,plain,
! [SV97: $i,SV23: $i,SV129: $i] :
( ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false )
| ( ( ~ ( ~ ! [SY2291: $i] :
( ! [SY2254: $i,SY2255: $i] :
( ~ ( in @ SY2254 @ SV23 )
| ~ ( in @ SY2255 @ SV97 )
| ( SY2291
!= ( ordered_pair @ SY2254 @ SY2255 ) ) )
| ( in @ SY2291 @ SV129 ) )
| ~ ! [SY2294: $i] :
( ~ ( in @ SY2294 @ SV129 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SY2294
!= ( ordered_pair @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(854,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( ! [SY2257: $i] :
( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SY2257 )
| ~ ( in @ SY2257 @ SV70 ) )
| ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) ) )
= $false )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(855,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) )
| ~ ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 ) )
| ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) ) )
= $false )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(856,plain,
! [SV99: $i,SV71: $i] :
( ( ( ~ ! [SY2258: $i] :
( ! [SY2220: $i] :
( ~ ( in @ SY2258 @ SY2220 )
| ~ ( in @ SY2220 @ SV71 ) )
| ( in @ SY2258 @ SV99 ) )
| ~ ! [SY2260: $i] :
( ~ ( in @ SY2260 @ SV99 )
| ~ ( ~ ( in @ SY2260 @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) @ SV71 ) ) ) )
= $false )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(857,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) )
| ~ ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) )
= $false )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(858,plain,
! [SV101: $i,SV24: $i,SV131: $i] :
( ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false )
| ( ( ~ ( ~ ! [SY2295: $i] :
( ~ ( in @ SY2295 @ SV131 )
| ( in @ SY2295 @ SV24 )
| ( in @ SY2295 @ SV101 ) )
| ~ ~ ( ~ ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) )
| ~ ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(859,plain,
! [SV72: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV72 ) )
= $false )
| ( ( disjoint @ SV72 @ SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(860,plain,
! [SV72: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV102 ) )
= $false )
| ( ( disjoint @ SV72 @ SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(861,plain,
! [SV103: $i,SV73: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV73 ) )
= $true )
| ( ( ~ ( in @ SV143 @ SV103 ) )
= $true )
| ( ( ~ ( disjoint @ SV73 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(862,plain,
! [SV58: $i,SV25: $i,SV164: $i] :
( ( ( ~ ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(863,plain,
! [SV58: $i,SV25: $i,SV165: $i] :
( ( ( ~ ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
| ( SV165
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2331: $i] :
( ~ ( element @ SY2331 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2331 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SY2331 ) @ SV58 ) )
| ~ ! [SY2332: $i] :
( ~ ( element @ SY2332 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2332 ) @ SV58 )
| ( in @ SY2332 @ SV165 ) ) ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(864,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) ) )
| ~ ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV26 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV104 ) ) )
= $false )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(865,plain,
! [SV105: $i,SV26: $i,SV133: $i] :
( ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false )
| ( ( ~ ( ~ ! [SY2298: $i] :
( ~ ( in @ SY2298 @ SV133 )
| ( SY2298 = SV26 )
| ( SY2298 = SV105 ) )
| ~ ~ ( ~ ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) )
| ~ ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(866,plain,
! [SV166: $i,SV134: $i,SV59: $i,SV27: $i] :
( ( ( ( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SV134 @ SV166 ) ) )
= $true )
| ( ( SV27 = SV134 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(867,plain,
! [SV144: $i,SV135: $i,SV59: $i,SV27: $i] :
( ( ( ( ( ordered_pair @ SV27 @ SV59 )
!= ( ordered_pair @ SV135 @ SV144 ) ) )
= $true )
| ( ( SV59 = SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(868,plain,
! [SV145: $i,SV60: $i,SV136: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV136 )
| ~ ( in @ SV60 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV136 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(869,plain,
! [SV60: $i,SV28: $i] :
( ( ! [SY2203: $i] :
( ! [SY2204: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2203 @ SY2204 ) )
| ( in @ SV28 @ SY2203 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(870,plain,
! [SV60: $i,SV28: $i] :
( ( ! [SY2205: $i,SY2206: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SY2205 @ SY2206 ) )
| ( in @ SV60 @ SY2206 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(871,plain,
! [SV29: $i,SV106: $i] :
( ( ( subset @ SV106 @ ( sK4_B @ SV29 ) )
= $false )
| ( ( are_equipotent @ SV106 @ ( sK4_B @ SV29 ) )
= $true )
| ( ( in @ SV106 @ ( sK4_B @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(872,plain,
! [SV29: $i,SV167: $i] :
( ( ~ ( ~ ! [SY2333: $i] :
( ~ ( subset @ SY2333 @ SV167 )
| ( in @ SY2333 @ ( sK5_SY2040 @ SV167 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SV167 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(873,plain,
! [SV29: $i] :
( ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) )
| ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(874,plain,
! [SV74: $i,SV107: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ~ ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) ) )
= $false )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[803]) ).
thf(875,plain,
! [SV74: $i,SV107: $i] :
( ( ( ~ ( ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) ) )
= $false )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[803]) ).
thf(876,plain,
! [SV75: $i,SV108: $i] :
( ( ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ SV108 )
| ( subset @ SY2272 @ SV75 ) )
| ~ ! [SY2273: $i] :
( ~ ( subset @ SY2273 @ SV75 )
| ( in @ SY2273 @ SV108 ) ) )
= $false )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(877,plain,
! [SV30: $i,SV146: $i] :
( ( ( ~ ( ~ ( ! [SY2311: $i] :
~ ( in @ ( ordered_pair @ SY2311 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV146 @ SV30 ) @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) ) ) )
= $true )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(878,plain,
! [SV30: $i,SV147: $i] :
( ( ( ( SV147
!= ( relation_rng @ SV30 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2312: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2312 ) @ SV30 )
| ( in @ SY2312 @ SV147 ) )
| ~ ! [SY2314: $i] :
( ~ ( in @ SY2314 @ SV147 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2314 @ SV147 @ SV30 ) @ SY2314 ) @ SV30 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(879,plain,
! [SV76: $i,SV109: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV76 ) )
= $false )
| ( ( subset @ SV76 @ SV109 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(880,plain,
! [SV76: $i,SV109: $i] :
( ( ( ~ ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV109 ) )
= $false )
| ( ( subset @ SV76 @ SV109 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(881,plain,
! [SV110: $i,SV77: $i,SV168: $i] :
( ( ( ~ ( in @ SV168 @ SV77 )
| ( in @ SV168 @ SV110 ) )
= $true )
| ( ( subset @ SV77 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(882,plain,
! [SV111: $i,SV137: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV137 ) )
= $true )
| ( ( ~ ( in @ SV111 @ SV137 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV32 @ SV111 ) @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(883,plain,
! [SV169: $i,SV32: $i] :
( ( ! [SY2334: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SV169 ) @ SY2334 )
| ( in @ SV32 @ SY2334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(884,plain,
! [SV170: $i,SV32: $i] :
( ( ! [SY2335: $i] :
( ~ ( subset @ ( unordered_pair @ SV32 @ SV170 ) @ SY2335 )
| ( in @ SV170 @ SY2335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(885,plain,
! [SV148: $i] :
( ( ( SV148 = empty_set )
= $true )
| ( ( ! [SY2315: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SY2315 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SY2315 @ SV148 ) @ ( sK33_SY2057 @ SY2315 @ SV148 ) ) )
| ~ ( in @ ( sK32_C @ SY2315 @ SV148 ) @ SY2315 ) )
| ~ ( ! [SY2316: $i] :
( ~ ( in @ SY2316 @ SV148 )
| ( in @ ( sK32_C @ SY2315 @ SV148 ) @ SY2316 ) )
| ( in @ ( sK32_C @ SY2315 @ SV148 ) @ SY2315 ) ) )
| ( SY2315
= ( set_meet @ SV148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(886,plain,
! [SV149: $i] :
( ( ( SV149 = empty_set )
= $true )
| ( ( ! [SY2317: $i] :
( ( SY2317
!= ( set_meet @ SV149 ) )
| ~ ( ~ ! [SY2318: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2318 @ SY2317 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SY2318 @ ( sK31_D @ SY2318 @ SY2317 @ SV149 ) ) )
| ( in @ SY2318 @ SY2317 ) )
| ~ ! [SY2319: $i] :
( ~ ( in @ SY2319 @ SY2317 )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV149 )
| ( in @ SY2319 @ SY2320 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(887,plain,
! [SV150: $i] :
( ( ( ( SV150 != empty_set ) )
= $true )
| ( ( ! [SY2321: $i] :
( ( SY2321
!= ( set_meet @ SV150 ) )
| ( SY2321 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(888,plain,
! [SV151: $i] :
( ( ( ( SV151 != empty_set ) )
= $true )
| ( ( ! [SY2322: $i] :
( ( SY2322 != empty_set )
| ( SY2322
= ( set_meet @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(889,plain,
! [SV33: $i,SV152: $i] :
( ( ( ~ ( ~ ( ! [SY2323: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SY2323 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ ( sK18_SY2050 @ SV152 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) ) ) )
= $true )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(890,plain,
! [SV33: $i,SV153: $i] :
( ( ( ( SV153
!= ( relation_dom @ SV33 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2324: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2324 @ SY2158 ) @ SV33 )
| ( in @ SY2324 @ SV153 ) )
| ~ ! [SY2326: $i] :
( ~ ( in @ SY2326 @ SV153 )
| ( in @ ( ordered_pair @ SY2326 @ ( sK16_D @ SY2326 @ SV153 @ SV33 ) ) @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(891,plain,
! [SV34: $i,SV114: $i] :
( ( ( subset @ SV114 @ ( sK39_B @ SV34 ) )
= $false )
| ( ( are_equipotent @ SV114 @ ( sK39_B @ SV34 ) )
= $true )
| ( ( in @ SV114 @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(892,plain,
! [SV34: $i,SV171: $i] :
( ( ~ ( in @ SV171 @ ( sK39_B @ SV34 ) )
| ( in @ ( powerset @ SV171 ) @ ( sK39_B @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(893,plain,
! [SV34: $i] :
( ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) )
| ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(894,plain,
! [SV80: $i,SV115: $i] :
( ( ( ~ ( ( ( sK30_C @ SV115 @ SV80 )
!= SV80 )
| ~ ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) ) )
= $false )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(895,plain,
! [SV80: $i,SV115: $i] :
( ( ( ~ ( ( ( sK30_C @ SV115 @ SV80 )
= SV80 )
| ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) ) )
= $false )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(896,plain,
! [SV116: $i,SV81: $i] :
( ( ( ~ ! [SY2276: $i] :
( ( SY2276 != SV81 )
| ( in @ SY2276 @ SV116 ) )
| ~ ! [SY2277: $i] :
( ~ ( in @ SY2277 @ SV116 )
| ( SY2277 = SV81 ) ) )
= $false )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(897,plain,
! [SV35: $i,SV62: $i] :
( ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
= $false )
| ( ( ~ ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 ) )
= $true )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(898,plain,
! [SV154: $i,SV63: $i,SV138: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ SV138 )
| ~ ( in @ SV63 @ SV154 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV138 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(899,plain,
! [SV63: $i,SV36: $i] :
( ( ! [SY2209: $i] :
( ! [SY2210: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2209 @ SY2210 ) )
| ( in @ SV36 @ SY2209 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(900,plain,
! [SV63: $i,SV36: $i] :
( ( ! [SY2211: $i,SY2212: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SY2211 @ SY2212 ) )
| ( in @ SV63 @ SY2212 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(901,plain,
! [SV82: $i] :
( ( ( ! [SY2238: $i,SY2239: $i] :
( ( sK36_B @ SV82 )
!= ( ordered_pair @ SY2238 @ SY2239 ) ) )
= $true )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(902,plain,
! [SV82: $i] :
( ( ( in @ ( sK36_B @ SV82 ) @ SV82 )
= $true )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(903,plain,
! [SV83: $i,SV155: $i] :
( ( ( SV155
= ( ordered_pair @ ( sK34_C @ SV155 @ SV83 ) @ ( sK35_SY2059 @ SV155 @ SV83 ) ) )
= $true )
| ( ( ~ ( in @ SV155 @ SV83 ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(904,plain,
! [SV37: $i,SV156: $i] :
( ( ( ~ ( relation @ SV156 ) )
= $true )
| ( ( ~ ( subset @ SV37 @ SV156 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SV156 ) ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(905,plain,
! [SV37: $i,SV157: $i] :
( ( ( ~ ( relation @ SV157 ) )
= $true )
| ( ( ~ ( subset @ SV37 @ SV157 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(906,plain,
! [SV118: $i,SV85: $i,SV158: $i] :
( ( ( in @ SV158 @ ( set_intersection2 @ SV85 @ SV118 ) )
= $false )
| ( ( ~ ( disjoint @ SV85 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(907,plain,
! [SV86: $i,SV119: $i] :
( ( ( in @ SV119 @ SV86 )
= $false )
| ( ( ( set_difference @ SV86 @ ( singleton @ SV119 ) )
= SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(908,plain,
! [SV89: $i,SV159: $i] :
( ( ( in @ SV159 @ SV89 )
= $false )
| ( ( SV89 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(909,plain,
! [SV160: $i] :
( ( ( empty @ SV160 )
= $true )
| ( ( ! [SY2327: $i] :
( ~ ( element @ SY2327 @ SV160 )
| ( in @ SY2327 @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(910,plain,
! [SV161: $i] :
( ( ( empty @ SV161 )
= $true )
| ( ( ! [SY2328: $i] :
( ~ ( in @ SY2328 @ SV161 )
| ( element @ SY2328 @ SV161 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(911,plain,
! [SV162: $i] :
( ( ( ~ ( empty @ SV162 ) )
= $true )
| ( ( ! [SY2329: $i] :
( ~ ( element @ SY2329 @ SV162 )
| ( empty @ SY2329 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(912,plain,
! [SV163: $i] :
( ( ( ~ ( empty @ SV163 ) )
= $true )
| ( ( ! [SY2330: $i] :
( ~ ( empty @ SY2330 )
| ( element @ SY2330 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(913,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) ) )
= $false )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(914,plain,
! [SV122: $i,SV38: $i,SV140: $i] :
( ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false )
| ( ( ~ ( ~ ! [SY2305: $i] :
( ~ ( in @ SY2305 @ SV38 )
| ( in @ SY2305 @ SV122 )
| ( in @ SY2305 @ SV140 ) )
| ~ ~ ( ~ ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) )
| ~ ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(915,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) ) )
= $false )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(916,plain,
! [SV124: $i,SV39: $i,SV142: $i] :
( ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false )
| ( ( ~ ( ~ ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV39 )
| ~ ( in @ SY2308 @ SV124 )
| ( in @ SY2308 @ SV142 ) )
| ~ ~ ( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) )
| ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(917,plain,
! [SV9: $i,SV64: $i,SV125: $i] :
( ( ( in @ SV125 @ SV64 )
= $true )
| ( ( in @ SV125 @ ( subset_complement @ SV9 @ SV64 ) )
= $true )
| ( ( element @ SV125 @ SV9 )
= $false )
| ( ( element @ SV64 @ ( powerset @ SV9 ) )
= $false )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(918,plain,
! [SV126: $i,SV94: $i,SV22: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV22 @ SV94 ) @ SV126 ) )
= $true )
| ( ( in @ SV22 @ ( relation_dom @ SV126 ) )
= $true )
| ( ( relation @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(919,plain,
! [SV127: $i,SV95: $i,SV22: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV22 @ SV95 ) @ SV127 ) )
= $true )
| ( ( in @ SV95 @ ( relation_rng @ SV127 ) )
= $true )
| ( ( relation @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(920,plain,
! [SV128: $i,SV96: $i,SV23: $i] :
( ( ( ~ ( ! [SY2289: $i,SY2290: $i] :
( ~ ( in @ SY2289 @ SV23 )
| ~ ( in @ SY2290 @ SV96 )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SY2289 @ SY2290 ) ) )
| ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) ) )
= $false )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(921,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) ) )
= $false )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(922,plain,
! [SV129: $i,SV97: $i,SV23: $i] :
( ( ( ~ ! [SY2291: $i] :
( ! [SY2254: $i,SY2255: $i] :
( ~ ( in @ SY2254 @ SV23 )
| ~ ( in @ SY2255 @ SV97 )
| ( SY2291
!= ( ordered_pair @ SY2254 @ SY2255 ) ) )
| ( in @ SY2291 @ SV129 ) )
| ~ ! [SY2294: $i] :
( ~ ( in @ SY2294 @ SV129 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SY2294
!= ( ordered_pair @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) ) ) ) ) )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(923,plain,
! [SV70: $i,SV98: $i] :
( ( ( ! [SY2257: $i] :
( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SY2257 )
| ~ ( in @ SY2257 @ SV70 ) )
| ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(924,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) )
| ~ ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 ) )
| ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(925,plain,
! [SV99: $i,SV71: $i] :
( ( ( ~ ! [SY2258: $i] :
( ! [SY2220: $i] :
( ~ ( in @ SY2258 @ SY2220 )
| ~ ( in @ SY2220 @ SV71 ) )
| ( in @ SY2258 @ SV99 ) ) )
= $false )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(926,plain,
! [SV71: $i,SV99: $i] :
( ( ( ~ ! [SY2260: $i] :
( ~ ( in @ SY2260 @ SV99 )
| ~ ( ~ ( in @ SY2260 @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) @ SV71 ) ) ) )
= $false )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(927,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) ) )
= $false )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(928,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) )
= $false )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(929,plain,
! [SV101: $i,SV24: $i,SV131: $i] :
( ( ( ~ ! [SY2295: $i] :
( ~ ( in @ SY2295 @ SV131 )
| ( in @ SY2295 @ SV24 )
| ( in @ SY2295 @ SV101 ) )
| ~ ~ ( ~ ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) )
| ~ ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) ) )
= $false )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(930,plain,
! [SV72: $i,SV102: $i] :
( ( ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV72 )
= $true )
| ( ( disjoint @ SV72 @ SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(931,plain,
! [SV72: $i,SV102: $i] :
( ( ( in @ ( sK38_C @ SV102 @ SV72 ) @ SV102 )
= $true )
| ( ( disjoint @ SV72 @ SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(932,plain,
! [SV103: $i,SV73: $i,SV143: $i] :
( ( ( in @ SV143 @ SV73 )
= $false )
| ( ( ~ ( in @ SV143 @ SV103 ) )
= $true )
| ( ( ~ ( disjoint @ SV73 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(933,plain,
! [SV58: $i,SV25: $i,SV164: $i] :
( ( ( ~ ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(934,plain,
! [SV58: $i,SV25: $i,SV165: $i] :
( ( ( ~ ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) ) )
= $true )
| ( ( ( SV165
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2331: $i] :
( ~ ( element @ SY2331 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2331 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SY2331 ) @ SV58 ) )
| ~ ! [SY2332: $i] :
( ~ ( element @ SY2332 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2332 ) @ SV58 )
| ( in @ SY2332 @ SV165 ) ) ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(935,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) ) ) )
= $false )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(936,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV26 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV104 ) ) )
= $false )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(937,plain,
! [SV105: $i,SV26: $i,SV133: $i] :
( ( ( ~ ! [SY2298: $i] :
( ~ ( in @ SY2298 @ SV133 )
| ( SY2298 = SV26 )
| ( SY2298 = SV105 ) )
| ~ ~ ( ~ ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) )
| ~ ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) ) )
= $false )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(938,plain,
! [SV166: $i,SV134: $i,SV59: $i,SV27: $i] :
( ( ( ( ordered_pair @ SV27 @ SV59 )
= ( ordered_pair @ SV134 @ SV166 ) )
= $false )
| ( ( SV27 = SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(939,plain,
! [SV144: $i,SV135: $i,SV59: $i,SV27: $i] :
( ( ( ( ordered_pair @ SV27 @ SV59 )
= ( ordered_pair @ SV135 @ SV144 ) )
= $false )
| ( ( SV59 = SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(940,plain,
! [SV145: $i,SV60: $i,SV136: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV136 ) )
= $true )
| ( ( ~ ( in @ SV60 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV136 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(941,plain,
! [SV172: $i,SV60: $i,SV28: $i] :
( ( ! [SY2336: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV172 @ SY2336 ) )
| ( in @ SV28 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(942,plain,
! [SV173: $i,SV60: $i,SV28: $i] :
( ( ! [SY2337: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV173 @ SY2337 ) )
| ( in @ SV60 @ SY2337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(943,plain,
! [SV29: $i,SV167: $i] :
( ( ( ~ ( ~ ! [SY2333: $i] :
( ~ ( subset @ SY2333 @ SV167 )
| ( in @ SY2333 @ ( sK5_SY2040 @ SV167 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SV167 @ SV29 ) @ ( sK4_B @ SV29 ) ) ) )
= $true )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(944,plain,
! [SV29: $i] :
( ( ~ ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(945,plain,
! [SV29: $i] :
( ( ~ ( in @ SV29 @ ( sK4_B @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(946,plain,
! [SV74: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ~ ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) )
= $true )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(947,plain,
! [SV74: $i,SV107: $i] :
( ( ( ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
| ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) )
= $true )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(948,plain,
! [SV75: $i,SV108: $i] :
( ( ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ SV108 )
| ( subset @ SY2272 @ SV75 ) ) )
= $false )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(949,plain,
! [SV108: $i,SV75: $i] :
( ( ( ~ ! [SY2273: $i] :
( ~ ( subset @ SY2273 @ SV75 )
| ( in @ SY2273 @ SV108 ) ) )
= $false )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(950,plain,
! [SV30: $i,SV146: $i] :
( ( ( ~ ( ! [SY2311: $i] :
~ ( in @ ( ordered_pair @ SY2311 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV146 @ SV30 ) @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) ) )
= $false )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(951,plain,
! [SV30: $i,SV147: $i] :
( ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( ~ ( ~ ! [SY2312: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2312 ) @ SV30 )
| ( in @ SY2312 @ SV147 ) )
| ~ ! [SY2314: $i] :
( ~ ( in @ SY2314 @ SV147 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2314 @ SV147 @ SV30 ) @ SY2314 ) @ SV30 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(952,plain,
! [SV76: $i,SV109: $i] :
( ( ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV76 )
= $true )
| ( ( subset @ SV76 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(953,plain,
! [SV76: $i,SV109: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV109 ) )
= $true )
| ( ( subset @ SV76 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(954,plain,
! [SV110: $i,SV77: $i,SV168: $i] :
( ( ( ~ ( in @ SV168 @ SV77 ) )
= $true )
| ( ( in @ SV168 @ SV110 )
= $true )
| ( ( subset @ SV77 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(955,plain,
! [SV111: $i,SV137: $i,SV32: $i] :
( ( ( in @ SV32 @ SV137 )
= $false )
| ( ( ~ ( in @ SV111 @ SV137 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV32 @ SV111 ) @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(956,plain,
! [SV174: $i,SV169: $i,SV32: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV32 @ SV169 ) @ SV174 )
| ( in @ SV32 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(957,plain,
! [SV175: $i,SV170: $i,SV32: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV32 @ SV170 ) @ SV175 )
| ( in @ SV170 @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(958,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) )
| ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
| ~ ( ! [SY2338: $i] :
( ~ ( in @ SY2338 @ SV148 )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SY2338 ) )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) ) )
| ( SV176
= ( set_meet @ SV148 ) ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(959,plain,
! [SV149: $i,SV177: $i] :
( ( ( ( SV177
!= ( set_meet @ SV149 ) )
| ~ ( ~ ! [SY2339: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SY2339 @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) ) )
| ( in @ SY2339 @ SV177 ) )
| ~ ! [SY2340: $i] :
( ~ ( in @ SY2340 @ SV177 )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV149 )
| ( in @ SY2340 @ SY2320 ) ) ) ) )
= $true )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(960,plain,
! [SV150: $i] :
( ( ( SV150 = empty_set )
= $false )
| ( ( ! [SY2321: $i] :
( ( SY2321
!= ( set_meet @ SV150 ) )
| ( SY2321 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(961,plain,
! [SV151: $i] :
( ( ( SV151 = empty_set )
= $false )
| ( ( ! [SY2322: $i] :
( ( SY2322 != empty_set )
| ( SY2322
= ( set_meet @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(962,plain,
! [SV33: $i,SV152: $i] :
( ( ( ~ ( ! [SY2323: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SY2323 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ ( sK18_SY2050 @ SV152 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) ) )
= $false )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(963,plain,
! [SV33: $i,SV153: $i] :
( ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( ~ ( ~ ! [SY2324: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2324 @ SY2158 ) @ SV33 )
| ( in @ SY2324 @ SV153 ) )
| ~ ! [SY2326: $i] :
( ~ ( in @ SY2326 @ SV153 )
| ( in @ ( ordered_pair @ SY2326 @ ( sK16_D @ SY2326 @ SV153 @ SV33 ) ) @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(964,plain,
! [SV34: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ ( sK39_B @ SV34 ) ) )
= $true )
| ( ( in @ ( powerset @ SV171 ) @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(965,plain,
! [SV34: $i] :
( ( ~ ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(966,plain,
! [SV34: $i] :
( ( ~ ( in @ SV34 @ ( sK39_B @ SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(967,plain,
! [SV80: $i,SV115: $i] :
( ( ( ( ( sK30_C @ SV115 @ SV80 )
!= SV80 )
| ~ ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) )
= $true )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(968,plain,
! [SV80: $i,SV115: $i] :
( ( ( ( ( sK30_C @ SV115 @ SV80 )
= SV80 )
| ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) )
= $true )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(969,plain,
! [SV116: $i,SV81: $i] :
( ( ( ~ ! [SY2276: $i] :
( ( SY2276 != SV81 )
| ( in @ SY2276 @ SV116 ) ) )
= $false )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(970,plain,
! [SV81: $i,SV116: $i] :
( ( ( ~ ! [SY2277: $i] :
( ~ ( in @ SY2277 @ SV116 )
| ( SY2277 = SV81 ) ) )
= $false )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(971,plain,
! [SV35: $i,SV62: $i] :
( ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV62 )
= $false )
| ( ( in @ ( sK6_C @ SV62 @ SV35 ) @ SV35 )
= $false )
| ( ( SV35 = SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(972,plain,
! [SV154: $i,SV63: $i,SV138: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ SV138 ) )
= $true )
| ( ( ~ ( in @ SV63 @ SV154 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV138 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(973,plain,
! [SV178: $i,SV63: $i,SV36: $i] :
( ( ! [SY2342: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV178 @ SY2342 ) )
| ( in @ SV36 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(974,plain,
! [SV179: $i,SV63: $i,SV36: $i] :
( ( ! [SY2343: $i] :
( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV179 @ SY2343 ) )
| ( in @ SV63 @ SY2343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(975,plain,
! [SV180: $i,SV82: $i] :
( ( ( ! [SY2344: $i] :
( ( sK36_B @ SV82 )
!= ( ordered_pair @ SV180 @ SY2344 ) ) )
= $true )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(976,plain,
! [SV83: $i,SV155: $i] :
( ( ( in @ SV155 @ SV83 )
= $false )
| ( ( SV155
= ( ordered_pair @ ( sK34_C @ SV155 @ SV83 ) @ ( sK35_SY2059 @ SV155 @ SV83 ) ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(977,plain,
! [SV37: $i,SV156: $i] :
( ( ( relation @ SV156 )
= $false )
| ( ( ~ ( subset @ SV37 @ SV156 )
| ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SV156 ) ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(978,plain,
! [SV37: $i,SV157: $i] :
( ( ( relation @ SV157 )
= $false )
| ( ( ~ ( subset @ SV37 @ SV157 )
| ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(979,plain,
! [SV158: $i,SV118: $i,SV85: $i] :
( ( ( disjoint @ SV85 @ SV118 )
= $false )
| ( ( in @ SV158 @ ( set_intersection2 @ SV85 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(980,plain,
! [SV160: $i,SV181: $i] :
( ( ( ~ ( element @ SV181 @ SV160 )
| ( in @ SV181 @ SV160 ) )
= $true )
| ( ( empty @ SV160 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(981,plain,
! [SV161: $i,SV182: $i] :
( ( ( ~ ( in @ SV182 @ SV161 )
| ( element @ SV182 @ SV161 ) )
= $true )
| ( ( empty @ SV161 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(982,plain,
! [SV162: $i] :
( ( ( empty @ SV162 )
= $false )
| ( ( ! [SY2329: $i] :
( ~ ( element @ SY2329 @ SV162 )
| ( empty @ SY2329 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(983,plain,
! [SV163: $i] :
( ( ( empty @ SV163 )
= $false )
| ( ( ! [SY2330: $i] :
( ~ ( empty @ SY2330 )
| ( element @ SY2330 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(984,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(985,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) ) )
= $false )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(986,plain,
! [SV140: $i,SV122: $i,SV38: $i] :
( ( ( ~ ! [SY2305: $i] :
( ~ ( in @ SY2305 @ SV38 )
| ( in @ SY2305 @ SV122 )
| ( in @ SY2305 @ SV140 ) )
| ~ ~ ( ~ ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) )
| ~ ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) ) )
= $false )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(987,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) )
= $false )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(988,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) ) )
= $false )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(989,plain,
! [SV142: $i,SV124: $i,SV39: $i] :
( ( ( ~ ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV39 )
| ~ ( in @ SY2308 @ SV124 )
| ( in @ SY2308 @ SV142 ) )
| ~ ~ ( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) )
| ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) ) )
= $false )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(990,plain,
! [SV126: $i,SV94: $i,SV22: $i] :
( ( ( in @ ( ordered_pair @ SV22 @ SV94 ) @ SV126 )
= $false )
| ( ( in @ SV22 @ ( relation_dom @ SV126 ) )
= $true )
| ( ( relation @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(991,plain,
! [SV127: $i,SV95: $i,SV22: $i] :
( ( ( in @ ( ordered_pair @ SV22 @ SV95 ) @ SV127 )
= $false )
| ( ( in @ SV95 @ ( relation_rng @ SV127 ) )
= $true )
| ( ( relation @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(992,plain,
! [SV128: $i,SV96: $i,SV23: $i] :
( ( ( ! [SY2289: $i,SY2290: $i] :
( ~ ( in @ SY2289 @ SV23 )
| ~ ( in @ SY2290 @ SV96 )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SY2289 @ SY2290 ) ) )
| ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(993,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) ) )
| ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(994,plain,
! [SV129: $i,SV97: $i,SV23: $i] :
( ( ( ~ ! [SY2291: $i] :
( ! [SY2254: $i,SY2255: $i] :
( ~ ( in @ SY2254 @ SV23 )
| ~ ( in @ SY2255 @ SV97 )
| ( SY2291
!= ( ordered_pair @ SY2254 @ SY2255 ) ) )
| ( in @ SY2291 @ SV129 ) ) )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(995,plain,
! [SV23: $i,SV97: $i,SV129: $i] :
( ( ( ~ ! [SY2294: $i] :
( ~ ( in @ SY2294 @ SV129 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SY2294
!= ( ordered_pair @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) ) ) ) ) )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(996,plain,
! [SV70: $i,SV98: $i] :
( ( ( ! [SY2257: $i] :
( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SY2257 )
| ~ ( in @ SY2257 @ SV70 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(997,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) )
| ~ ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 ) ) )
= $true )
| ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(998,plain,
! [SV99: $i,SV71: $i] :
( ( ( ! [SY2258: $i] :
( ! [SY2220: $i] :
( ~ ( in @ SY2258 @ SY2220 )
| ~ ( in @ SY2220 @ SV71 ) )
| ( in @ SY2258 @ SV99 ) ) )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(999,plain,
! [SV71: $i,SV99: $i] :
( ( ( ! [SY2260: $i] :
( ~ ( in @ SY2260 @ SV99 )
| ~ ( ~ ( in @ SY2260 @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SY2260 @ SV99 @ SV71 ) @ SV71 ) ) ) )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[926]) ).
thf(1000,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(1001,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(1002,plain,
! [SV101: $i,SV24: $i,SV131: $i] :
( ( ( ~ ! [SY2295: $i] :
( ~ ( in @ SY2295 @ SV131 )
| ( in @ SY2295 @ SV24 )
| ( in @ SY2295 @ SV101 ) ) )
= $false )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(1003,plain,
! [SV101: $i,SV131: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) )
| ~ ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) ) )
= $false )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(1004,plain,
! [SV73: $i,SV103: $i,SV143: $i] :
( ( ( in @ SV143 @ SV103 )
= $false )
| ( ( in @ SV143 @ SV73 )
= $false )
| ( ( ~ ( disjoint @ SV73 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1005,plain,
! [SV58: $i,SV25: $i,SV164: $i] :
( ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
| ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1006,plain,
! [SV58: $i,SV25: $i,SV165: $i] :
( ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( ( SV165
!= ( complements_of_subsets @ SV25 @ SV58 ) )
| ~ ( ~ ! [SY2331: $i] :
( ~ ( element @ SY2331 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2331 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SY2331 ) @ SV58 ) )
| ~ ! [SY2332: $i] :
( ~ ( element @ SY2332 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2332 ) @ SV58 )
| ( in @ SY2332 @ SV165 ) ) ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1007,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) ) ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(1008,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV26 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV104 ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[936]) ).
thf(1009,plain,
! [SV105: $i,SV26: $i,SV133: $i] :
( ( ( ~ ! [SY2298: $i] :
( ~ ( in @ SY2298 @ SV133 )
| ( SY2298 = SV26 )
| ( SY2298 = SV105 ) ) )
= $false )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(1010,plain,
! [SV105: $i,SV133: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) )
| ~ ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) ) )
= $false )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(1011,plain,
! [SV145: $i,SV60: $i,SV136: $i,SV28: $i] :
( ( ( in @ SV28 @ SV136 )
= $false )
| ( ( ~ ( in @ SV60 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV136 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1012,plain,
! [SV172: $i,SV60: $i,SV28: $i] :
( ( ( ! [SY2336: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV172 @ SY2336 ) ) )
= $true )
| ( ( in @ SV28 @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1013,plain,
! [SV183: $i,SV173: $i,SV60: $i,SV28: $i] :
( ( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV173 @ SV183 ) )
| ( in @ SV60 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1014,plain,
! [SV29: $i,SV167: $i] :
( ( ( ~ ! [SY2333: $i] :
( ~ ( subset @ SY2333 @ SV167 )
| ( in @ SY2333 @ ( sK5_SY2040 @ SV167 @ SV29 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SV167 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
= $false )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1015,plain,
! [SV29: $i] :
( ( ! [SY2139: $i,SY2140: $i] :
( ~ ( in @ SY2139 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2140 @ SY2139 )
| ( in @ SY2140 @ ( sK4_B @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(1016,plain,
! [SV29: $i] :
( ( in @ SV29 @ ( sK4_B @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(1017,plain,
! [SV74: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 ) )
= $true )
| ( ( ~ ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) )
= $true )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1018,plain,
! [SV74: $i,SV107: $i] :
( ( ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
= $true )
| ( ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 )
= $true )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1019,plain,
! [SV75: $i,SV108: $i] :
( ( ( ! [SY2272: $i] :
( ~ ( in @ SY2272 @ SV108 )
| ( subset @ SY2272 @ SV75 ) ) )
= $true )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1020,plain,
! [SV108: $i,SV75: $i] :
( ( ( ! [SY2273: $i] :
( ~ ( subset @ SY2273 @ SV75 )
| ( in @ SY2273 @ SV108 ) ) )
= $true )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1021,plain,
! [SV30: $i,SV146: $i] :
( ( ( ~ ( ! [SY2311: $i] :
~ ( in @ ( ordered_pair @ SY2311 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) ) )
= $false )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1022,plain,
! [SV30: $i,SV146: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV146 @ SV30 ) @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) ) )
= $false )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1023,plain,
! [SV147: $i,SV30: $i] :
( ( ( ~ ! [SY2312: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2312 ) @ SV30 )
| ( in @ SY2312 @ SV147 ) )
| ~ ! [SY2314: $i] :
( ~ ( in @ SY2314 @ SV147 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2314 @ SV147 @ SV30 ) @ SY2314 ) @ SV30 ) ) )
= $false )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1024,plain,
! [SV76: $i,SV109: $i] :
( ( ( in @ ( sK20_C @ SV109 @ SV76 ) @ SV109 )
= $false )
| ( ( subset @ SV76 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1025,plain,
! [SV110: $i,SV77: $i,SV168: $i] :
( ( ( in @ SV168 @ SV77 )
= $false )
| ( ( in @ SV168 @ SV110 )
= $true )
| ( ( subset @ SV77 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1026,plain,
! [SV32: $i,SV137: $i,SV111: $i] :
( ( ( in @ SV111 @ SV137 )
= $false )
| ( ( in @ SV32 @ SV137 )
= $false )
| ( ( subset @ ( unordered_pair @ SV32 @ SV111 ) @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1027,plain,
! [SV174: $i,SV169: $i,SV32: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV32 @ SV169 ) @ SV174 ) )
= $true )
| ( ( in @ SV32 @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1028,plain,
! [SV175: $i,SV170: $i,SV32: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV32 @ SV170 ) @ SV175 ) )
= $true )
| ( ( in @ SV170 @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1029,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) )
| ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
| ~ ( ! [SY2338: $i] :
( ~ ( in @ SY2338 @ SV148 )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SY2338 ) )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) ) ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1030,plain,
! [SV149: $i,SV177: $i] :
( ( ( ( SV177
!= ( set_meet @ SV149 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2339: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SY2339 @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) ) )
| ( in @ SY2339 @ SV177 ) )
| ~ ! [SY2340: $i] :
( ~ ( in @ SY2340 @ SV177 )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV149 )
| ( in @ SY2340 @ SY2320 ) ) ) ) )
= $true )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1031,plain,
! [SV150: $i,SV184: $i] :
( ( ( ( SV184
!= ( set_meet @ SV150 ) )
| ( SV184 = empty_set ) )
= $true )
| ( ( SV150 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1032,plain,
! [SV151: $i,SV185: $i] :
( ( ( ( SV185 != empty_set )
| ( SV185
= ( set_meet @ SV151 ) ) )
= $true )
| ( ( SV151 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1033,plain,
! [SV33: $i,SV152: $i] :
( ( ( ~ ( ! [SY2323: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SY2323 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) ) )
= $false )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1034,plain,
! [SV33: $i,SV152: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ ( sK18_SY2050 @ SV152 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) ) )
= $false )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1035,plain,
! [SV153: $i,SV33: $i] :
( ( ( ~ ! [SY2324: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2324 @ SY2158 ) @ SV33 )
| ( in @ SY2324 @ SV153 ) )
| ~ ! [SY2326: $i] :
( ~ ( in @ SY2326 @ SV153 )
| ( in @ ( ordered_pair @ SY2326 @ ( sK16_D @ SY2326 @ SV153 @ SV33 ) ) @ SV33 ) ) )
= $false )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1036,plain,
! [SV34: $i,SV171: $i] :
( ( ( in @ SV171 @ ( sK39_B @ SV34 ) )
= $false )
| ( ( in @ ( powerset @ SV171 ) @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1037,plain,
! [SV34: $i] :
( ( ! [SY2162: $i,SY2163: $i] :
( ~ ( in @ SY2162 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2163 @ SY2162 )
| ( in @ SY2163 @ ( sK39_B @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1038,plain,
! [SV34: $i] :
( ( in @ SV34 @ ( sK39_B @ SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1039,plain,
! [SV80: $i,SV115: $i] :
( ( ( ( ( sK30_C @ SV115 @ SV80 )
!= SV80 ) )
= $true )
| ( ( ~ ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) )
= $true )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1040,plain,
! [SV80: $i,SV115: $i] :
( ( ( ( sK30_C @ SV115 @ SV80 )
= SV80 )
= $true )
| ( ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 )
= $true )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1041,plain,
! [SV116: $i,SV81: $i] :
( ( ( ! [SY2276: $i] :
( ( SY2276 != SV81 )
| ( in @ SY2276 @ SV116 ) ) )
= $true )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1042,plain,
! [SV81: $i,SV116: $i] :
( ( ( ! [SY2277: $i] :
( ~ ( in @ SY2277 @ SV116 )
| ( SY2277 = SV81 ) ) )
= $true )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1043,plain,
! [SV154: $i,SV63: $i,SV138: $i,SV36: $i] :
( ( ( in @ SV36 @ SV138 )
= $false )
| ( ( ~ ( in @ SV63 @ SV154 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV138 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1044,plain,
! [SV178: $i,SV63: $i,SV36: $i] :
( ( ( ! [SY2342: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV178 @ SY2342 ) ) )
= $true )
| ( ( in @ SV36 @ SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1045,plain,
! [SV186: $i,SV179: $i,SV63: $i,SV36: $i] :
( ( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV179 @ SV186 ) )
| ( in @ SV63 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1046,plain,
! [SV187: $i,SV180: $i,SV82: $i] :
( ( ( ( ( sK36_B @ SV82 )
!= ( ordered_pair @ SV180 @ SV187 ) ) )
= $true )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1047,plain,
! [SV156: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV156 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SV156 ) )
= $true )
| ( ( relation @ SV156 )
= $false )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1048,plain,
! [SV157: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV157 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( relation @ SV157 )
= $false )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1049,plain,
! [SV160: $i,SV181: $i] :
( ( ( ~ ( element @ SV181 @ SV160 ) )
= $true )
| ( ( in @ SV181 @ SV160 )
= $true )
| ( ( empty @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1050,plain,
! [SV161: $i,SV182: $i] :
( ( ( ~ ( in @ SV182 @ SV161 ) )
= $true )
| ( ( element @ SV182 @ SV161 )
= $true )
| ( ( empty @ SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1051,plain,
! [SV162: $i,SV188: $i] :
( ( ( ~ ( element @ SV188 @ SV162 )
| ( empty @ SV188 ) )
= $true )
| ( ( empty @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1052,plain,
! [SV163: $i,SV189: $i] :
( ( ( ~ ( empty @ SV189 )
| ( element @ SV189 @ SV163 ) )
= $true )
| ( ( empty @ SV163 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1053,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1054,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) ) )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1055,plain,
! [SV140: $i,SV122: $i,SV38: $i] :
( ( ( ~ ! [SY2305: $i] :
( ~ ( in @ SY2305 @ SV38 )
| ( in @ SY2305 @ SV122 )
| ( in @ SY2305 @ SV140 ) ) )
= $false )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1056,plain,
! [SV122: $i,SV38: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) )
| ~ ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) ) )
= $false )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1057,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1058,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1059,plain,
! [SV142: $i,SV124: $i,SV39: $i] :
( ( ( ~ ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV39 )
| ~ ( in @ SY2308 @ SV124 )
| ( in @ SY2308 @ SV142 ) ) )
= $false )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1060,plain,
! [SV124: $i,SV39: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) )
| ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) ) )
= $false )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1061,plain,
! [SV128: $i,SV96: $i,SV23: $i] :
( ( ( ! [SY2289: $i,SY2290: $i] :
( ~ ( in @ SY2289 @ SV23 )
| ~ ( in @ SY2290 @ SV96 )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SY2289 @ SY2290 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1062,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1063,plain,
! [SV129: $i,SV97: $i,SV23: $i] :
( ( ( ! [SY2291: $i] :
( ! [SY2254: $i,SY2255: $i] :
( ~ ( in @ SY2254 @ SV23 )
| ~ ( in @ SY2255 @ SV97 )
| ( SY2291
!= ( ordered_pair @ SY2254 @ SY2255 ) ) )
| ( in @ SY2291 @ SV129 ) ) )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1064,plain,
! [SV23: $i,SV97: $i,SV129: $i] :
( ( ( ! [SY2294: $i] :
( ~ ( in @ SY2294 @ SV129 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SY2294
!= ( ordered_pair @ ( sK21_E @ SY2294 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SY2294 @ SV129 @ SV97 @ SV23 ) ) ) ) ) )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1065,plain,
! [SV190: $i,SV70: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV190 )
| ~ ( in @ SV190 @ SV70 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1066,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) )
| ~ ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 ) )
= $false )
| ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1067,plain,
! [SV99: $i,SV71: $i,SV191: $i] :
( ( ( ! [SY2345: $i] :
( ~ ( in @ SV191 @ SY2345 )
| ~ ( in @ SY2345 @ SV71 ) )
| ( in @ SV191 @ SV99 ) )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1068,plain,
! [SV71: $i,SV99: $i,SV192: $i] :
( ( ( ~ ( in @ SV192 @ SV99 )
| ~ ( ~ ( in @ SV192 @ ( sK13_D @ SV192 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SV192 @ SV99 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1069,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) )
= $false )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1070,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
= $true )
| ( ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 )
| ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1071,plain,
! [SV101: $i,SV24: $i,SV131: $i] :
( ( ( ! [SY2295: $i] :
( ~ ( in @ SY2295 @ SV131 )
| ( in @ SY2295 @ SV24 )
| ( in @ SY2295 @ SV101 ) ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1072,plain,
! [SV101: $i,SV131: $i,SV24: $i] :
( ( ( ~ ( ~ ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) )
| ~ ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1073,plain,
! [SV143: $i,SV103: $i,SV73: $i] :
( ( ( disjoint @ SV73 @ SV103 )
= $false )
| ( ( in @ SV143 @ SV73 )
= $false )
| ( ( in @ SV143 @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1074,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( ~ ( element @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) ) ) )
= $true )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1075,plain,
! [SV58: $i,SV25: $i,SV165: $i] :
( ( ( ( SV165
!= ( complements_of_subsets @ SV25 @ SV58 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2331: $i] :
( ~ ( element @ SY2331 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2331 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SY2331 ) @ SV58 ) )
| ~ ! [SY2332: $i] :
( ~ ( element @ SY2332 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2332 ) @ SV58 )
| ( in @ SY2332 @ SV165 ) ) ) )
= $true )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1076,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) ) )
= $false )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1077,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
= $true )
| ( ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV26 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV104 ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1078,plain,
! [SV105: $i,SV26: $i,SV133: $i] :
( ( ( ! [SY2298: $i] :
( ~ ( in @ SY2298 @ SV133 )
| ( SY2298 = SV26 )
| ( SY2298 = SV105 ) ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1079,plain,
! [SV105: $i,SV133: $i,SV26: $i] :
( ( ( ~ ( ~ ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) )
| ~ ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1080,plain,
! [SV136: $i,SV28: $i,SV145: $i,SV60: $i] :
( ( ( in @ SV60 @ SV145 )
= $false )
| ( ( in @ SV28 @ SV136 )
= $false )
| ( ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV136 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1081,plain,
! [SV193: $i,SV172: $i,SV60: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV172 @ SV193 ) ) )
= $true )
| ( ( in @ SV28 @ SV172 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1082,plain,
! [SV183: $i,SV173: $i,SV60: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV173 @ SV183 ) ) )
= $true )
| ( ( in @ SV60 @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1083,plain,
! [SV29: $i,SV167: $i] :
( ( ( ~ ! [SY2333: $i] :
( ~ ( subset @ SY2333 @ SV167 )
| ( in @ SY2333 @ ( sK5_SY2040 @ SV167 @ SV29 ) ) ) )
= $false )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1084,plain,
! [SV29: $i,SV167: $i] :
( ( ( ~ ( in @ ( sK5_SY2040 @ SV167 @ SV29 ) @ ( sK4_B @ SV29 ) ) )
= $false )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1085,plain,
! [SV29: $i,SV194: $i] :
( ( ! [SY2346: $i] :
( ~ ( in @ SV194 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SY2346 @ SV194 )
| ( in @ SY2346 @ ( sK4_B @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1086,plain,
! [SV74: $i,SV107: $i] :
( ( ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
= $false )
| ( ( ~ ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 ) )
= $true )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1087,plain,
! [SV75: $i,SV108: $i,SV195: $i] :
( ( ( ~ ( in @ SV195 @ SV108 )
| ( subset @ SV195 @ SV75 ) )
= $true )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1088,plain,
! [SV108: $i,SV75: $i,SV196: $i] :
( ( ( ~ ( subset @ SV196 @ SV75 )
| ( in @ SV196 @ SV108 ) )
= $true )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1089,plain,
! [SV30: $i,SV146: $i] :
( ( ( ! [SY2311: $i] :
~ ( in @ ( ordered_pair @ SY2311 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) )
= $true )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1090,plain,
! [SV30: $i,SV146: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV146 @ SV30 ) @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
| ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) )
= $true )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1091,plain,
! [SV147: $i,SV30: $i] :
( ( ( ~ ! [SY2312: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2312 ) @ SV30 )
| ( in @ SY2312 @ SV147 ) ) )
= $false )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1092,plain,
! [SV30: $i,SV147: $i] :
( ( ( ~ ! [SY2314: $i] :
( ~ ( in @ SY2314 @ SV147 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2314 @ SV147 @ SV30 ) @ SY2314 ) @ SV30 ) ) )
= $false )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1093,plain,
! [SV174: $i,SV169: $i,SV32: $i] :
( ( ( subset @ ( unordered_pair @ SV32 @ SV169 ) @ SV174 )
= $false )
| ( ( in @ SV32 @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1094,plain,
! [SV175: $i,SV170: $i,SV32: $i] :
( ( ( subset @ ( unordered_pair @ SV32 @ SV170 ) @ SV175 )
= $false )
| ( ( in @ SV170 @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1095,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) )
| ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
| ~ ( ! [SY2338: $i] :
( ~ ( in @ SY2338 @ SV148 )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SY2338 ) )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) ) )
= $false )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1096,plain,
! [SV149: $i,SV177: $i] :
( ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( ~ ( ~ ! [SY2339: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SY2339 @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) ) )
| ( in @ SY2339 @ SV177 ) )
| ~ ! [SY2340: $i] :
( ~ ( in @ SY2340 @ SV177 )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV149 )
| ( in @ SY2340 @ SY2320 ) ) ) ) )
= $true )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1097,plain,
! [SV150: $i,SV184: $i] :
( ( ( ( SV184
!= ( set_meet @ SV150 ) ) )
= $true )
| ( ( SV184 = empty_set )
= $true )
| ( ( SV150 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1098,plain,
! [SV151: $i,SV185: $i] :
( ( ( ( SV185 != empty_set ) )
= $true )
| ( ( SV185
= ( set_meet @ SV151 ) )
= $true )
| ( ( SV151 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1099,plain,
! [SV33: $i,SV152: $i] :
( ( ( ! [SY2323: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SY2323 ) @ SV33 )
| ~ ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) )
= $true )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1100,plain,
! [SV33: $i,SV152: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ ( sK18_SY2050 @ SV152 @ SV33 ) ) @ SV33 )
| ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) )
= $true )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1101,plain,
! [SV153: $i,SV33: $i] :
( ( ( ~ ! [SY2324: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2324 @ SY2158 ) @ SV33 )
| ( in @ SY2324 @ SV153 ) ) )
= $false )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1102,plain,
! [SV33: $i,SV153: $i] :
( ( ( ~ ! [SY2326: $i] :
( ~ ( in @ SY2326 @ SV153 )
| ( in @ ( ordered_pair @ SY2326 @ ( sK16_D @ SY2326 @ SV153 @ SV33 ) ) @ SV33 ) ) )
= $false )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1103,plain,
! [SV34: $i,SV197: $i] :
( ( ! [SY2347: $i] :
( ~ ( in @ SV197 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SY2347 @ SV197 )
| ( in @ SY2347 @ ( sK39_B @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1104,plain,
! [SV80: $i,SV115: $i] :
( ( ( ( sK30_C @ SV115 @ SV80 )
= SV80 )
= $false )
| ( ( ~ ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 ) )
= $true )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1105,plain,
! [SV116: $i,SV81: $i,SV198: $i] :
( ( ( ( SV198 != SV81 )
| ( in @ SV198 @ SV116 ) )
= $true )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1106,plain,
! [SV81: $i,SV116: $i,SV199: $i] :
( ( ( ~ ( in @ SV199 @ SV116 )
| ( SV199 = SV81 ) )
= $true )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1107,plain,
! [SV138: $i,SV36: $i,SV154: $i,SV63: $i] :
( ( ( in @ SV63 @ SV154 )
= $false )
| ( ( in @ SV36 @ SV138 )
= $false )
| ( ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV138 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1108,plain,
! [SV200: $i,SV178: $i,SV63: $i,SV36: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV178 @ SV200 ) ) )
= $true )
| ( ( in @ SV36 @ SV178 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1109,plain,
! [SV186: $i,SV179: $i,SV63: $i,SV36: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV179 @ SV186 ) ) )
= $true )
| ( ( in @ SV63 @ SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1110,plain,
! [SV187: $i,SV180: $i,SV82: $i] :
( ( ( ( sK36_B @ SV82 )
= ( ordered_pair @ SV180 @ SV187 ) )
= $false )
| ( ( relation @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1111,plain,
! [SV156: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV156 )
= $false )
| ( ( subset @ ( relation_dom @ SV37 ) @ ( relation_dom @ SV156 ) )
= $true )
| ( ( relation @ SV156 )
= $false )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1112,plain,
! [SV157: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV157 )
= $false )
| ( ( subset @ ( relation_rng @ SV37 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( relation @ SV157 )
= $false )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1113,plain,
! [SV160: $i,SV181: $i] :
( ( ( element @ SV181 @ SV160 )
= $false )
| ( ( in @ SV181 @ SV160 )
= $true )
| ( ( empty @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1114,plain,
! [SV161: $i,SV182: $i] :
( ( ( in @ SV182 @ SV161 )
= $false )
| ( ( element @ SV182 @ SV161 )
= $true )
| ( ( empty @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1115,plain,
! [SV162: $i,SV188: $i] :
( ( ( ~ ( element @ SV188 @ SV162 ) )
= $true )
| ( ( empty @ SV188 )
= $true )
| ( ( empty @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1116,plain,
! [SV163: $i,SV189: $i] :
( ( ( ~ ( empty @ SV189 ) )
= $true )
| ( ( element @ SV189 @ SV163 )
= $true )
| ( ( empty @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1117,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1118,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1119,plain,
! [SV140: $i,SV122: $i,SV38: $i] :
( ( ( ! [SY2305: $i] :
( ~ ( in @ SY2305 @ SV38 )
| ( in @ SY2305 @ SV122 )
| ( in @ SY2305 @ SV140 ) ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1120,plain,
! [SV122: $i,SV38: $i,SV140: $i] :
( ( ( ~ ( ~ ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) )
| ~ ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1121,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1122,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
| ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) )
= $false )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1123,plain,
! [SV142: $i,SV124: $i,SV39: $i] :
( ( ( ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV39 )
| ~ ( in @ SY2308 @ SV124 )
| ( in @ SY2308 @ SV142 ) ) )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1124,plain,
! [SV124: $i,SV39: $i,SV142: $i] :
( ( ( ~ ( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) )
| ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) ) )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1125,plain,
! [SV128: $i,SV96: $i,SV23: $i,SV201: $i] :
( ( ( ! [SY2348: $i] :
( ~ ( in @ SV201 @ SV23 )
| ~ ( in @ SY2348 @ SV96 )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SV201 @ SY2348 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1126,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1127,plain,
! [SV129: $i,SV202: $i,SV97: $i,SV23: $i] :
( ( ( ! [SY2349: $i,SY2350: $i] :
( ~ ( in @ SY2349 @ SV23 )
| ~ ( in @ SY2350 @ SV97 )
| ( SV202
!= ( ordered_pair @ SY2349 @ SY2350 ) ) )
| ( in @ SV202 @ SV129 ) )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1128,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV129 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SV203
!= ( ordered_pair @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) ) ) ) )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1129,plain,
! [SV190: $i,SV70: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV190 ) )
= $true )
| ( ( ~ ( in @ SV190 @ SV70 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1130,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) ) )
= $false )
| ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1131,plain,
! [SV70: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 ) )
= $false )
| ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1132,plain,
! [SV99: $i,SV71: $i,SV191: $i] :
( ( ( ! [SY2345: $i] :
( ~ ( in @ SV191 @ SY2345 )
| ~ ( in @ SY2345 @ SV71 ) ) )
= $true )
| ( ( in @ SV191 @ SV99 )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1133,plain,
! [SV71: $i,SV99: $i,SV192: $i] :
( ( ( ~ ( in @ SV192 @ SV99 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV192 @ ( sK13_D @ SV192 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SV192 @ SV99 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1134,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) ) )
= $false )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1135,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) ) )
= $false )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1136,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 )
= $true )
| ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 )
= $true )
| ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1137,plain,
! [SV101: $i,SV24: $i,SV131: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV131 )
| ( in @ SV204 @ SV24 )
| ( in @ SV204 @ SV101 ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1138,plain,
! [SV101: $i,SV131: $i,SV24: $i] :
( ( ( ~ ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) )
| ~ ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) )
= $false )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1139,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( element @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
= $false )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1140,plain,
! [SV58: $i,SV25: $i,SV165: $i] :
( ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( ~ ( ~ ! [SY2331: $i] :
( ~ ( element @ SY2331 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2331 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SY2331 ) @ SV58 ) )
| ~ ! [SY2332: $i] :
( ~ ( element @ SY2332 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2332 ) @ SV58 )
| ( in @ SY2332 @ SV165 ) ) ) )
= $true )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1141,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) ) )
= $false )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1142,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) ) )
= $false )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1143,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV26 )
= $true )
| ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV104 )
= $true )
| ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1144,plain,
! [SV105: $i,SV26: $i,SV133: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV133 )
| ( SV205 = SV26 )
| ( SV205 = SV105 ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1145,plain,
! [SV105: $i,SV133: $i,SV26: $i] :
( ( ( ~ ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) )
| ~ ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) )
= $false )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1146,plain,
! [SV193: $i,SV172: $i,SV60: $i,SV28: $i] :
( ( ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV172 @ SV193 ) )
= $false )
| ( ( in @ SV28 @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1147,plain,
! [SV183: $i,SV173: $i,SV60: $i,SV28: $i] :
( ( ( in @ ( ordered_pair @ SV28 @ SV60 ) @ ( cartesian_product2 @ SV173 @ SV183 ) )
= $false )
| ( ( in @ SV60 @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1148,plain,
! [SV29: $i,SV167: $i] :
( ( ( ! [SY2333: $i] :
( ~ ( subset @ SY2333 @ SV167 )
| ( in @ SY2333 @ ( sK5_SY2040 @ SV167 @ SV29 ) ) ) )
= $true )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1149,plain,
! [SV29: $i,SV167: $i] :
( ( ( in @ ( sK5_SY2040 @ SV167 @ SV29 ) @ ( sK4_B @ SV29 ) )
= $true )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1150,plain,
! [SV206: $i,SV29: $i,SV194: $i] :
( ( ~ ( in @ SV194 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SV206 @ SV194 )
| ( in @ SV206 @ ( sK4_B @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1151,plain,
! [SV74: $i,SV107: $i] :
( ( ( subset @ ( sK28_C @ SV107 @ SV74 ) @ SV74 )
= $false )
| ( ( in @ ( sK28_C @ SV107 @ SV74 ) @ SV107 )
= $false )
| ( ( SV107
= ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1152,plain,
! [SV75: $i,SV108: $i,SV195: $i] :
( ( ( ~ ( in @ SV195 @ SV108 ) )
= $true )
| ( ( subset @ SV195 @ SV75 )
= $true )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1153,plain,
! [SV108: $i,SV75: $i,SV196: $i] :
( ( ( ~ ( subset @ SV196 @ SV75 ) )
= $true )
| ( ( in @ SV196 @ SV108 )
= $true )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1154,plain,
! [SV30: $i,SV146: $i] :
( ( ( ! [SY2311: $i] :
~ ( in @ ( ordered_pair @ SY2311 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) )
= $true )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1155,plain,
! [SV30: $i,SV146: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV146 @ SV30 ) @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
= $true )
| ( ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 )
= $true )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1156,plain,
! [SV147: $i,SV30: $i] :
( ( ( ! [SY2312: $i] :
( ! [SY2145: $i] :
~ ( in @ ( ordered_pair @ SY2145 @ SY2312 ) @ SV30 )
| ( in @ SY2312 @ SV147 ) ) )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1157,plain,
! [SV30: $i,SV147: $i] :
( ( ( ! [SY2314: $i] :
( ~ ( in @ SY2314 @ SV147 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2314 @ SV147 @ SV30 ) @ SY2314 ) @ SV30 ) ) )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1158,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) )
| ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) ) )
= $false )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1159,plain,
! [SV176: $i,SV148: $i] :
( ( ( ~ ( ! [SY2338: $i] :
( ~ ( in @ SY2338 @ SV148 )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SY2338 ) )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) ) )
= $false )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1160,plain,
! [SV149: $i,SV177: $i] :
( ( ( ~ ! [SY2339: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SY2339 @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) ) )
| ( in @ SY2339 @ SV177 ) )
| ~ ! [SY2340: $i] :
( ~ ( in @ SY2340 @ SV177 )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV149 )
| ( in @ SY2340 @ SY2320 ) ) ) )
= $false )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1161,plain,
! [SV150: $i,SV184: $i] :
( ( ( SV184
= ( set_meet @ SV150 ) )
= $false )
| ( ( SV184 = empty_set )
= $true )
| ( ( SV150 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1162,plain,
! [SV151: $i,SV185: $i] :
( ( ( SV185 = empty_set )
= $false )
| ( ( SV185
= ( set_meet @ SV151 ) )
= $true )
| ( ( SV151 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1163,plain,
! [SV33: $i,SV152: $i] :
( ( ( ! [SY2323: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SY2323 ) @ SV33 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) )
= $true )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1164,plain,
! [SV33: $i,SV152: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ ( sK18_SY2050 @ SV152 @ SV33 ) ) @ SV33 )
= $true )
| ( ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 )
= $true )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1165,plain,
! [SV153: $i,SV33: $i] :
( ( ( ! [SY2324: $i] :
( ! [SY2158: $i] :
~ ( in @ ( ordered_pair @ SY2324 @ SY2158 ) @ SV33 )
| ( in @ SY2324 @ SV153 ) ) )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1166,plain,
! [SV33: $i,SV153: $i] :
( ( ( ! [SY2326: $i] :
( ~ ( in @ SY2326 @ SV153 )
| ( in @ ( ordered_pair @ SY2326 @ ( sK16_D @ SY2326 @ SV153 @ SV33 ) ) @ SV33 ) ) )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1167,plain,
! [SV207: $i,SV34: $i,SV197: $i] :
( ( ~ ( in @ SV197 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SV207 @ SV197 )
| ( in @ SV207 @ ( sK39_B @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1168,plain,
! [SV80: $i,SV115: $i] :
( ( ( in @ ( sK30_C @ SV115 @ SV80 ) @ SV115 )
= $false )
| ( ( ( sK30_C @ SV115 @ SV80 )
= SV80 )
= $false )
| ( ( SV115
= ( singleton @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1169,plain,
! [SV116: $i,SV81: $i,SV198: $i] :
( ( ( ( SV198 != SV81 ) )
= $true )
| ( ( in @ SV198 @ SV116 )
= $true )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1170,plain,
! [SV81: $i,SV116: $i,SV199: $i] :
( ( ( ~ ( in @ SV199 @ SV116 ) )
= $true )
| ( ( SV199 = SV81 )
= $true )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1171,plain,
! [SV200: $i,SV178: $i,SV63: $i,SV36: $i] :
( ( ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV178 @ SV200 ) )
= $false )
| ( ( in @ SV36 @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1172,plain,
! [SV186: $i,SV179: $i,SV63: $i,SV36: $i] :
( ( ( in @ ( ordered_pair @ SV36 @ SV63 ) @ ( cartesian_product2 @ SV179 @ SV186 ) )
= $false )
| ( ( in @ SV63 @ SV186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1173,plain,
! [SV162: $i,SV188: $i] :
( ( ( element @ SV188 @ SV162 )
= $false )
| ( ( empty @ SV188 )
= $true )
| ( ( empty @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1174,plain,
! [SV163: $i,SV189: $i] :
( ( ( empty @ SV189 )
= $false )
| ( ( element @ SV189 @ SV163 )
= $true )
| ( ( empty @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1175,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 ) )
= $true )
| ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1176,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1177,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1178,plain,
! [SV140: $i,SV122: $i,SV38: $i,SV208: $i] :
( ( ( ~ ( in @ SV208 @ SV38 )
| ( in @ SV208 @ SV122 )
| ( in @ SV208 @ SV140 ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1179,plain,
! [SV122: $i,SV38: $i,SV140: $i] :
( ( ( ~ ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) )
| ~ ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) )
= $false )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1180,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1181,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) )
= $false )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1182,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) ) )
= $false )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1183,plain,
! [SV142: $i,SV124: $i,SV39: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV39 )
| ~ ( in @ SV209 @ SV124 )
| ( in @ SV209 @ SV142 ) )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1184,plain,
! [SV124: $i,SV39: $i,SV142: $i] :
( ( ( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) )
| ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) )
= $false )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1185,plain,
! [SV128: $i,SV96: $i,SV210: $i,SV23: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV23 )
| ~ ( in @ SV210 @ SV96 )
| ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SV201 @ SV210 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1186,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1187,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1188,plain,
! [SV129: $i,SV202: $i,SV97: $i,SV23: $i] :
( ( ( ! [SY2349: $i,SY2350: $i] :
( ~ ( in @ SY2349 @ SV23 )
| ~ ( in @ SY2350 @ SV97 )
| ( SV202
!= ( ordered_pair @ SY2349 @ SY2350 ) ) ) )
= $true )
| ( ( in @ SV202 @ SV129 )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1189,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SV203
!= ( ordered_pair @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) ) ) ) )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1190,plain,
! [SV190: $i,SV70: $i,SV98: $i] :
( ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV190 )
= $false )
| ( ( ~ ( in @ SV190 @ SV70 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1191,plain,
! [SV70: $i,SV98: $i] :
( ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ ( sK15_SY2048 @ SV98 @ SV70 ) )
= $true )
| ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1192,plain,
! [SV70: $i,SV98: $i] :
( ( ( in @ ( sK15_SY2048 @ SV98 @ SV70 ) @ SV70 )
= $true )
| ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1193,plain,
! [SV99: $i,SV71: $i,SV211: $i,SV191: $i] :
( ( ( ~ ( in @ SV191 @ SV211 )
| ~ ( in @ SV211 @ SV71 ) )
= $true )
| ( ( in @ SV191 @ SV99 )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1194,plain,
! [SV71: $i,SV99: $i,SV192: $i] :
( ( ( in @ SV192 @ SV99 )
= $false )
| ( ( ~ ( ~ ( in @ SV192 @ ( sK13_D @ SV192 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SV192 @ SV99 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1195,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1196,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
| ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1197,plain,
! [SV101: $i,SV24: $i,SV131: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV131 ) )
= $true )
| ( ( ( in @ SV204 @ SV24 )
| ( in @ SV204 @ SV101 ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1198,plain,
! [SV101: $i,SV131: $i,SV24: $i] :
( ( ( ~ ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) ) )
= $false )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1199,plain,
! [SV24: $i,SV131: $i,SV101: $i] :
( ( ( ~ ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) )
= $false )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1200,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( element @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) ) )
= $false )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1139]) ).
thf(1201,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
= $false )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1139]) ).
thf(1202,plain,
! [SV58: $i,SV165: $i,SV25: $i] :
( ( ( ~ ! [SY2331: $i] :
( ~ ( element @ SY2331 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2331 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SY2331 ) @ SV58 ) )
| ~ ! [SY2332: $i] :
( ~ ( element @ SY2332 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2332 ) @ SV58 )
| ( in @ SY2332 @ SV165 ) ) )
= $false )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1203,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1204,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
| ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1205,plain,
! [SV105: $i,SV26: $i,SV133: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV133 ) )
= $true )
| ( ( ( SV205 = SV26 )
| ( SV205 = SV105 ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1206,plain,
! [SV105: $i,SV133: $i,SV26: $i] :
( ( ( ~ ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) ) )
= $false )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1145]) ).
thf(1207,plain,
! [SV26: $i,SV133: $i,SV105: $i] :
( ( ( ~ ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) )
= $false )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1145]) ).
thf(1208,plain,
! [SV29: $i,SV167: $i,SV212: $i] :
( ( ( ~ ( subset @ SV212 @ SV167 )
| ( in @ SV212 @ ( sK5_SY2040 @ SV167 @ SV29 ) ) )
= $true )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1209,plain,
! [SV29: $i,SV167: $i] :
( ( ( in @ SV167 @ ( sK4_B @ SV29 ) )
= $false )
| ( ( in @ ( sK5_SY2040 @ SV167 @ SV29 ) @ ( sK4_B @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1210,plain,
! [SV206: $i,SV29: $i,SV194: $i] :
( ( ( ~ ( in @ SV194 @ ( sK4_B @ SV29 ) )
| ~ ( subset @ SV206 @ SV194 ) )
= $true )
| ( ( in @ SV206 @ ( sK4_B @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1211,plain,
! [SV75: $i,SV108: $i,SV195: $i] :
( ( ( in @ SV195 @ SV108 )
= $false )
| ( ( subset @ SV195 @ SV75 )
= $true )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1212,plain,
! [SV108: $i,SV75: $i,SV196: $i] :
( ( ( subset @ SV196 @ SV75 )
= $false )
| ( ( in @ SV196 @ SV108 )
= $true )
| ( ( SV108
= ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1213,plain,
! [SV30: $i,SV146: $i,SV213: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV213 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) )
= $true )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1214,plain,
! [SV147: $i,SV30: $i,SV214: $i] :
( ( ( ! [SY2351: $i] :
~ ( in @ ( ordered_pair @ SY2351 @ SV214 ) @ SV30 )
| ( in @ SV214 @ SV147 ) )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1215,plain,
! [SV30: $i,SV147: $i,SV215: $i] :
( ( ( ~ ( in @ SV215 @ SV147 )
| ( in @ ( ordered_pair @ ( sK9_D @ SV215 @ SV147 @ SV30 ) @ SV215 ) @ SV30 ) )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1216,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) )
| ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1217,plain,
! [SV176: $i,SV148: $i] :
( ( ( ! [SY2338: $i] :
( ~ ( in @ SY2338 @ SV148 )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SY2338 ) )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1218,plain,
! [SV149: $i,SV177: $i] :
( ( ( ~ ! [SY2339: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SY2339 @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) ) )
| ( in @ SY2339 @ SV177 ) ) )
= $false )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1219,plain,
! [SV149: $i,SV177: $i] :
( ( ( ~ ! [SY2340: $i] :
( ~ ( in @ SY2340 @ SV177 )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV149 )
| ( in @ SY2340 @ SY2320 ) ) ) )
= $false )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1220,plain,
! [SV216: $i,SV33: $i,SV152: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SV216 ) @ SV33 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) )
= $true )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1221,plain,
! [SV153: $i,SV33: $i,SV217: $i] :
( ( ( ! [SY2352: $i] :
~ ( in @ ( ordered_pair @ SV217 @ SY2352 ) @ SV33 )
| ( in @ SV217 @ SV153 ) )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1222,plain,
! [SV33: $i,SV153: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV153 )
| ( in @ ( ordered_pair @ SV218 @ ( sK16_D @ SV218 @ SV153 @ SV33 ) ) @ SV33 ) )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1223,plain,
! [SV207: $i,SV34: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ ( sK39_B @ SV34 ) )
| ~ ( subset @ SV207 @ SV197 ) )
= $true )
| ( ( in @ SV207 @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1224,plain,
! [SV116: $i,SV81: $i,SV198: $i] :
( ( ( SV198 = SV81 )
= $false )
| ( ( in @ SV198 @ SV116 )
= $true )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1225,plain,
! [SV81: $i,SV116: $i,SV199: $i] :
( ( ( in @ SV199 @ SV116 )
= $false )
| ( ( SV199 = SV81 )
= $true )
| ( ( SV116
= ( singleton @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1226,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
= $false )
| ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1227,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1228,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
| ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1229,plain,
! [SV140: $i,SV122: $i,SV38: $i,SV208: $i] :
( ( ( ~ ( in @ SV208 @ SV38 )
| ( in @ SV208 @ SV122 ) )
= $true )
| ( ( in @ SV208 @ SV140 )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1230,plain,
! [SV122: $i,SV38: $i,SV140: $i] :
( ( ( ~ ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) ) )
= $false )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1179]) ).
thf(1231,plain,
! [SV38: $i,SV122: $i,SV140: $i] :
( ( ( ~ ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) )
= $false )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1179]) ).
thf(1232,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1233,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1234,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
| ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1235,plain,
! [SV142: $i,SV124: $i,SV39: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV39 )
| ~ ( in @ SV209 @ SV124 ) )
= $true )
| ( ( in @ SV209 @ SV142 )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1236,plain,
! [SV124: $i,SV39: $i,SV142: $i] :
( ( ( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) ) )
= $false )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1237,plain,
! [SV39: $i,SV124: $i,SV142: $i] :
( ( ( ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) )
= $false )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1238,plain,
! [SV128: $i,SV96: $i,SV210: $i,SV23: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV23 )
| ~ ( in @ SV210 @ SV96 ) )
= $true )
| ( ( ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SV201 @ SV210 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1239,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1240,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ( sK23_D @ SV128 @ SV96 @ SV23 )
= ( ordered_pair @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1241,plain,
! [SV129: $i,SV202: $i,SV97: $i,SV23: $i,SV219: $i] :
( ( ( ! [SY2353: $i] :
( ~ ( in @ SV219 @ SV23 )
| ~ ( in @ SY2353 @ SV97 )
| ( SV202
!= ( ordered_pair @ SV219 @ SY2353 ) ) ) )
= $true )
| ( ( in @ SV202 @ SV129 )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1242,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( in @ SV203 @ SV129 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SV203
!= ( ordered_pair @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) ) ) ) )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1243,plain,
! [SV98: $i,SV70: $i,SV190: $i] :
( ( ( in @ SV190 @ SV70 )
= $false )
| ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV190 )
= $false )
| ( ( ~ ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 ) )
= $true )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1244,plain,
! [SV99: $i,SV71: $i,SV211: $i,SV191: $i] :
( ( ( ~ ( in @ SV191 @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV211 @ SV71 ) )
= $true )
| ( ( in @ SV191 @ SV99 )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1245,plain,
! [SV71: $i,SV99: $i,SV192: $i] :
( ( ( ~ ( in @ SV192 @ ( sK13_D @ SV192 @ SV99 @ SV71 ) )
| ~ ( in @ ( sK13_D @ SV192 @ SV99 @ SV71 ) @ SV71 ) )
= $false )
| ( ( in @ SV192 @ SV99 )
= $false )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1246,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1247,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1248,plain,
! [SV101: $i,SV24: $i,SV131: $i,SV204: $i] :
( ( ( in @ SV204 @ SV131 )
= $false )
| ( ( ( in @ SV204 @ SV24 )
| ( in @ SV204 @ SV101 ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1249,plain,
! [SV101: $i,SV131: $i,SV24: $i] :
( ( ( ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV24 )
| ( in @ SY2296 @ SV131 ) ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1250,plain,
! [SV24: $i,SV131: $i,SV101: $i] :
( ( ( ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV101 )
| ( in @ SY2297 @ SV131 ) ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1251,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( element @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ ( powerset @ SV25 ) )
= $true )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1252,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) ) )
= $true )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1253,plain,
! [SV58: $i,SV165: $i,SV25: $i] :
( ( ( ~ ! [SY2331: $i] :
( ~ ( element @ SY2331 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2331 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SY2331 ) @ SV58 ) ) )
= $false )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1254,plain,
! [SV165: $i,SV58: $i,SV25: $i] :
( ( ( ~ ! [SY2332: $i] :
( ~ ( element @ SY2332 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2332 ) @ SV58 )
| ( in @ SY2332 @ SV165 ) ) )
= $false )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1255,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 ) )
= $true )
| ( ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1256,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 ) )
= $true )
| ( ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1257,plain,
! [SV105: $i,SV26: $i,SV133: $i,SV205: $i] :
( ( ( in @ SV205 @ SV133 )
= $false )
| ( ( ( SV205 = SV26 )
| ( SV205 = SV105 ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1258,plain,
! [SV105: $i,SV133: $i,SV26: $i] :
( ( ( ! [SY2299: $i] :
( ( SY2299 != SV26 )
| ( in @ SY2299 @ SV133 ) ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1259,plain,
! [SV26: $i,SV133: $i,SV105: $i] :
( ( ( ! [SY2300: $i] :
( ( SY2300 != SV105 )
| ( in @ SY2300 @ SV133 ) ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1260,plain,
! [SV29: $i,SV167: $i,SV212: $i] :
( ( ( ~ ( subset @ SV212 @ SV167 ) )
= $true )
| ( ( in @ SV212 @ ( sK5_SY2040 @ SV167 @ SV29 ) )
= $true )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1261,plain,
! [SV206: $i,SV29: $i,SV194: $i] :
( ( ( ~ ( in @ SV194 @ ( sK4_B @ SV29 ) ) )
= $true )
| ( ( ~ ( subset @ SV206 @ SV194 ) )
= $true )
| ( ( in @ SV206 @ ( sK4_B @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1262,plain,
! [SV30: $i,SV146: $i,SV213: $i] :
( ( ( in @ ( ordered_pair @ SV213 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
= $false )
| ( ( ~ ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 ) )
= $true )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1263,plain,
! [SV147: $i,SV30: $i,SV214: $i] :
( ( ( ! [SY2351: $i] :
~ ( in @ ( ordered_pair @ SY2351 @ SV214 ) @ SV30 ) )
= $true )
| ( ( in @ SV214 @ SV147 )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1264,plain,
! [SV30: $i,SV147: $i,SV215: $i] :
( ( ( ~ ( in @ SV215 @ SV147 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV215 @ SV147 @ SV30 ) @ SV215 ) @ SV30 )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1265,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1266,plain,
! [SV176: $i,SV148: $i] :
( ( ( ! [SY2338: $i] :
( ~ ( in @ SY2338 @ SV148 )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SY2338 ) ) )
= $true )
| ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1267,plain,
! [SV149: $i,SV177: $i] :
( ( ( ! [SY2339: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SY2339 @ ( sK31_D @ SY2339 @ SV177 @ SV149 ) ) )
| ( in @ SY2339 @ SV177 ) ) )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1268,plain,
! [SV149: $i,SV177: $i] :
( ( ( ! [SY2340: $i] :
( ~ ( in @ SY2340 @ SV177 )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV149 )
| ( in @ SY2340 @ SY2320 ) ) ) )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1269,plain,
! [SV216: $i,SV33: $i,SV152: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SV216 ) @ SV33 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 ) )
= $true )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1270,plain,
! [SV153: $i,SV33: $i,SV217: $i] :
( ( ( ! [SY2352: $i] :
~ ( in @ ( ordered_pair @ SV217 @ SY2352 ) @ SV33 ) )
= $true )
| ( ( in @ SV217 @ SV153 )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1271,plain,
! [SV33: $i,SV153: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV153 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV218 @ ( sK16_D @ SV218 @ SV153 @ SV33 ) ) @ SV33 )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1272,plain,
! [SV207: $i,SV34: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ ( sK39_B @ SV34 ) ) )
= $true )
| ( ( ~ ( subset @ SV207 @ SV197 ) )
= $true )
| ( ( in @ SV207 @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1273,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 )
= $false )
| ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
= $true )
| ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
= $false )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1274,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV38 )
= $true )
| ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1275,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 ) )
= $true )
| ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1276,plain,
! [SV140: $i,SV122: $i,SV38: $i,SV208: $i] :
( ( ( ~ ( in @ SV208 @ SV38 ) )
= $true )
| ( ( in @ SV208 @ SV122 )
= $true )
| ( ( in @ SV208 @ SV140 )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1277,plain,
! [SV122: $i,SV38: $i,SV140: $i] :
( ( ( ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV140 )
| ( in @ SY2306 @ SV38 ) ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1278,plain,
! [SV38: $i,SV122: $i,SV140: $i] :
( ( ( ! [SY2307: $i] :
( ~ ( in @ SY2307 @ SV140 )
| ~ ( in @ SY2307 @ SV122 ) ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1279,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
= $false )
| ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 ) )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1280,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
= $true )
| ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1281,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
= $true )
| ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 )
= $true )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1282,plain,
! [SV142: $i,SV124: $i,SV39: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV39 ) )
= $true )
| ( ( ~ ( in @ SV209 @ SV124 ) )
= $true )
| ( ( in @ SV209 @ SV142 )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1283,plain,
! [SV124: $i,SV39: $i,SV142: $i] :
( ( ( ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV142 )
| ( in @ SY2309 @ SV39 ) ) )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1284,plain,
! [SV39: $i,SV124: $i,SV142: $i] :
( ( ( ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV142 )
| ( in @ SY2310 @ SV124 ) ) )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1285,plain,
! [SV128: $i,SV96: $i,SV210: $i,SV23: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV210 @ SV96 ) )
= $true )
| ( ( ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SV201 @ SV210 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1286,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
= $false )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1287,plain,
! [SV129: $i,SV202: $i,SV97: $i,SV220: $i,SV23: $i,SV219: $i] :
( ( ( ~ ( in @ SV219 @ SV23 )
| ~ ( in @ SV220 @ SV97 )
| ( SV202
!= ( ordered_pair @ SV219 @ SV220 ) ) )
= $true )
| ( ( in @ SV202 @ SV129 )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1288,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
| ( SV203
!= ( ordered_pair @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) ) ) )
= $false )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1289,plain,
! [SV190: $i,SV70: $i,SV98: $i] :
( ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV98 )
= $false )
| ( ( in @ ( sK14_C @ SV98 @ SV70 ) @ SV190 )
= $false )
| ( ( in @ SV190 @ SV70 )
= $false )
| ( ( SV98
= ( union @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1290,plain,
! [SV99: $i,SV71: $i,SV211: $i,SV191: $i] :
( ( ( in @ SV191 @ SV211 )
= $false )
| ( ( ~ ( in @ SV211 @ SV71 ) )
= $true )
| ( ( in @ SV191 @ SV99 )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1291,plain,
! [SV71: $i,SV99: $i,SV192: $i] :
( ( ( ~ ( in @ SV192 @ ( sK13_D @ SV192 @ SV99 @ SV71 ) ) )
= $false )
| ( ( in @ SV192 @ SV99 )
= $false )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1245]) ).
thf(1292,plain,
! [SV71: $i,SV99: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV192 @ SV99 @ SV71 ) @ SV71 ) )
= $false )
| ( ( in @ SV192 @ SV99 )
= $false )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1245]) ).
thf(1293,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1294,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 ) )
= $true )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1295,plain,
! [SV131: $i,SV101: $i,SV24: $i,SV204: $i] :
( ( ( in @ SV204 @ SV24 )
= $true )
| ( ( in @ SV204 @ SV101 )
= $true )
| ( ( in @ SV204 @ SV131 )
= $false )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1296,plain,
! [SV101: $i,SV131: $i,SV24: $i,SV221: $i] :
( ( ( ~ ( in @ SV221 @ SV24 )
| ( in @ SV221 @ SV131 ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1297,plain,
! [SV24: $i,SV131: $i,SV101: $i,SV222: $i] :
( ( ( ~ ( in @ SV222 @ SV101 )
| ( in @ SV222 @ SV131 ) )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1298,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
| ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) )
= $false )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1299,plain,
! [SV58: $i,SV165: $i,SV25: $i] :
( ( ( ! [SY2331: $i] :
( ~ ( element @ SY2331 @ ( powerset @ SV25 ) )
| ~ ( in @ SY2331 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SY2331 ) @ SV58 ) ) )
= $true )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1253]) ).
thf(1300,plain,
! [SV165: $i,SV58: $i,SV25: $i] :
( ( ( ! [SY2332: $i] :
( ~ ( element @ SY2332 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SY2332 ) @ SV58 )
| ( in @ SY2332 @ SV165 ) ) )
= $true )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1301,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
= $false )
| ( ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV26 ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1302,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
= $false )
| ( ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
!= SV104 ) )
= $true )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1303,plain,
! [SV133: $i,SV105: $i,SV26: $i,SV205: $i] :
( ( ( SV205 = SV26 )
= $true )
| ( ( SV205 = SV105 )
= $true )
| ( ( in @ SV205 @ SV133 )
= $false )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1304,plain,
! [SV105: $i,SV133: $i,SV26: $i,SV223: $i] :
( ( ( ( SV223 != SV26 )
| ( in @ SV223 @ SV133 ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1305,plain,
! [SV26: $i,SV133: $i,SV105: $i,SV224: $i] :
( ( ( ( SV224 != SV105 )
| ( in @ SV224 @ SV133 ) )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1306,plain,
! [SV29: $i,SV167: $i,SV212: $i] :
( ( ( subset @ SV212 @ SV167 )
= $false )
| ( ( in @ SV212 @ ( sK5_SY2040 @ SV167 @ SV29 ) )
= $true )
| ( ( ~ ( in @ SV167 @ ( sK4_B @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1307,plain,
! [SV206: $i,SV29: $i,SV194: $i] :
( ( ( in @ SV194 @ ( sK4_B @ SV29 ) )
= $false )
| ( ( ~ ( subset @ SV206 @ SV194 ) )
= $true )
| ( ( in @ SV206 @ ( sK4_B @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1308,plain,
! [SV213: $i,SV30: $i,SV146: $i] :
( ( ( in @ ( sK10_C @ SV146 @ SV30 ) @ SV146 )
= $false )
| ( ( in @ ( ordered_pair @ SV213 @ ( sK10_C @ SV146 @ SV30 ) ) @ SV30 )
= $false )
| ( ( SV146
= ( relation_rng @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1309,plain,
! [SV147: $i,SV30: $i,SV214: $i,SV225: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV225 @ SV214 ) @ SV30 ) )
= $true )
| ( ( in @ SV214 @ SV147 )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1310,plain,
! [SV30: $i,SV147: $i,SV215: $i] :
( ( ( in @ SV215 @ SV147 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV215 @ SV147 @ SV30 ) @ SV215 ) @ SV30 )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1311,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
| ~ ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1312,plain,
! [SV176: $i,SV148: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ SV148 )
| ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV226 ) )
= $true )
| ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1313,plain,
! [SV149: $i,SV177: $i,SV227: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_D @ SV227 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SV227 @ ( sK31_D @ SV227 @ SV177 @ SV149 ) ) )
| ( in @ SV227 @ SV177 ) )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1314,plain,
! [SV149: $i,SV177: $i,SV228: $i] :
( ( ( ~ ( in @ SV228 @ SV177 )
| ! [SY2354: $i] :
( ~ ( in @ SY2354 @ SV149 )
| ( in @ SV228 @ SY2354 ) ) )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1315,plain,
! [SV216: $i,SV33: $i,SV152: $i] :
( ( ( in @ ( sK17_C @ SV152 @ SV33 ) @ SV152 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_C @ SV152 @ SV33 ) @ SV216 ) @ SV33 )
= $false )
| ( ( SV152
= ( relation_dom @ SV33 ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1316,plain,
! [SV153: $i,SV33: $i,SV229: $i,SV217: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV217 @ SV229 ) @ SV33 ) )
= $true )
| ( ( in @ SV217 @ SV153 )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1317,plain,
! [SV33: $i,SV153: $i,SV218: $i] :
( ( ( in @ SV218 @ SV153 )
= $false )
| ( ( in @ ( ordered_pair @ SV218 @ ( sK16_D @ SV218 @ SV153 @ SV33 ) ) @ SV33 )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1318,plain,
! [SV207: $i,SV34: $i,SV197: $i] :
( ( ( in @ SV197 @ ( sK39_B @ SV34 ) )
= $false )
| ( ( ~ ( subset @ SV207 @ SV197 ) )
= $true )
| ( ( in @ SV207 @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1319,plain,
! [SV38: $i,SV121: $i,SV139: $i] :
( ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV121 )
= $false )
| ( ( in @ ( sK12_D @ SV139 @ SV121 @ SV38 ) @ SV139 )
= $true )
| ( ( SV139
= ( set_difference @ SV38 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1320,plain,
! [SV140: $i,SV122: $i,SV38: $i,SV208: $i] :
( ( ( in @ SV208 @ SV38 )
= $false )
| ( ( in @ SV208 @ SV122 )
= $true )
| ( ( in @ SV208 @ SV140 )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1321,plain,
! [SV122: $i,SV38: $i,SV140: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV140 )
| ( in @ SV230 @ SV38 ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1322,plain,
! [SV38: $i,SV122: $i,SV140: $i,SV231: $i] :
( ( ( ~ ( in @ SV231 @ SV140 )
| ~ ( in @ SV231 @ SV122 ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1323,plain,
! [SV39: $i,SV123: $i,SV141: $i] :
( ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV141 )
= $false )
| ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV39 )
= $false )
| ( ( in @ ( sK19_D @ SV141 @ SV123 @ SV39 ) @ SV123 )
= $false )
| ( ( SV141
= ( set_intersection2 @ SV39 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1324,plain,
! [SV142: $i,SV124: $i,SV39: $i,SV209: $i] :
( ( ( in @ SV209 @ SV39 )
= $false )
| ( ( ~ ( in @ SV209 @ SV124 ) )
= $true )
| ( ( in @ SV209 @ SV142 )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1325,plain,
! [SV124: $i,SV39: $i,SV142: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV142 )
| ( in @ SV232 @ SV39 ) )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1326,plain,
! [SV39: $i,SV124: $i,SV142: $i,SV233: $i] :
( ( ( ~ ( in @ SV233 @ SV142 )
| ( in @ SV233 @ SV124 ) )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1327,plain,
! [SV128: $i,SV96: $i,SV210: $i,SV23: $i,SV201: $i] :
( ( ( in @ SV201 @ SV23 )
= $false )
| ( ( ~ ( in @ SV210 @ SV96 ) )
= $true )
| ( ( ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SV201 @ SV210 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1328,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 ) )
= $false )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1329,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( ~ ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 ) )
= $false )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1330,plain,
! [SV129: $i,SV202: $i,SV97: $i,SV220: $i,SV23: $i,SV219: $i] :
( ( ( ~ ( in @ SV219 @ SV23 )
| ~ ( in @ SV220 @ SV97 ) )
= $true )
| ( ( ( SV202
!= ( ordered_pair @ SV219 @ SV220 ) ) )
= $true )
| ( ( in @ SV202 @ SV129 )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1331,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 ) ) )
= $false )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1288]) ).
thf(1332,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ( SV203
!= ( ordered_pair @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) ) ) )
= $false )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1288]) ).
thf(1333,plain,
! [SV99: $i,SV191: $i,SV71: $i,SV211: $i] :
( ( ( in @ SV211 @ SV71 )
= $false )
| ( ( in @ SV191 @ SV211 )
= $false )
| ( ( in @ SV191 @ SV99 )
= $true )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1334,plain,
! [SV71: $i,SV99: $i,SV192: $i] :
( ( ( in @ SV192 @ ( sK13_D @ SV192 @ SV99 @ SV71 ) )
= $true )
| ( ( in @ SV192 @ SV99 )
= $false )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1291]) ).
thf(1335,plain,
! [SV71: $i,SV99: $i,SV192: $i] :
( ( ( in @ ( sK13_D @ SV192 @ SV99 @ SV71 ) @ SV71 )
= $true )
| ( ( in @ SV192 @ SV99 )
= $false )
| ( ( SV99
= ( union @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1292]) ).
thf(1336,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV24 )
= $false )
| ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
= $false )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1337,plain,
! [SV24: $i,SV100: $i,SV130: $i] :
( ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV100 )
= $false )
| ( ( in @ ( sK26_D @ SV130 @ SV100 @ SV24 ) @ SV130 )
= $false )
| ( ( SV130
= ( set_union2 @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1338,plain,
! [SV101: $i,SV131: $i,SV24: $i,SV221: $i] :
( ( ( ~ ( in @ SV221 @ SV24 ) )
= $true )
| ( ( in @ SV221 @ SV131 )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1339,plain,
! [SV24: $i,SV131: $i,SV101: $i,SV222: $i] :
( ( ( ~ ( in @ SV222 @ SV101 ) )
= $true )
| ( ( in @ SV222 @ SV131 )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1340,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) )
= $false )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1341,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) ) )
= $false )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1342,plain,
! [SV58: $i,SV165: $i,SV25: $i,SV234: $i] :
( ( ( ~ ( element @ SV234 @ ( powerset @ SV25 ) )
| ~ ( in @ SV234 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SV234 ) @ SV58 ) )
= $true )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1343,plain,
! [SV165: $i,SV58: $i,SV25: $i,SV235: $i] :
( ( ( ~ ( element @ SV235 @ ( powerset @ SV25 ) )
| ~ ( in @ ( subset_complement @ SV25 @ SV235 ) @ SV58 )
| ( in @ SV235 @ SV165 ) )
= $true )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1344,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV26 )
= $false )
| ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
= $false )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1345,plain,
! [SV26: $i,SV104: $i,SV132: $i] :
( ( ( ( sK27_D @ SV132 @ SV104 @ SV26 )
= SV104 )
= $false )
| ( ( in @ ( sK27_D @ SV132 @ SV104 @ SV26 ) @ SV132 )
= $false )
| ( ( SV132
= ( unordered_pair @ SV26 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1346,plain,
! [SV105: $i,SV133: $i,SV26: $i,SV223: $i] :
( ( ( ( SV223 != SV26 ) )
= $true )
| ( ( in @ SV223 @ SV133 )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1347,plain,
! [SV26: $i,SV133: $i,SV105: $i,SV224: $i] :
( ( ( ( SV224 != SV105 ) )
= $true )
| ( ( in @ SV224 @ SV133 )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1348,plain,
! [SV212: $i,SV29: $i,SV167: $i] :
( ( ( in @ SV167 @ ( sK4_B @ SV29 ) )
= $false )
| ( ( in @ SV212 @ ( sK5_SY2040 @ SV167 @ SV29 ) )
= $true )
| ( ( subset @ SV212 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1349,plain,
! [SV29: $i,SV194: $i,SV206: $i] :
( ( ( subset @ SV206 @ SV194 )
= $false )
| ( ( in @ SV194 @ ( sK4_B @ SV29 ) )
= $false )
| ( ( in @ SV206 @ ( sK4_B @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1350,plain,
! [SV147: $i,SV30: $i,SV214: $i,SV225: $i] :
( ( ( in @ ( ordered_pair @ SV225 @ SV214 ) @ SV30 )
= $false )
| ( ( in @ SV214 @ SV147 )
= $true )
| ( ( SV147
= ( relation_rng @ SV30 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1351,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1352,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1353,plain,
! [SV176: $i,SV148: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ SV148 ) )
= $true )
| ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV226 )
= $true )
| ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1354,plain,
! [SV149: $i,SV177: $i,SV227: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_D @ SV227 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SV227 @ ( sK31_D @ SV227 @ SV177 @ SV149 ) ) ) )
= $true )
| ( ( in @ SV227 @ SV177 )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1355,plain,
! [SV149: $i,SV177: $i,SV228: $i] :
( ( ( ~ ( in @ SV228 @ SV177 ) )
= $true )
| ( ( ! [SY2354: $i] :
( ~ ( in @ SY2354 @ SV149 )
| ( in @ SV228 @ SY2354 ) ) )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1356,plain,
! [SV153: $i,SV33: $i,SV229: $i,SV217: $i] :
( ( ( in @ ( ordered_pair @ SV217 @ SV229 ) @ SV33 )
= $false )
| ( ( in @ SV217 @ SV153 )
= $true )
| ( ( SV153
= ( relation_dom @ SV33 ) )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1357,plain,
! [SV34: $i,SV197: $i,SV207: $i] :
( ( ( subset @ SV207 @ SV197 )
= $false )
| ( ( in @ SV197 @ ( sK39_B @ SV34 ) )
= $false )
| ( ( in @ SV207 @ ( sK39_B @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1358,plain,
! [SV122: $i,SV38: $i,SV140: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV140 ) )
= $true )
| ( ( in @ SV230 @ SV38 )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1359,plain,
! [SV38: $i,SV122: $i,SV140: $i,SV231: $i] :
( ( ( ~ ( in @ SV231 @ SV140 ) )
= $true )
| ( ( ~ ( in @ SV231 @ SV122 ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1360,plain,
! [SV142: $i,SV39: $i,SV124: $i,SV209: $i] :
( ( ( in @ SV209 @ SV124 )
= $false )
| ( ( in @ SV209 @ SV39 )
= $false )
| ( ( in @ SV209 @ SV142 )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1361,plain,
! [SV124: $i,SV39: $i,SV142: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV142 ) )
= $true )
| ( ( in @ SV232 @ SV39 )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1362,plain,
! [SV39: $i,SV124: $i,SV142: $i,SV233: $i] :
( ( ( ~ ( in @ SV233 @ SV142 ) )
= $true )
| ( ( in @ SV233 @ SV124 )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1363,plain,
! [SV128: $i,SV23: $i,SV201: $i,SV96: $i,SV210: $i] :
( ( ( in @ SV210 @ SV96 )
= $false )
| ( ( in @ SV201 @ SV23 )
= $false )
| ( ( ( ( sK23_D @ SV128 @ SV96 @ SV23 )
!= ( ordered_pair @ SV201 @ SV210 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1364,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( in @ ( sK24_SY2054 @ SV128 @ SV96 @ SV23 ) @ SV23 )
= $true )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1365,plain,
! [SV23: $i,SV96: $i,SV128: $i] :
( ( ( in @ ( sK25_SY2056 @ SV128 @ SV96 @ SV23 ) @ SV96 )
= $true )
| ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1366,plain,
! [SV129: $i,SV202: $i,SV97: $i,SV220: $i,SV23: $i,SV219: $i] :
( ( ( ~ ( in @ SV219 @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV220 @ SV97 ) )
= $true )
| ( ( ( SV202
!= ( ordered_pair @ SV219 @ SV220 ) ) )
= $true )
| ( ( in @ SV202 @ SV129 )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1367,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 ) ) )
= $true )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1331]) ).
thf(1368,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( SV203
= ( ordered_pair @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) ) )
= $true )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1369,plain,
! [SV101: $i,SV131: $i,SV24: $i,SV221: $i] :
( ( ( in @ SV221 @ SV24 )
= $false )
| ( ( in @ SV221 @ SV131 )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1370,plain,
! [SV24: $i,SV131: $i,SV101: $i,SV222: $i] :
( ( ( in @ SV222 @ SV101 )
= $false )
| ( ( in @ SV222 @ SV131 )
= $true )
| ( ( SV131
= ( set_union2 @ SV24 @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1371,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
= $true )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1372,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
| ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
= $true )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1341]) ).
thf(1373,plain,
! [SV58: $i,SV165: $i,SV25: $i,SV234: $i] :
( ( ( ~ ( element @ SV234 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ~ ( in @ SV234 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SV234 ) @ SV58 ) )
= $true )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1374,plain,
! [SV165: $i,SV58: $i,SV25: $i,SV235: $i] :
( ( ( ~ ( element @ SV235 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ~ ( in @ ( subset_complement @ SV25 @ SV235 ) @ SV58 )
| ( in @ SV235 @ SV165 ) )
= $true )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1375,plain,
! [SV105: $i,SV133: $i,SV26: $i,SV223: $i] :
( ( ( SV223 = SV26 )
= $false )
| ( ( in @ SV223 @ SV133 )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1376,plain,
! [SV26: $i,SV133: $i,SV105: $i,SV224: $i] :
( ( ( SV224 = SV105 )
= $false )
| ( ( in @ SV224 @ SV133 )
= $true )
| ( ( SV133
= ( unordered_pair @ SV26 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1377,plain,
! [SV148: $i,SV176: $i] :
( ( ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1378,plain,
! [SV148: $i,SV176: $i] :
( ( ( ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1379,plain,
! [SV176: $i,SV148: $i,SV226: $i] :
( ( ( in @ SV226 @ SV148 )
= $false )
| ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV226 )
= $true )
| ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1380,plain,
! [SV149: $i,SV177: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK31_D @ SV227 @ SV177 @ SV149 ) @ SV149 )
| ~ ~ ( in @ SV227 @ ( sK31_D @ SV227 @ SV177 @ SV149 ) ) )
= $false )
| ( ( in @ SV227 @ SV177 )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1381,plain,
! [SV149: $i,SV177: $i,SV228: $i] :
( ( ( in @ SV228 @ SV177 )
= $false )
| ( ( ! [SY2354: $i] :
( ~ ( in @ SY2354 @ SV149 )
| ( in @ SV228 @ SY2354 ) ) )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1382,plain,
! [SV122: $i,SV38: $i,SV140: $i,SV230: $i] :
( ( ( in @ SV230 @ SV140 )
= $false )
| ( ( in @ SV230 @ SV38 )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1383,plain,
! [SV38: $i,SV122: $i,SV140: $i,SV231: $i] :
( ( ( in @ SV231 @ SV140 )
= $false )
| ( ( ~ ( in @ SV231 @ SV122 ) )
= $true )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1384,plain,
! [SV124: $i,SV39: $i,SV142: $i,SV232: $i] :
( ( ( in @ SV232 @ SV142 )
= $false )
| ( ( in @ SV232 @ SV39 )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1385,plain,
! [SV39: $i,SV124: $i,SV142: $i,SV233: $i] :
( ( ( in @ SV233 @ SV142 )
= $false )
| ( ( in @ SV233 @ SV124 )
= $true )
| ( ( SV142
= ( set_intersection2 @ SV39 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1386,plain,
! [SV210: $i,SV201: $i,SV23: $i,SV96: $i,SV128: $i] :
( ( ( ( sK23_D @ SV128 @ SV96 @ SV23 )
= ( ordered_pair @ SV201 @ SV210 ) )
= $false )
| ( ( in @ SV201 @ SV23 )
= $false )
| ( ( in @ SV210 @ SV96 )
= $false )
| ( ( ~ ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1387,plain,
! [SV129: $i,SV202: $i,SV97: $i,SV220: $i,SV23: $i,SV219: $i] :
( ( ( in @ SV219 @ SV23 )
= $false )
| ( ( ~ ( in @ SV220 @ SV97 ) )
= $true )
| ( ( ( SV202
!= ( ordered_pair @ SV219 @ SV220 ) ) )
= $true )
| ( ( in @ SV202 @ SV129 )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1388,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 )
| ~ ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
= $false )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1389,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 ) )
= $true )
| ( ( ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
= $true )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1390,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
= $true )
| ( ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 )
= $true )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1391,plain,
! [SV58: $i,SV165: $i,SV25: $i,SV234: $i] :
( ( ( element @ SV234 @ ( powerset @ SV25 ) )
= $false )
| ( ( ~ ( in @ SV234 @ SV165 )
| ( in @ ( subset_complement @ SV25 @ SV234 ) @ SV58 ) )
= $true )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1392,plain,
! [SV165: $i,SV58: $i,SV25: $i,SV235: $i] :
( ( ( element @ SV235 @ ( powerset @ SV25 ) )
= $false )
| ( ( ~ ( in @ ( subset_complement @ SV25 @ SV235 ) @ SV58 )
| ( in @ SV235 @ SV165 ) )
= $true )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1393,plain,
! [SV148: $i,SV176: $i] :
( ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 )
= $false )
| ( ( in @ ( sK33_SY2057 @ SV176 @ SV148 ) @ SV148 )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1394,plain,
! [SV148: $i,SV176: $i] :
( ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 ) )
= $true )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1395,plain,
! [SV149: $i,SV177: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK31_D @ SV227 @ SV177 @ SV149 ) @ SV149 ) )
= $false )
| ( ( in @ SV227 @ SV177 )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1396,plain,
! [SV149: $i,SV177: $i,SV227: $i] :
( ( ( ~ ~ ( in @ SV227 @ ( sK31_D @ SV227 @ SV177 @ SV149 ) ) )
= $false )
| ( ( in @ SV227 @ SV177 )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1397,plain,
! [SV177: $i,SV228: $i,SV149: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV149 )
| ( in @ SV228 @ SV236 ) )
= $true )
| ( ( in @ SV228 @ SV177 )
= $false )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1398,plain,
! [SV38: $i,SV140: $i,SV122: $i,SV231: $i] :
( ( ( in @ SV231 @ SV122 )
= $false )
| ( ( in @ SV231 @ SV140 )
= $false )
| ( ( SV140
= ( set_difference @ SV38 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1399,plain,
! [SV201: $i,SV210: $i,SV23: $i,SV96: $i,SV128: $i] :
( ( ( in @ ( sK23_D @ SV128 @ SV96 @ SV23 ) @ SV128 )
= $false )
| ( ( in @ SV210 @ SV96 )
= $false )
| ( ( in @ SV201 @ SV23 )
= $false )
| ( ( ( sK23_D @ SV128 @ SV96 @ SV23 )
= ( ordered_pair @ SV201 @ SV210 ) )
= $false )
| ( ( SV128
= ( cartesian_product2 @ SV23 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1400,plain,
! [SV129: $i,SV202: $i,SV23: $i,SV219: $i,SV97: $i,SV220: $i] :
( ( ( in @ SV220 @ SV97 )
= $false )
| ( ( in @ SV219 @ SV23 )
= $false )
| ( ( ( SV202
!= ( ordered_pair @ SV219 @ SV220 ) ) )
= $true )
| ( ( in @ SV202 @ SV129 )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1401,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 ) )
= $false )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1402,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 ) )
= $false )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1403,plain,
! [SV25: $i,SV58: $i,SV164: $i] :
( ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
= $false )
| ( ( ~ ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 ) )
= $true )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1404,plain,
! [SV58: $i,SV25: $i,SV165: $i,SV234: $i] :
( ( ( ~ ( in @ SV234 @ SV165 ) )
= $true )
| ( ( in @ ( subset_complement @ SV25 @ SV234 ) @ SV58 )
= $true )
| ( ( element @ SV234 @ ( powerset @ SV25 ) )
= $false )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1405,plain,
! [SV165: $i,SV58: $i,SV235: $i,SV25: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV25 @ SV235 ) @ SV58 ) )
= $true )
| ( ( in @ SV235 @ SV165 )
= $true )
| ( ( element @ SV235 @ ( powerset @ SV25 ) )
= $false )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1406,plain,
! [SV148: $i,SV176: $i] :
( ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ SV176 )
= $false )
| ( ( in @ ( sK32_C @ SV176 @ SV148 ) @ ( sK33_SY2057 @ SV176 @ SV148 ) )
= $false )
| ( ( SV176
= ( set_meet @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1407,plain,
! [SV149: $i,SV177: $i,SV227: $i] :
( ( ( in @ ( sK31_D @ SV227 @ SV177 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV227 @ SV177 )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1408,plain,
! [SV149: $i,SV177: $i,SV227: $i] :
( ( ( ~ ( in @ SV227 @ ( sK31_D @ SV227 @ SV177 @ SV149 ) ) )
= $true )
| ( ( in @ SV227 @ SV177 )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1409,plain,
! [SV177: $i,SV228: $i,SV149: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV149 ) )
= $true )
| ( ( in @ SV228 @ SV236 )
= $true )
| ( ( in @ SV228 @ SV177 )
= $false )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1410,plain,
! [SV129: $i,SV97: $i,SV23: $i,SV220: $i,SV219: $i,SV202: $i] :
( ( ( SV202
= ( ordered_pair @ SV219 @ SV220 ) )
= $false )
| ( ( in @ SV219 @ SV23 )
= $false )
| ( ( in @ SV220 @ SV97 )
= $false )
| ( ( in @ SV202 @ SV129 )
= $true )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1411,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( in @ ( sK21_E @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV23 )
= $true )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1412,plain,
! [SV23: $i,SV97: $i,SV129: $i,SV203: $i] :
( ( ( in @ ( sK22_SY2051 @ SV203 @ SV129 @ SV97 @ SV23 ) @ SV97 )
= $true )
| ( ( in @ SV203 @ SV129 )
= $false )
| ( ( SV129
= ( cartesian_product2 @ SV23 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1413,plain,
! [SV58: $i,SV164: $i,SV25: $i] :
( ( ( in @ ( subset_complement @ SV25 @ ( sK8_D @ SV164 @ SV58 @ SV25 ) ) @ SV58 )
= $false )
| ( ( in @ ( sK8_D @ SV164 @ SV58 @ SV25 ) @ SV164 )
= $false )
| ( ( SV164
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $true )
| ( ( element @ SV164 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1414,plain,
! [SV58: $i,SV25: $i,SV165: $i,SV234: $i] :
( ( ( in @ SV234 @ SV165 )
= $false )
| ( ( in @ ( subset_complement @ SV25 @ SV234 ) @ SV58 )
= $true )
| ( ( element @ SV234 @ ( powerset @ SV25 ) )
= $false )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1415,plain,
! [SV165: $i,SV58: $i,SV235: $i,SV25: $i] :
( ( ( in @ ( subset_complement @ SV25 @ SV235 ) @ SV58 )
= $false )
| ( ( in @ SV235 @ SV165 )
= $true )
| ( ( element @ SV235 @ ( powerset @ SV25 ) )
= $false )
| ( ( SV165
= ( complements_of_subsets @ SV25 @ SV58 ) )
= $false )
| ( ( element @ SV165 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false )
| ( ( element @ SV58 @ ( powerset @ ( powerset @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1416,plain,
! [SV149: $i,SV177: $i,SV227: $i] :
( ( ( in @ SV227 @ ( sK31_D @ SV227 @ SV177 @ SV149 ) )
= $false )
| ( ( in @ SV227 @ SV177 )
= $true )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1417,plain,
! [SV177: $i,SV228: $i,SV149: $i,SV236: $i] :
( ( ( in @ SV236 @ SV149 )
= $false )
| ( ( in @ SV228 @ SV236 )
= $true )
| ( ( in @ SV228 @ SV177 )
= $false )
| ( ( SV177
= ( set_meet @ SV149 ) )
= $false )
| ( ( SV149 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1418,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[320,1417,1416,1415,1414,1413,1412,1411,1410,1407,1406,1399,1398,1393,1390,1385,1384,1382,1379,1376,1375,1370,1369,1368,1365,1364,1360,1357,1356,1350,1349,1348,1345,1344,1337,1336,1335,1334,1333,1323,1320,1319,1317,1315,1310,1308,1303,1295,1289,1281,1280,1274,1273,1251,1240,1225,1224,1212,1211,1209,1192,1191,1174,1173,1172,1171,1168,1164,1162,1161,1155,1151,1147,1146,1143,1136,1114,1113,1112,1111,1110,1107,1094,1093,1080,1073,1040,1038,1036,1026,1025,1024,1018,1016,991,990,979,976,971,952,939,938,931,930,917,908,907,902,891,871,849,848,827,820,819,807,780,779,777,774,764,761,733,703,700,689,633,630,628,623,562,559,556,555,551,505,504,489,488,482,478,421,376,321]) ).
thf(1419,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(1420,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(1421,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(1422,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)],[263]) ).
thf(1423,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(1424,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)],[261]) ).
thf(1425,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(1426,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(1427,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK40_C @ B @ A ) @ A )
& ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(1428,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(1429,plain,
( ( ! [A: $i] :
( ! [SY2062: $i] :
( ~ ( subset @ SY2062 @ ( sK39_B @ A ) )
| ( are_equipotent @ SY2062 @ ( sK39_B @ A ) )
| ( in @ SY2062 @ ( sK39_B @ A ) ) )
& ! [SY2063: $i] :
( ~ ( in @ SY2063 @ ( sK39_B @ A ) )
| ( in @ ( powerset @ SY2063 ) @ ( sK39_B @ A ) ) )
& ! [SY2064: $i,SY2065: $i] :
( ~ ( in @ SY2064 @ ( sK39_B @ A ) )
| ~ ( subset @ SY2065 @ SY2064 )
| ( in @ SY2065 @ ( sK39_B @ A ) ) )
& ( in @ A @ ( sK39_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(1430,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(1431,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(1432,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(1433,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(1434,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)],[251]) ).
thf(1435,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)],[250]) ).
thf(1436,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK38_C @ B @ A ) @ A )
& ( in @ ( sK38_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(1437,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(1438,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK37_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)],[247]) ).
thf(1439,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)],[246]) ).
thf(1440,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)],[245]) ).
thf(1441,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)],[244]) ).
thf(1442,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(1443,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(1444,plain,
( ( ! [A: $i] :
( ( ! [SY2060: $i,SY2061: $i] :
( ( sK36_B @ A )
!= ( ordered_pair @ SY2060 @ SY2061 ) )
& ( in @ ( sK36_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK34_C @ B @ A ) @ ( sK35_SY2059 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(1445,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK33_SY2057 @ B @ A ) @ A )
& ~ ( in @ ( sK32_C @ B @ A ) @ ( sK33_SY2057 @ B @ A ) ) )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ! [SY2058: $i] :
( ~ ( in @ SY2058 @ A )
| ( in @ ( sK32_C @ B @ A ) @ SY2058 ) )
| ( in @ ( sK32_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK31_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK31_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)],[240]) ).
thf(1446,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK30_C @ B @ A )
!= A )
| ~ ( in @ ( sK30_C @ B @ A ) @ B ) )
& ( ( ( sK30_C @ B @ A )
= A )
| ( in @ ( sK30_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)],[239]) ).
thf(1447,plain,
( ( ! [A: $i] :
( ( in @ ( sK29_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(1448,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK28_C @ B @ A ) @ B )
| ~ ( subset @ ( sK28_C @ B @ A ) @ A ) )
& ( ( in @ ( sK28_C @ B @ A ) @ B )
| ( subset @ ( sK28_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)],[237]) ).
thf(1449,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)],[236]) ).
thf(1450,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
= A )
| ( ( sK27_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)],[235]) ).
thf(1451,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ( in @ ( sK26_D @ C @ B @ A ) @ A )
| ( in @ ( sK26_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)],[234]) ).
thf(1452,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY2052: $i,SY2053: $i] :
( ~ ( in @ SY2052 @ A )
| ~ ( in @ SY2053 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY2052 @ SY2053 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY2054 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY2056 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY2054 @ C @ B @ A ) @ ( sK25_SY2056 @ C @ B @ A ) ) ) )
| ( in @ ( sK23_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK21_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK22_SY2051 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY2051 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(1453,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK20_C @ B @ A ) @ A )
& ~ ( in @ ( sK20_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)],[232]) ).
thf(1454,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ( in @ ( sK19_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ B )
| ( in @ ( sK19_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)],[231]) ).
thf(1455,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY2049: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ SY2049 ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY2050 @ B @ A ) ) @ A )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK16_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(1456,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY2047: $i] :
( ~ ( in @ ( sK14_C @ B @ A ) @ SY2047 )
| ~ ( in @ SY2047 @ A ) )
| ~ ( in @ ( sK14_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK14_C @ B @ A ) @ ( sK15_SY2048 @ B @ A ) )
& ( in @ ( sK15_SY2048 @ B @ A ) @ A ) )
| ( in @ ( sK14_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 @ ( sK13_D @ C @ B @ A ) )
& ( in @ ( sK13_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(1457,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ( in @ ( sK12_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)],[228]) ).
thf(1458,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY2045: $i] :
~ ( in @ ( ordered_pair @ SY2045 @ ( sK10_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(1459,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(1460,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(1461,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( ( element @ ( sK8_D @ C @ B @ A ) @ ( powerset @ A ) )
& ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ C )
| ~ ( in @ ( subset_complement @ A @ ( sK8_D @ C @ B @ A ) ) @ B ) )
& ( ( in @ ( sK8_D @ C @ B @ A ) @ C )
| ( in @ ( subset_complement @ A @ ( sK8_D @ C @ B @ A ) ) @ B ) ) )
| ( C
= ( complements_of_subsets @ A @ B ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( C
!= ( complements_of_subsets @ A @ B ) )
| ( ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ ( subset_complement @ A @ D ) @ B ) )
& ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ ( subset_complement @ A @ D ) @ B )
| ( in @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(1462,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(1463,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(1464,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(1465,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(1466,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(1467,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)],[220]) ).
thf(1468,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(1469,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(1470,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(1471,plain,
( ( ! [A: $i] :
( ! [SY2038: $i] :
( ~ ( subset @ SY2038 @ ( sK4_B @ A ) )
| ( are_equipotent @ SY2038 @ ( sK4_B @ A ) )
| ( in @ SY2038 @ ( sK4_B @ A ) ) )
& ! [SY2039: $i] :
( ( ! [SY2044: $i] :
( ~ ( subset @ SY2044 @ SY2039 )
| ( in @ SY2044 @ ( sK5_SY2040 @ SY2039 @ A ) ) )
& ( in @ ( sK5_SY2040 @ SY2039 @ A ) @ ( sK4_B @ A ) ) )
| ~ ( in @ SY2039 @ ( sK4_B @ A ) ) )
& ! [SY2042: $i,SY2043: $i] :
( ~ ( in @ SY2042 @ ( sK4_B @ A ) )
| ~ ( subset @ SY2043 @ SY2042 )
| ( in @ SY2043 @ ( sK4_B @ A ) ) )
& ( in @ A @ ( sK4_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(1472,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY2035 ) @ sK3_SY2037 )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(1473,plain,
( ( relation @ sK3_SY2037 )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(1474,plain,
( ( ~ ( in @ sK2_SY2035 @ ( relation_field @ sK3_SY2037 ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(1475,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1447]) ).
thf(1476,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)],[1449]) ).
thf(1477,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_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)],[1446]) ).
thf(1478,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_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)],[1436]) ).
thf(1479,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY2048 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK15_SY2048 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK14_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 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1456]) ).
thf(1480,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( subset_complement @ SX0 @ ( sK8_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( subset_complement @ SX0 @ ( sK8_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX2
= ( complements_of_subsets @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( SX2
!= ( complements_of_subsets @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( in @ SX3 @ SX2 )
| ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1461]) ).
thf(1481,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1427]) ).
thf(1482,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK19_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)],[1454]) ).
thf(1483,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY2050 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1455]) ).
thf(1484,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)],[1435]) ).
thf(1485,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_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)],[1448]) ).
thf(1486,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1445]) ).
thf(1487,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK27_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)],[1450]) ).
thf(1488,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)],[1422]) ).
thf(1489,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1430]) ).
thf(1490,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)],[1434]) ).
thf(1491,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SX1 @ SX0 ) @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1458]) ).
thf(1492,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)],[1467]) ).
thf(1493,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK4_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK4_B @ SX0 ) )
| ( in @ SX1 @ ( sK4_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK5_SY2040 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SX1 @ SX0 ) @ ( sK4_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK4_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK4_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK4_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK4_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1471]) ).
thf(1494,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1428]) ).
thf(1495,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK36_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK36_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY2059 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1444]) ).
thf(1496,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)],[1441]) ).
thf(1497,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1433]) ).
thf(1498,plain,
( ( ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1464]) ).
thf(1499,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_SY2056 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK24_SY2054 @ SX2 @ SX1 @ SX0 ) @ ( sK25_SY2056 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK22_SY2051 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY2051 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1452]) ).
thf(1500,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK26_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)],[1451]) ).
thf(1501,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK39_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK39_B @ SX0 ) )
| ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK39_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK39_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK39_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK39_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1429]) ).
thf(1502,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1432]) ).
thf(1503,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1426]) ).
thf(1504,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK37_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)],[1438]) ).
thf(1505,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK20_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)],[1453]) ).
thf(1506,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK12_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)],[1457]) ).
thf(1507,plain,
! [SV237: $i] :
( ( ! [SY2355: $i] :
( ~ ( in @ SV237 @ SY2355 )
| ( ( set_union2 @ ( singleton @ SV237 ) @ SY2355 )
= SY2355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1508,plain,
! [SV238: $i] :
( ( ! [SY2356: $i] :
( ~ ( disjoint @ ( singleton @ SV238 ) @ SY2356 )
| ~ ( in @ SV238 @ SY2356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1509,plain,
! [SV239: $i] :
( ( ! [SY2357: $i] :
( ( in @ SV239 @ SY2357 )
| ( disjoint @ ( singleton @ SV239 ) @ SY2357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1510,plain,
! [SV240: $i] :
( ( ! [SY2358: $i] :
( ~ ( element @ SY2358 @ ( powerset @ SV240 ) )
| ! [SY2359: $i] :
( ~ ( in @ SY2359 @ SY2358 )
| ( in @ SY2359 @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1511,plain,
! [SV241: $i] :
( ( ! [SY2360: $i] :
( ~ ( subset @ SV241 @ SY2360 )
| ! [SY2361: $i] :
( ( in @ SY2361 @ SV241 )
| ( subset @ SV241 @ ( set_difference @ SY2360 @ ( singleton @ SY2361 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1512,plain,
! [SV242: $i] :
( ( ! [SY2362: $i] :
( ~ ( in @ SV242 @ SY2362 )
| ( subset @ SV242 @ ( union @ SY2362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1513,plain,
! [SV243: $i] :
( ( ~ ( relation @ SV243 )
| ( subset @ SV243 @ ( cartesian_product2 @ ( relation_dom @ SV243 ) @ ( relation_rng @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1514,plain,
! [SV244: $i] :
( ( ! [SY2363: $i] :
( ~ ( in @ SV244 @ SY2363 )
| ( ( set_union2 @ ( singleton @ SV244 ) @ SY2363 )
= SY2363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1515,plain,
! [SV245: $i] :
( ( ( SV245 = empty_set )
| ! [SY2364: $i] :
( ~ ( element @ SY2364 @ ( powerset @ SV245 ) )
| ! [SY2365: $i] :
( ~ ( element @ SY2365 @ SV245 )
| ( in @ SY2365 @ SY2364 )
| ( in @ SY2365 @ ( subset_complement @ SV245 @ SY2364 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1516,plain,
! [SV246: $i] :
( ( ! [SY2366: $i,SY2367: $i] :
( ~ ( element @ SY2367 @ ( powerset @ SV246 ) )
| ~ ( in @ SY2366 @ ( subset_complement @ SV246 @ SY2367 ) )
| ~ ( in @ SY2366 @ SY2367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1517,plain,
! [SV247: $i] :
( ( ! [SY2368: $i] :
( ~ ( in @ SV247 @ SY2368 )
| ( subset @ SV247 @ ( union @ SY2368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1518,plain,
! [SV248: $i] :
( ( ! [SY2369: $i] :
( ~ ( in @ SV248 @ SY2369 )
| ~ ( in @ SY2369 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1519,plain,
! [SV249: $i] :
( ( ! [SY2370: $i] :
( ( ordered_pair @ SV249 @ SY2370 )
= ( unordered_pair @ ( unordered_pair @ SV249 @ SY2370 ) @ ( singleton @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1520,plain,
! [SV250: $i] :
( ( ~ ( relation @ SV250 )
| ( ( relation_field @ SV250 )
= ( set_union2 @ ( relation_dom @ SV250 ) @ ( relation_rng @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1521,plain,
! [SV251: $i] :
( ( ! [SY2371: $i] :
~ ( empty @ ( ordered_pair @ SV251 @ SY2371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1522,plain,
! [SV252: $i] :
( ( ! [SY2372: $i] :
( ~ ( relation @ SV252 )
| ~ ( relation @ SY2372 )
| ( relation @ ( set_union2 @ SV252 @ SY2372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1523,plain,
! [SV253: $i] :
( ( ! [SY2373: $i] :
( ~ ( in @ SV253 @ SY2373 )
| ( element @ SV253 @ SY2373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1524,plain,
! [SV254: $i] :
( ( ! [SY2374: $i] :
( ~ ( element @ SV254 @ SY2374 )
| ( empty @ SY2374 )
| ( in @ SV254 @ SY2374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1525,plain,
! [SV255: $i] :
( ( ! [SY2375: $i,SY2376: $i] :
( ~ ( element @ SY2375 @ ( powerset @ SY2376 ) )
| ~ ( in @ SV255 @ SY2375 )
| ( element @ SV255 @ SY2376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1526,plain,
! [SV256: $i] :
( ( ! [SY2377: $i,SY2378: $i] :
( ~ ( element @ SY2377 @ ( powerset @ SY2378 ) )
| ~ ( in @ SV256 @ SY2377 )
| ~ ( empty @ SY2378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1527,plain,
! [SV257: $i] :
( ( ! [SY2379: $i] :
( ~ ( empty @ SY2379 )
| ~ ( in @ SV257 @ SY2379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1528,plain,
( ( in @ sK2_SY2035 @ ( relation_field @ sK3_SY2037 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1529,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1530,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)],[1476]) ).
thf(1531,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_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)],[1477]) ).
thf(1532,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_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)],[1478]) ).
thf(1533,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY2048 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK15_SY2048 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK14_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 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1534,plain,
! [SV258: $i] :
( ( ! [SY2380: $i] :
( ~ ( element @ SY2380 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ! [SY2381: $i] :
( ~ ( element @ SY2381 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2381 @ SY2380 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2381 @ SY2380 @ SV258 ) @ SY2381 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2381 @ SY2380 @ SV258 ) ) @ SY2380 ) )
| ~ ( ( in @ ( sK8_D @ SY2381 @ SY2380 @ SV258 ) @ SY2381 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2381 @ SY2380 @ SV258 ) ) @ SY2380 ) ) ) )
| ( SY2381
= ( complements_of_subsets @ SV258 @ SY2380 ) ) )
| ~ ! [SY2382: $i] :
( ~ ( element @ SY2382 @ ( powerset @ ( powerset @ SV258 ) ) )
| ( SY2382
!= ( complements_of_subsets @ SV258 @ SY2380 ) )
| ~ ( ~ ! [SY2383: $i] :
( ~ ( element @ SY2383 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2383 @ SY2382 )
| ( in @ ( subset_complement @ SV258 @ SY2383 ) @ SY2380 ) )
| ~ ! [SY2384: $i] :
( ~ ( element @ SY2384 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2384 ) @ SY2380 )
| ( in @ SY2384 @ SY2382 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1535,plain,
! [SV259: $i] :
( ( ! [SY2385: $i] :
( ~ ( ~ ( in @ ( sK40_C @ SY2385 @ SV259 ) @ SV259 )
| ~ ~ ( in @ ( sK40_C @ SY2385 @ SV259 ) @ SY2385 ) )
| ( element @ SV259 @ ( powerset @ SY2385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1536,plain,
! [SV260: $i] :
( ( ~ ( ~ ! [SY2386: $i,SY2387: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2386 )
| ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) )
| ~ ( ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2386 )
| ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) ) ) )
| ( SY2387
= ( set_intersection2 @ SV260 @ SY2386 ) ) )
| ~ ! [SY2388: $i,SY2389: $i] :
( ( SY2389
!= ( set_intersection2 @ SV260 @ SY2388 ) )
| ~ ( ~ ! [SY2390: $i] :
( ~ ( in @ SY2390 @ SV260 )
| ~ ( in @ SY2390 @ SY2388 )
| ( in @ SY2390 @ SY2389 ) )
| ~ ~ ( ~ ! [SY2391: $i] :
( ~ ( in @ SY2391 @ SY2389 )
| ( in @ SY2391 @ SV260 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2389 )
| ( in @ SX3 @ SY2388 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1537,plain,
! [SV261: $i] :
( ( ~ ( relation @ SV261 )
| ~ ( ~ ! [SY2393: $i] :
( ~ ( ~ ( ! [SY2394: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ SY2394 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ ( sK18_SY2050 @ SY2393 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) ) )
| ( SY2393
= ( relation_dom @ SV261 ) ) )
| ~ ! [SY2395: $i] :
( ( SY2395
!= ( relation_dom @ SV261 ) )
| ~ ( ~ ! [SY2396: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2396 @ SY2397 ) @ SV261 )
| ( in @ SY2396 @ SY2395 ) )
| ~ ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SY2395 )
| ( in @ ( ordered_pair @ SY2398 @ ( sK16_D @ SY2398 @ SY2395 @ SV261 ) ) @ SV261 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1538,plain,
! [SV262: $i] :
( ( ~ ( ~ ! [SY2399: $i,SY2400: $i] :
( ~ ( in @ SV262 @ SY2400 )
| ~ ( in @ SY2399 @ SY2400 )
| ( subset @ ( unordered_pair @ SV262 @ SY2399 ) @ SY2400 ) )
| ~ ~ ( ~ ! [SY2401: $i,SY2402: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2401 ) @ SY2402 )
| ( in @ SV262 @ SY2402 ) )
| ~ ! [SY2403: $i,SY2404: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2403 ) @ SY2404 )
| ( in @ SY2403 @ SY2404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1539,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_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)],[1485]) ).
thf(1540,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1486]) ).
thf(1541,plain,
! [SV263: $i] :
( ( ~ ( ~ ! [SY2405: $i,SY2406: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
!= SY2405 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
= SV263 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
= SY2405 ) ) )
| ( SY2406
= ( unordered_pair @ SV263 @ SY2405 ) ) )
| ~ ! [SY2407: $i,SY2408: $i] :
( ( SY2408
!= ( unordered_pair @ SV263 @ SY2407 ) )
| ~ ( ~ ! [SY2409: $i] :
( ~ ( in @ SY2409 @ SY2408 )
| ( SY2409 = SV263 )
| ( SY2409 = SY2407 ) )
| ~ ~ ( ~ ! [SY2410: $i] :
( ( SY2410 != SV263 )
| ( in @ SY2410 @ SY2408 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY2407 )
| ( in @ SX3 @ SY2408 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1542,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)],[1488]) ).
thf(1543,plain,
! [SV264: $i] :
( ( ~ ( ~ ! [SY2412: $i,SY2413: $i] :
( ~ ( relation @ SY2413 )
| ~ ( in @ ( ordered_pair @ SV264 @ SY2412 ) @ SY2413 )
| ( in @ SV264 @ ( relation_dom @ SY2413 ) ) )
| ~ ! [SY2414: $i,SY2415: $i] :
( ~ ( relation @ SY2415 )
| ~ ( in @ ( ordered_pair @ SV264 @ SY2414 ) @ SY2415 )
| ( in @ SY2414 @ ( relation_rng @ SY2415 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1544,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)],[1490]) ).
thf(1545,plain,
! [SV265: $i] :
( ( ~ ( relation @ SV265 )
| ~ ( ~ ! [SY2416: $i] :
( ~ ( ~ ( ! [SY2417: $i] :
~ ( in @ ( ordered_pair @ SY2417 @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2416 @ SV265 ) @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) ) )
| ( SY2416
= ( relation_rng @ SV265 ) ) )
| ~ ! [SY2418: $i] :
( ( SY2418
!= ( relation_rng @ SV265 ) )
| ~ ( ~ ! [SY2419: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2419 ) @ SV265 )
| ( in @ SY2419 @ SY2418 ) )
| ~ ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SY2418 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2421 @ SY2418 @ SV265 ) @ SY2421 ) @ SV265 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1546,plain,
! [SV266: $i] :
( ( ! [SY2422: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SY2422 @ SV266 ) @ SV266 )
| ~ ( in @ ( sK6_C @ SY2422 @ SV266 ) @ SY2422 ) )
| ~ ( ( in @ ( sK6_C @ SY2422 @ SV266 ) @ SV266 )
| ( in @ ( sK6_C @ SY2422 @ SV266 ) @ SY2422 ) ) )
| ( SV266 = SY2422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1547,plain,
! [SV267: $i] :
( ( ~ ( ~ ! [SY2423: $i] :
( ~ ( subset @ SY2423 @ ( sK4_B @ SV267 ) )
| ( are_equipotent @ SY2423 @ ( sK4_B @ SV267 ) )
| ( in @ SY2423 @ ( sK4_B @ SV267 ) ) )
| ~ ~ ( ~ ! [SY2424: $i] :
( ~ ( ~ ! [SY2425: $i] :
( ~ ( subset @ SY2425 @ SY2424 )
| ( in @ SY2425 @ ( sK5_SY2040 @ SY2424 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2424 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SY2424 @ ( sK4_B @ SV267 ) ) )
| ~ ~ ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1548,plain,
! [SV268: $i] :
( ( ! [SY2428: $i] :
~ ( ~ ! [SY2429: $i,SY2430: $i] :
( ~ ( in @ SV268 @ SY2429 )
| ~ ( in @ SY2428 @ SY2430 )
| ( in @ ( ordered_pair @ SV268 @ SY2428 ) @ ( cartesian_product2 @ SY2429 @ SY2430 ) ) )
| ~ ~ ( ~ ! [SY2431: $i] :
( ! [SY2432: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SY2428 ) @ ( cartesian_product2 @ SY2431 @ SY2432 ) )
| ( in @ SV268 @ SY2431 ) )
| ~ ! [SY2433: $i,SY2434: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SY2428 ) @ ( cartesian_product2 @ SY2433 @ SY2434 ) )
| ( in @ SY2428 @ SY2434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1549,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK36_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK36_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY2059 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1550,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)],[1496]) ).
thf(1551,plain,
! [SV269: $i] :
( ( ! [SY2435: $i] :
~ ( ~ ! [SY2436: $i] :
( ! [SY2437: $i] :
( ( ordered_pair @ SV269 @ SY2435 )
!= ( ordered_pair @ SY2436 @ SY2437 ) )
| ( SV269 = SY2436 ) )
| ~ ! [SY2438: $i,SY2439: $i] :
( ( ( ordered_pair @ SV269 @ SY2435 )
!= ( ordered_pair @ SY2438 @ SY2439 ) )
| ( SY2435 = SY2439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1552,plain,
( ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1553,plain,
! [SV270: $i] :
( ( ~ ( ~ ! [SY2440: $i,SY2441: $i] :
( ~ ( ~ ( ! [SY2442: $i,SY2443: $i] :
( ~ ( in @ SY2442 @ SV270 )
| ~ ( in @ SY2443 @ SY2440 )
| ( ( sK23_D @ SY2441 @ SY2440 @ SV270 )
!= ( ordered_pair @ SY2442 @ SY2443 ) ) )
| ~ ( in @ ( sK23_D @ SY2441 @ SY2440 @ SV270 ) @ SY2441 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2441 @ SY2440 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SY2441 @ SY2440 @ SV270 ) @ SY2440 ) )
| ( ( sK23_D @ SY2441 @ SY2440 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2441 @ SY2440 @ SV270 ) @ ( sK25_SY2056 @ SY2441 @ SY2440 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SY2441 @ SY2440 @ SV270 ) @ SY2441 ) ) )
| ( SY2441
= ( cartesian_product2 @ SV270 @ SY2440 ) ) )
| ~ ! [SY2444: $i,SY2445: $i] :
( ( SY2445
!= ( cartesian_product2 @ SV270 @ SY2444 ) )
| ~ ( ~ ! [SY2446: $i] :
( ! [SY2447: $i,SY2448: $i] :
( ~ ( in @ SY2447 @ SV270 )
| ~ ( in @ SY2448 @ SY2444 )
| ( SY2446
!= ( ordered_pair @ SY2447 @ SY2448 ) ) )
| ( in @ SY2446 @ SY2445 ) )
| ~ ! [SY2449: $i] :
( ~ ( in @ SY2449 @ SY2445 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ SY2444 ) )
| ( SY2449
!= ( ordered_pair @ ( sK21_E @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ ( sK22_SY2051 @ SY2449 @ SY2445 @ SY2444 @ SV270 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1554,plain,
! [SV271: $i] :
( ( ~ ( ~ ! [SY2450: $i,SY2451: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2450 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2450 ) ) )
| ( SY2451
= ( set_union2 @ SV271 @ SY2450 ) ) )
| ~ ! [SY2452: $i,SY2453: $i] :
( ( SY2453
!= ( set_union2 @ SV271 @ SY2452 ) )
| ~ ( ~ ! [SY2454: $i] :
( ~ ( in @ SY2454 @ SY2453 )
| ( in @ SY2454 @ SV271 )
| ( in @ SY2454 @ SY2452 ) )
| ~ ~ ( ~ ! [SY2455: $i] :
( ~ ( in @ SY2455 @ SV271 )
| ( in @ SY2455 @ SY2453 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2452 )
| ( in @ SX3 @ SY2453 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1555,plain,
! [SV272: $i] :
( ( ~ ( ~ ! [SY2457: $i] :
( ~ ( subset @ SY2457 @ ( sK39_B @ SV272 ) )
| ( are_equipotent @ SY2457 @ ( sK39_B @ SV272 ) )
| ( in @ SY2457 @ ( sK39_B @ SV272 ) ) )
| ~ ~ ( ~ ! [SY2458: $i] :
( ~ ( in @ SY2458 @ ( sK39_B @ SV272 ) )
| ( in @ ( powerset @ SY2458 ) @ ( sK39_B @ SV272 ) ) )
| ~ ~ ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) )
| ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1556,plain,
! [SV273: $i] :
( ( ~ ( relation @ SV273 )
| ~ ( ~ ! [SY2461: $i] :
( ~ ( relation @ SY2461 )
| ~ ( subset @ SV273 @ SY2461 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SY2461 ) ) )
| ~ ! [SY2462: $i] :
( ~ ( relation @ SY2462 )
| ~ ( subset @ SV273 @ SY2462 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SY2462 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1557,plain,
! [SV274: $i] :
( ( ! [SY2463: $i] :
~ ( ~ ! [SY2464: $i,SY2465: $i] :
( ~ ( in @ SV274 @ SY2464 )
| ~ ( in @ SY2463 @ SY2465 )
| ( in @ ( ordered_pair @ SV274 @ SY2463 ) @ ( cartesian_product2 @ SY2464 @ SY2465 ) ) )
| ~ ~ ( ~ ! [SY2466: $i] :
( ! [SY2467: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY2463 ) @ ( cartesian_product2 @ SY2466 @ SY2467 ) )
| ( in @ SV274 @ SY2466 ) )
| ~ ! [SY2468: $i,SY2469: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SY2463 ) @ ( cartesian_product2 @ SY2468 @ SY2469 ) )
| ( in @ SY2463 @ SY2469 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1558,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK37_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)],[1504]) ).
thf(1559,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK20_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)],[1505]) ).
thf(1560,plain,
! [SV275: $i] :
( ( ~ ( ~ ! [SY2470: $i,SY2471: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2470 )
| ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2470 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) ) ) )
| ( SY2471
= ( set_difference @ SV275 @ SY2470 ) ) )
| ~ ! [SY2472: $i,SY2473: $i] :
( ( SY2473
!= ( set_difference @ SV275 @ SY2472 ) )
| ~ ( ~ ! [SY2474: $i] :
( ~ ( in @ SY2474 @ SV275 )
| ( in @ SY2474 @ SY2472 )
| ( in @ SY2474 @ SY2473 ) )
| ~ ~ ( ~ ! [SY2475: $i] :
( ~ ( in @ SY2475 @ SY2473 )
| ( in @ SY2475 @ SV275 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2473 )
| ~ ( in @ SX3 @ SY2472 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1561,plain,
! [SV276: $i,SV237: $i] :
( ( ~ ( in @ SV237 @ SV276 )
| ( ( set_union2 @ ( singleton @ SV237 ) @ SV276 )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1562,plain,
! [SV277: $i,SV238: $i] :
( ( ~ ( disjoint @ ( singleton @ SV238 ) @ SV277 )
| ~ ( in @ SV238 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1563,plain,
! [SV278: $i,SV239: $i] :
( ( ( in @ SV239 @ SV278 )
| ( disjoint @ ( singleton @ SV239 ) @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1564,plain,
! [SV240: $i,SV279: $i] :
( ( ~ ( element @ SV279 @ ( powerset @ SV240 ) )
| ! [SY2477: $i] :
( ~ ( in @ SY2477 @ SV279 )
| ( in @ SY2477 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1565,plain,
! [SV280: $i,SV241: $i] :
( ( ~ ( subset @ SV241 @ SV280 )
| ! [SY2478: $i] :
( ( in @ SY2478 @ SV241 )
| ( subset @ SV241 @ ( set_difference @ SV280 @ ( singleton @ SY2478 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1566,plain,
! [SV281: $i,SV242: $i] :
( ( ~ ( in @ SV242 @ SV281 )
| ( subset @ SV242 @ ( union @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1567,plain,
! [SV243: $i] :
( ( ( ~ ( relation @ SV243 ) )
= $true )
| ( ( subset @ SV243 @ ( cartesian_product2 @ ( relation_dom @ SV243 ) @ ( relation_rng @ SV243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1568,plain,
! [SV282: $i,SV244: $i] :
( ( ~ ( in @ SV244 @ SV282 )
| ( ( set_union2 @ ( singleton @ SV244 ) @ SV282 )
= SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1569,plain,
! [SV245: $i] :
( ( ( SV245 = empty_set )
= $true )
| ( ( ! [SY2364: $i] :
( ~ ( element @ SY2364 @ ( powerset @ SV245 ) )
| ! [SY2365: $i] :
( ~ ( element @ SY2365 @ SV245 )
| ( in @ SY2365 @ SY2364 )
| ( in @ SY2365 @ ( subset_complement @ SV245 @ SY2364 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1570,plain,
! [SV283: $i,SV246: $i] :
( ( ! [SY2479: $i] :
( ~ ( element @ SY2479 @ ( powerset @ SV246 ) )
| ~ ( in @ SV283 @ ( subset_complement @ SV246 @ SY2479 ) )
| ~ ( in @ SV283 @ SY2479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1571,plain,
! [SV284: $i,SV247: $i] :
( ( ~ ( in @ SV247 @ SV284 )
| ( subset @ SV247 @ ( union @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1572,plain,
! [SV285: $i,SV248: $i] :
( ( ~ ( in @ SV248 @ SV285 )
| ~ ( in @ SV285 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1573,plain,
! [SV286: $i,SV249: $i] :
( ( ( ordered_pair @ SV249 @ SV286 )
= ( unordered_pair @ ( unordered_pair @ SV249 @ SV286 ) @ ( singleton @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1574,plain,
! [SV250: $i] :
( ( ( ~ ( relation @ SV250 ) )
= $true )
| ( ( ( relation_field @ SV250 )
= ( set_union2 @ ( relation_dom @ SV250 ) @ ( relation_rng @ SV250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1575,plain,
! [SV287: $i,SV251: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV251 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1576,plain,
! [SV288: $i,SV252: $i] :
( ( ~ ( relation @ SV252 )
| ~ ( relation @ SV288 )
| ( relation @ ( set_union2 @ SV252 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1577,plain,
! [SV289: $i,SV253: $i] :
( ( ~ ( in @ SV253 @ SV289 )
| ( element @ SV253 @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1578,plain,
! [SV290: $i,SV254: $i] :
( ( ~ ( element @ SV254 @ SV290 )
| ( empty @ SV290 )
| ( in @ SV254 @ SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1579,plain,
! [SV255: $i,SV291: $i] :
( ( ! [SY2480: $i] :
( ~ ( element @ SV291 @ ( powerset @ SY2480 ) )
| ~ ( in @ SV255 @ SV291 )
| ( element @ SV255 @ SY2480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1580,plain,
! [SV256: $i,SV292: $i] :
( ( ! [SY2481: $i] :
( ~ ( element @ SV292 @ ( powerset @ SY2481 ) )
| ~ ( in @ SV256 @ SV292 )
| ~ ( empty @ SY2481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1581,plain,
! [SV257: $i,SV293: $i] :
( ( ~ ( empty @ SV293 )
| ~ ( in @ SV257 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1582,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1583,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1584,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)],[1530]) ).
thf(1585,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)],[1530]) ).
thf(1586,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1587,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)],[1531]) ).
thf(1588,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1589,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1590,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY2048 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK15_SY2048 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1591,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 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1592,plain,
! [SV258: $i,SV294: $i] :
( ( ~ ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ! [SY2482: $i] :
( ~ ( element @ SY2482 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SY2482
= ( complements_of_subsets @ SV258 @ SV294 ) ) )
| ~ ! [SY2483: $i] :
( ~ ( element @ SY2483 @ ( powerset @ ( powerset @ SV258 ) ) )
| ( SY2483
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2484: $i] :
( ~ ( element @ SY2484 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2484 @ SY2483 )
| ( in @ ( subset_complement @ SV258 @ SY2484 ) @ SV294 ) )
| ~ ! [SY2485: $i] :
( ~ ( element @ SY2485 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2485 ) @ SV294 )
| ( in @ SY2485 @ SY2483 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1593,plain,
! [SV259: $i,SV295: $i] :
( ( ~ ( ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV259 )
| ~ ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV295 ) )
| ( element @ SV259 @ ( powerset @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1594,plain,
! [SV260: $i] :
( ( ~ ! [SY2386: $i,SY2387: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2386 )
| ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) )
| ~ ( ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2386 )
| ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) ) ) )
| ( SY2387
= ( set_intersection2 @ SV260 @ SY2386 ) ) )
| ~ ! [SY2388: $i,SY2389: $i] :
( ( SY2389
!= ( set_intersection2 @ SV260 @ SY2388 ) )
| ~ ( ~ ! [SY2390: $i] :
( ~ ( in @ SY2390 @ SV260 )
| ~ ( in @ SY2390 @ SY2388 )
| ( in @ SY2390 @ SY2389 ) )
| ~ ~ ( ~ ! [SY2391: $i] :
( ~ ( in @ SY2391 @ SY2389 )
| ( in @ SY2391 @ SV260 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2389 )
| ( in @ SX3 @ SY2388 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1595,plain,
! [SV261: $i] :
( ( ( ~ ( relation @ SV261 ) )
= $true )
| ( ( ~ ( ~ ! [SY2393: $i] :
( ~ ( ~ ( ! [SY2394: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ SY2394 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ ( sK18_SY2050 @ SY2393 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) ) )
| ( SY2393
= ( relation_dom @ SV261 ) ) )
| ~ ! [SY2395: $i] :
( ( SY2395
!= ( relation_dom @ SV261 ) )
| ~ ( ~ ! [SY2396: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2396 @ SY2397 ) @ SV261 )
| ( in @ SY2396 @ SY2395 ) )
| ~ ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SY2395 )
| ( in @ ( ordered_pair @ SY2398 @ ( sK16_D @ SY2398 @ SY2395 @ SV261 ) ) @ SV261 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1596,plain,
! [SV262: $i] :
( ( ~ ! [SY2399: $i,SY2400: $i] :
( ~ ( in @ SV262 @ SY2400 )
| ~ ( in @ SY2399 @ SY2400 )
| ( subset @ ( unordered_pair @ SV262 @ SY2399 ) @ SY2400 ) )
| ~ ~ ( ~ ! [SY2401: $i,SY2402: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2401 ) @ SY2402 )
| ( in @ SV262 @ SY2402 ) )
| ~ ! [SY2403: $i,SY2404: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2403 ) @ SY2404 )
| ( in @ SY2403 @ SY2404 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1597,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1539]) ).
thf(1598,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)],[1539]) ).
thf(1599,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1540]) ).
thf(1600,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)],[1540]) ).
thf(1601,plain,
! [SV263: $i] :
( ( ~ ! [SY2405: $i,SY2406: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
!= SY2405 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
= SV263 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
= SY2405 ) ) )
| ( SY2406
= ( unordered_pair @ SV263 @ SY2405 ) ) )
| ~ ! [SY2407: $i,SY2408: $i] :
( ( SY2408
!= ( unordered_pair @ SV263 @ SY2407 ) )
| ~ ( ~ ! [SY2409: $i] :
( ~ ( in @ SY2409 @ SY2408 )
| ( SY2409 = SV263 )
| ( SY2409 = SY2407 ) )
| ~ ~ ( ~ ! [SY2410: $i] :
( ( SY2410 != SV263 )
| ( in @ SY2410 @ SY2408 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY2407 )
| ( in @ SX3 @ SY2408 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1602,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1603,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1604,plain,
! [SV264: $i] :
( ( ~ ! [SY2412: $i,SY2413: $i] :
( ~ ( relation @ SY2413 )
| ~ ( in @ ( ordered_pair @ SV264 @ SY2412 ) @ SY2413 )
| ( in @ SV264 @ ( relation_dom @ SY2413 ) ) )
| ~ ! [SY2414: $i,SY2415: $i] :
( ~ ( relation @ SY2415 )
| ~ ( in @ ( ordered_pair @ SV264 @ SY2414 ) @ SY2415 )
| ( in @ SY2414 @ ( relation_rng @ SY2415 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1605,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1606,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1607,plain,
! [SV265: $i] :
( ( ( ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( ~ ! [SY2416: $i] :
( ~ ( ~ ( ! [SY2417: $i] :
~ ( in @ ( ordered_pair @ SY2417 @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2416 @ SV265 ) @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) ) )
| ( SY2416
= ( relation_rng @ SV265 ) ) )
| ~ ! [SY2418: $i] :
( ( SY2418
!= ( relation_rng @ SV265 ) )
| ~ ( ~ ! [SY2419: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2419 ) @ SV265 )
| ( in @ SY2419 @ SY2418 ) )
| ~ ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SY2418 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2421 @ SY2418 @ SV265 ) @ SY2421 ) @ SV265 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1608,plain,
! [SV266: $i,SV296: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) )
| ~ ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) ) )
| ( SV266 = SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1609,plain,
! [SV267: $i] :
( ( ~ ! [SY2423: $i] :
( ~ ( subset @ SY2423 @ ( sK4_B @ SV267 ) )
| ( are_equipotent @ SY2423 @ ( sK4_B @ SV267 ) )
| ( in @ SY2423 @ ( sK4_B @ SV267 ) ) )
| ~ ~ ( ~ ! [SY2424: $i] :
( ~ ( ~ ! [SY2425: $i] :
( ~ ( subset @ SY2425 @ SY2424 )
| ( in @ SY2425 @ ( sK5_SY2040 @ SY2424 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2424 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SY2424 @ ( sK4_B @ SV267 ) ) )
| ~ ~ ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1610,plain,
! [SV297: $i,SV268: $i] :
( ( ~ ( ~ ! [SY2486: $i,SY2487: $i] :
( ~ ( in @ SV268 @ SY2486 )
| ~ ( in @ SV297 @ SY2487 )
| ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2486 @ SY2487 ) ) )
| ~ ~ ( ~ ! [SY2488: $i] :
( ! [SY2489: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2488 @ SY2489 ) )
| ( in @ SV268 @ SY2488 ) )
| ~ ! [SY2490: $i,SY2491: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2490 @ SY2491 ) )
| ( in @ SV297 @ SY2491 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1611,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK36_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK36_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1612,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY2059 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1613,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1614,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1615,plain,
! [SV298: $i,SV269: $i] :
( ( ~ ( ~ ! [SY2492: $i] :
( ! [SY2493: $i] :
( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SY2492 @ SY2493 ) )
| ( SV269 = SY2492 ) )
| ~ ! [SY2494: $i,SY2495: $i] :
( ( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SY2494 @ SY2495 ) )
| ( SV298 = SY2495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1616,plain,
( ( ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1617,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1618,plain,
! [SV270: $i] :
( ( ~ ! [SY2440: $i,SY2441: $i] :
( ~ ( ~ ( ! [SY2442: $i,SY2443: $i] :
( ~ ( in @ SY2442 @ SV270 )
| ~ ( in @ SY2443 @ SY2440 )
| ( ( sK23_D @ SY2441 @ SY2440 @ SV270 )
!= ( ordered_pair @ SY2442 @ SY2443 ) ) )
| ~ ( in @ ( sK23_D @ SY2441 @ SY2440 @ SV270 ) @ SY2441 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2441 @ SY2440 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SY2441 @ SY2440 @ SV270 ) @ SY2440 ) )
| ( ( sK23_D @ SY2441 @ SY2440 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2441 @ SY2440 @ SV270 ) @ ( sK25_SY2056 @ SY2441 @ SY2440 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SY2441 @ SY2440 @ SV270 ) @ SY2441 ) ) )
| ( SY2441
= ( cartesian_product2 @ SV270 @ SY2440 ) ) )
| ~ ! [SY2444: $i,SY2445: $i] :
( ( SY2445
!= ( cartesian_product2 @ SV270 @ SY2444 ) )
| ~ ( ~ ! [SY2446: $i] :
( ! [SY2447: $i,SY2448: $i] :
( ~ ( in @ SY2447 @ SV270 )
| ~ ( in @ SY2448 @ SY2444 )
| ( SY2446
!= ( ordered_pair @ SY2447 @ SY2448 ) ) )
| ( in @ SY2446 @ SY2445 ) )
| ~ ! [SY2449: $i] :
( ~ ( in @ SY2449 @ SY2445 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ SY2444 ) )
| ( SY2449
!= ( ordered_pair @ ( sK21_E @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ ( sK22_SY2051 @ SY2449 @ SY2445 @ SY2444 @ SV270 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1619,plain,
! [SV271: $i] :
( ( ~ ! [SY2450: $i,SY2451: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2450 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2450 ) ) )
| ( SY2451
= ( set_union2 @ SV271 @ SY2450 ) ) )
| ~ ! [SY2452: $i,SY2453: $i] :
( ( SY2453
!= ( set_union2 @ SV271 @ SY2452 ) )
| ~ ( ~ ! [SY2454: $i] :
( ~ ( in @ SY2454 @ SY2453 )
| ( in @ SY2454 @ SV271 )
| ( in @ SY2454 @ SY2452 ) )
| ~ ~ ( ~ ! [SY2455: $i] :
( ~ ( in @ SY2455 @ SV271 )
| ( in @ SY2455 @ SY2453 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2452 )
| ( in @ SX3 @ SY2453 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1620,plain,
! [SV272: $i] :
( ( ~ ! [SY2457: $i] :
( ~ ( subset @ SY2457 @ ( sK39_B @ SV272 ) )
| ( are_equipotent @ SY2457 @ ( sK39_B @ SV272 ) )
| ( in @ SY2457 @ ( sK39_B @ SV272 ) ) )
| ~ ~ ( ~ ! [SY2458: $i] :
( ~ ( in @ SY2458 @ ( sK39_B @ SV272 ) )
| ( in @ ( powerset @ SY2458 ) @ ( sK39_B @ SV272 ) ) )
| ~ ~ ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) )
| ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1621,plain,
! [SV273: $i] :
( ( ( ~ ( relation @ SV273 ) )
= $true )
| ( ( ~ ( ~ ! [SY2461: $i] :
( ~ ( relation @ SY2461 )
| ~ ( subset @ SV273 @ SY2461 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SY2461 ) ) )
| ~ ! [SY2462: $i] :
( ~ ( relation @ SY2462 )
| ~ ( subset @ SV273 @ SY2462 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SY2462 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1622,plain,
! [SV299: $i,SV274: $i] :
( ( ~ ( ~ ! [SY2496: $i,SY2497: $i] :
( ~ ( in @ SV274 @ SY2496 )
| ~ ( in @ SV299 @ SY2497 )
| ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2496 @ SY2497 ) ) )
| ~ ~ ( ~ ! [SY2498: $i] :
( ! [SY2499: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2498 @ SY2499 ) )
| ( in @ SV274 @ SY2498 ) )
| ~ ! [SY2500: $i,SY2501: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2500 @ SY2501 ) )
| ( in @ SV299 @ SY2501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1623,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK37_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1624,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1625,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1626,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1627,plain,
! [SV275: $i] :
( ( ~ ! [SY2470: $i,SY2471: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2470 )
| ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2470 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) ) ) )
| ( SY2471
= ( set_difference @ SV275 @ SY2470 ) ) )
| ~ ! [SY2472: $i,SY2473: $i] :
( ( SY2473
!= ( set_difference @ SV275 @ SY2472 ) )
| ~ ( ~ ! [SY2474: $i] :
( ~ ( in @ SY2474 @ SV275 )
| ( in @ SY2474 @ SY2472 )
| ( in @ SY2474 @ SY2473 ) )
| ~ ~ ( ~ ! [SY2475: $i] :
( ~ ( in @ SY2475 @ SY2473 )
| ( in @ SY2475 @ SV275 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2473 )
| ~ ( in @ SX3 @ SY2472 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1628,plain,
! [SV276: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ SV276 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV237 ) @ SV276 )
= SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1629,plain,
! [SV277: $i,SV238: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV238 ) @ SV277 ) )
= $true )
| ( ( ~ ( in @ SV238 @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1630,plain,
! [SV278: $i,SV239: $i] :
( ( ( in @ SV239 @ SV278 )
= $true )
| ( ( disjoint @ ( singleton @ SV239 ) @ SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1631,plain,
! [SV240: $i,SV279: $i] :
( ( ( ~ ( element @ SV279 @ ( powerset @ SV240 ) ) )
= $true )
| ( ( ! [SY2477: $i] :
( ~ ( in @ SY2477 @ SV279 )
| ( in @ SY2477 @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1632,plain,
! [SV280: $i,SV241: $i] :
( ( ( ~ ( subset @ SV241 @ SV280 ) )
= $true )
| ( ( ! [SY2478: $i] :
( ( in @ SY2478 @ SV241 )
| ( subset @ SV241 @ ( set_difference @ SV280 @ ( singleton @ SY2478 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1633,plain,
! [SV281: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV281 ) )
= $true )
| ( ( subset @ SV242 @ ( union @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1634,plain,
! [SV243: $i] :
( ( ( relation @ SV243 )
= $false )
| ( ( subset @ SV243 @ ( cartesian_product2 @ ( relation_dom @ SV243 ) @ ( relation_rng @ SV243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1635,plain,
! [SV282: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV282 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV244 ) @ SV282 )
= SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1636,plain,
! [SV245: $i,SV300: $i] :
( ( ( ~ ( element @ SV300 @ ( powerset @ SV245 ) )
| ! [SY2502: $i] :
( ~ ( element @ SY2502 @ SV245 )
| ( in @ SY2502 @ SV300 )
| ( in @ SY2502 @ ( subset_complement @ SV245 @ SV300 ) ) ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1637,plain,
! [SV283: $i,SV246: $i,SV301: $i] :
( ( ~ ( element @ SV301 @ ( powerset @ SV246 ) )
| ~ ( in @ SV283 @ ( subset_complement @ SV246 @ SV301 ) )
| ~ ( in @ SV283 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1638,plain,
! [SV284: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV284 ) )
= $true )
| ( ( subset @ SV247 @ ( union @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1639,plain,
! [SV285: $i,SV248: $i] :
( ( ( ~ ( in @ SV248 @ SV285 ) )
= $true )
| ( ( ~ ( in @ SV285 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1640,plain,
! [SV250: $i] :
( ( ( relation @ SV250 )
= $false )
| ( ( ( relation_field @ SV250 )
= ( set_union2 @ ( relation_dom @ SV250 ) @ ( relation_rng @ SV250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1641,plain,
! [SV287: $i,SV251: $i] :
( ( empty @ ( ordered_pair @ SV251 @ SV287 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1642,plain,
! [SV288: $i,SV252: $i] :
( ( ( ~ ( relation @ SV252 )
| ~ ( relation @ SV288 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV252 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1643,plain,
! [SV289: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV289 ) )
= $true )
| ( ( element @ SV253 @ SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1644,plain,
! [SV290: $i,SV254: $i] :
( ( ( ~ ( element @ SV254 @ SV290 ) )
= $true )
| ( ( ( empty @ SV290 )
| ( in @ SV254 @ SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1578]) ).
thf(1645,plain,
! [SV255: $i,SV302: $i,SV291: $i] :
( ( ~ ( element @ SV291 @ ( powerset @ SV302 ) )
| ~ ( in @ SV255 @ SV291 )
| ( element @ SV255 @ SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1646,plain,
! [SV256: $i,SV303: $i,SV292: $i] :
( ( ~ ( element @ SV292 @ ( powerset @ SV303 ) )
| ~ ( in @ SV256 @ SV292 )
| ~ ( empty @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1647,plain,
! [SV257: $i,SV293: $i] :
( ( ( ~ ( empty @ SV293 ) )
= $true )
| ( ( ~ ( in @ SV257 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1648,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1649,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1650,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)],[1584]) ).
thf(1651,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)],[1585]) ).
thf(1652,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1653,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)],[1587]) ).
thf(1654,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1655,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1656,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY2048 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK15_SY2048 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1657,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 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1658,plain,
! [SV258: $i,SV294: $i] :
( ( ( ~ ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2482: $i] :
( ~ ( element @ SY2482 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SY2482
= ( complements_of_subsets @ SV258 @ SV294 ) ) )
| ~ ! [SY2483: $i] :
( ~ ( element @ SY2483 @ ( powerset @ ( powerset @ SV258 ) ) )
| ( SY2483
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2484: $i] :
( ~ ( element @ SY2484 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2484 @ SY2483 )
| ( in @ ( subset_complement @ SV258 @ SY2484 ) @ SV294 ) )
| ~ ! [SY2485: $i] :
( ~ ( element @ SY2485 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2485 ) @ SV294 )
| ( in @ SY2485 @ SY2483 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1659,plain,
! [SV259: $i,SV295: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV259 )
| ~ ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV295 ) ) )
= $true )
| ( ( element @ SV259 @ ( powerset @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1660,plain,
! [SV260: $i] :
( ( ~ ! [SY2386: $i,SY2387: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2386 )
| ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) )
| ~ ( ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2386 )
| ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) ) ) )
| ( SY2387
= ( set_intersection2 @ SV260 @ SY2386 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1661,plain,
! [SV260: $i] :
( ( ~ ! [SY2388: $i,SY2389: $i] :
( ( SY2389
!= ( set_intersection2 @ SV260 @ SY2388 ) )
| ~ ( ~ ! [SY2390: $i] :
( ~ ( in @ SY2390 @ SV260 )
| ~ ( in @ SY2390 @ SY2388 )
| ( in @ SY2390 @ SY2389 ) )
| ~ ~ ( ~ ! [SY2391: $i] :
( ~ ( in @ SY2391 @ SY2389 )
| ( in @ SY2391 @ SV260 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2389 )
| ( in @ SX3 @ SY2388 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1662,plain,
! [SV261: $i] :
( ( ( relation @ SV261 )
= $false )
| ( ( ~ ( ~ ! [SY2393: $i] :
( ~ ( ~ ( ! [SY2394: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ SY2394 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ ( sK18_SY2050 @ SY2393 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) ) )
| ( SY2393
= ( relation_dom @ SV261 ) ) )
| ~ ! [SY2395: $i] :
( ( SY2395
!= ( relation_dom @ SV261 ) )
| ~ ( ~ ! [SY2396: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2396 @ SY2397 ) @ SV261 )
| ( in @ SY2396 @ SY2395 ) )
| ~ ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SY2395 )
| ( in @ ( ordered_pair @ SY2398 @ ( sK16_D @ SY2398 @ SY2395 @ SV261 ) ) @ SV261 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1663,plain,
! [SV262: $i] :
( ( ~ ! [SY2399: $i,SY2400: $i] :
( ~ ( in @ SV262 @ SY2400 )
| ~ ( in @ SY2399 @ SY2400 )
| ( subset @ ( unordered_pair @ SV262 @ SY2399 ) @ SY2400 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1664,plain,
! [SV262: $i] :
( ( ~ ~ ( ~ ! [SY2401: $i,SY2402: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2401 ) @ SY2402 )
| ( in @ SV262 @ SY2402 ) )
| ~ ! [SY2403: $i,SY2404: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2403 ) @ SY2404 )
| ( in @ SY2403 @ SY2404 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1665,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1597]) ).
thf(1666,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)],[1598]) ).
thf(1667,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1599]) ).
thf(1668,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)],[1600]) ).
thf(1669,plain,
! [SV263: $i] :
( ( ~ ! [SY2405: $i,SY2406: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
!= SY2405 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
= SV263 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
= SY2405 ) ) )
| ( SY2406
= ( unordered_pair @ SV263 @ SY2405 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1670,plain,
! [SV263: $i] :
( ( ~ ! [SY2407: $i,SY2408: $i] :
( ( SY2408
!= ( unordered_pair @ SV263 @ SY2407 ) )
| ~ ( ~ ! [SY2409: $i] :
( ~ ( in @ SY2409 @ SY2408 )
| ( SY2409 = SV263 )
| ( SY2409 = SY2407 ) )
| ~ ~ ( ~ ! [SY2410: $i] :
( ( SY2410 != SV263 )
| ( in @ SY2410 @ SY2408 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY2407 )
| ( in @ SX3 @ SY2408 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1671,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1672,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1673,plain,
! [SV264: $i] :
( ( ~ ! [SY2412: $i,SY2413: $i] :
( ~ ( relation @ SY2413 )
| ~ ( in @ ( ordered_pair @ SV264 @ SY2412 ) @ SY2413 )
| ( in @ SV264 @ ( relation_dom @ SY2413 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1674,plain,
! [SV264: $i] :
( ( ~ ! [SY2414: $i,SY2415: $i] :
( ~ ( relation @ SY2415 )
| ~ ( in @ ( ordered_pair @ SV264 @ SY2414 ) @ SY2415 )
| ( in @ SY2414 @ ( relation_rng @ SY2415 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1675,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1676,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1677,plain,
! [SV265: $i] :
( ( ( relation @ SV265 )
= $false )
| ( ( ~ ( ~ ! [SY2416: $i] :
( ~ ( ~ ( ! [SY2417: $i] :
~ ( in @ ( ordered_pair @ SY2417 @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2416 @ SV265 ) @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) ) )
| ( SY2416
= ( relation_rng @ SV265 ) ) )
| ~ ! [SY2418: $i] :
( ( SY2418
!= ( relation_rng @ SV265 ) )
| ~ ( ~ ! [SY2419: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2419 ) @ SV265 )
| ( in @ SY2419 @ SY2418 ) )
| ~ ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SY2418 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2421 @ SY2418 @ SV265 ) @ SY2421 ) @ SV265 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1678,plain,
! [SV266: $i,SV296: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) )
| ~ ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) ) ) )
= $true )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1608]) ).
thf(1679,plain,
! [SV267: $i] :
( ( ~ ! [SY2423: $i] :
( ~ ( subset @ SY2423 @ ( sK4_B @ SV267 ) )
| ( are_equipotent @ SY2423 @ ( sK4_B @ SV267 ) )
| ( in @ SY2423 @ ( sK4_B @ SV267 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1680,plain,
! [SV267: $i] :
( ( ~ ~ ( ~ ! [SY2424: $i] :
( ~ ( ~ ! [SY2425: $i] :
( ~ ( subset @ SY2425 @ SY2424 )
| ( in @ SY2425 @ ( sK5_SY2040 @ SY2424 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2424 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SY2424 @ ( sK4_B @ SV267 ) ) )
| ~ ~ ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1681,plain,
! [SV297: $i,SV268: $i] :
( ( ~ ! [SY2486: $i,SY2487: $i] :
( ~ ( in @ SV268 @ SY2486 )
| ~ ( in @ SV297 @ SY2487 )
| ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2486 @ SY2487 ) ) )
| ~ ~ ( ~ ! [SY2488: $i] :
( ! [SY2489: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2488 @ SY2489 ) )
| ( in @ SV268 @ SY2488 ) )
| ~ ! [SY2490: $i,SY2491: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2490 @ SY2491 ) )
| ( in @ SV297 @ SY2491 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1682,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK36_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK36_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1683,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY2059 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1684,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1685,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1686,plain,
! [SV298: $i,SV269: $i] :
( ( ~ ! [SY2492: $i] :
( ! [SY2493: $i] :
( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SY2492 @ SY2493 ) )
| ( SV269 = SY2492 ) )
| ~ ! [SY2494: $i,SY2495: $i] :
( ( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SY2494 @ SY2495 ) )
| ( SV298 = SY2495 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1687,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1688,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1689,plain,
! [SV270: $i] :
( ( ~ ! [SY2440: $i,SY2441: $i] :
( ~ ( ~ ( ! [SY2442: $i,SY2443: $i] :
( ~ ( in @ SY2442 @ SV270 )
| ~ ( in @ SY2443 @ SY2440 )
| ( ( sK23_D @ SY2441 @ SY2440 @ SV270 )
!= ( ordered_pair @ SY2442 @ SY2443 ) ) )
| ~ ( in @ ( sK23_D @ SY2441 @ SY2440 @ SV270 ) @ SY2441 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2441 @ SY2440 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SY2441 @ SY2440 @ SV270 ) @ SY2440 ) )
| ( ( sK23_D @ SY2441 @ SY2440 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2441 @ SY2440 @ SV270 ) @ ( sK25_SY2056 @ SY2441 @ SY2440 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SY2441 @ SY2440 @ SV270 ) @ SY2441 ) ) )
| ( SY2441
= ( cartesian_product2 @ SV270 @ SY2440 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1690,plain,
! [SV270: $i] :
( ( ~ ! [SY2444: $i,SY2445: $i] :
( ( SY2445
!= ( cartesian_product2 @ SV270 @ SY2444 ) )
| ~ ( ~ ! [SY2446: $i] :
( ! [SY2447: $i,SY2448: $i] :
( ~ ( in @ SY2447 @ SV270 )
| ~ ( in @ SY2448 @ SY2444 )
| ( SY2446
!= ( ordered_pair @ SY2447 @ SY2448 ) ) )
| ( in @ SY2446 @ SY2445 ) )
| ~ ! [SY2449: $i] :
( ~ ( in @ SY2449 @ SY2445 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ SY2444 ) )
| ( SY2449
!= ( ordered_pair @ ( sK21_E @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ ( sK22_SY2051 @ SY2449 @ SY2445 @ SY2444 @ SV270 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1691,plain,
! [SV271: $i] :
( ( ~ ! [SY2450: $i,SY2451: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2450 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2450 ) ) )
| ( SY2451
= ( set_union2 @ SV271 @ SY2450 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1692,plain,
! [SV271: $i] :
( ( ~ ! [SY2452: $i,SY2453: $i] :
( ( SY2453
!= ( set_union2 @ SV271 @ SY2452 ) )
| ~ ( ~ ! [SY2454: $i] :
( ~ ( in @ SY2454 @ SY2453 )
| ( in @ SY2454 @ SV271 )
| ( in @ SY2454 @ SY2452 ) )
| ~ ~ ( ~ ! [SY2455: $i] :
( ~ ( in @ SY2455 @ SV271 )
| ( in @ SY2455 @ SY2453 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2452 )
| ( in @ SX3 @ SY2453 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1693,plain,
! [SV272: $i] :
( ( ~ ! [SY2457: $i] :
( ~ ( subset @ SY2457 @ ( sK39_B @ SV272 ) )
| ( are_equipotent @ SY2457 @ ( sK39_B @ SV272 ) )
| ( in @ SY2457 @ ( sK39_B @ SV272 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1694,plain,
! [SV272: $i] :
( ( ~ ~ ( ~ ! [SY2458: $i] :
( ~ ( in @ SY2458 @ ( sK39_B @ SV272 ) )
| ( in @ ( powerset @ SY2458 ) @ ( sK39_B @ SV272 ) ) )
| ~ ~ ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) )
| ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1695,plain,
! [SV273: $i] :
( ( ( relation @ SV273 )
= $false )
| ( ( ~ ( ~ ! [SY2461: $i] :
( ~ ( relation @ SY2461 )
| ~ ( subset @ SV273 @ SY2461 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SY2461 ) ) )
| ~ ! [SY2462: $i] :
( ~ ( relation @ SY2462 )
| ~ ( subset @ SV273 @ SY2462 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SY2462 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1696,plain,
! [SV299: $i,SV274: $i] :
( ( ~ ! [SY2496: $i,SY2497: $i] :
( ~ ( in @ SV274 @ SY2496 )
| ~ ( in @ SV299 @ SY2497 )
| ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2496 @ SY2497 ) ) )
| ~ ~ ( ~ ! [SY2498: $i] :
( ! [SY2499: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2498 @ SY2499 ) )
| ( in @ SV274 @ SY2498 ) )
| ~ ! [SY2500: $i,SY2501: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2500 @ SY2501 ) )
| ( in @ SV299 @ SY2501 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1697,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK37_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1698,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1699,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1700,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1701,plain,
! [SV275: $i] :
( ( ~ ! [SY2470: $i,SY2471: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2470 )
| ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2470 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) ) ) )
| ( SY2471
= ( set_difference @ SV275 @ SY2470 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1702,plain,
! [SV275: $i] :
( ( ~ ! [SY2472: $i,SY2473: $i] :
( ( SY2473
!= ( set_difference @ SV275 @ SY2472 ) )
| ~ ( ~ ! [SY2474: $i] :
( ~ ( in @ SY2474 @ SV275 )
| ( in @ SY2474 @ SY2472 )
| ( in @ SY2474 @ SY2473 ) )
| ~ ~ ( ~ ! [SY2475: $i] :
( ~ ( in @ SY2475 @ SY2473 )
| ( in @ SY2475 @ SV275 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2473 )
| ~ ( in @ SX3 @ SY2472 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1703,plain,
! [SV276: $i,SV237: $i] :
( ( ( in @ SV237 @ SV276 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV237 ) @ SV276 )
= SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1704,plain,
! [SV277: $i,SV238: $i] :
( ( ( disjoint @ ( singleton @ SV238 ) @ SV277 )
= $false )
| ( ( ~ ( in @ SV238 @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1705,plain,
! [SV240: $i,SV279: $i] :
( ( ( element @ SV279 @ ( powerset @ SV240 ) )
= $false )
| ( ( ! [SY2477: $i] :
( ~ ( in @ SY2477 @ SV279 )
| ( in @ SY2477 @ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1706,plain,
! [SV280: $i,SV241: $i] :
( ( ( subset @ SV241 @ SV280 )
= $false )
| ( ( ! [SY2478: $i] :
( ( in @ SY2478 @ SV241 )
| ( subset @ SV241 @ ( set_difference @ SV280 @ ( singleton @ SY2478 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1707,plain,
! [SV281: $i,SV242: $i] :
( ( ( in @ SV242 @ SV281 )
= $false )
| ( ( subset @ SV242 @ ( union @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1708,plain,
! [SV282: $i,SV244: $i] :
( ( ( in @ SV244 @ SV282 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV244 ) @ SV282 )
= SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1709,plain,
! [SV245: $i,SV300: $i] :
( ( ( ~ ( element @ SV300 @ ( powerset @ SV245 ) ) )
= $true )
| ( ( ! [SY2502: $i] :
( ~ ( element @ SY2502 @ SV245 )
| ( in @ SY2502 @ SV300 )
| ( in @ SY2502 @ ( subset_complement @ SV245 @ SV300 ) ) ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1710,plain,
! [SV283: $i,SV246: $i,SV301: $i] :
( ( ( ~ ( element @ SV301 @ ( powerset @ SV246 ) ) )
= $true )
| ( ( ~ ( in @ SV283 @ ( subset_complement @ SV246 @ SV301 ) )
| ~ ( in @ SV283 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1711,plain,
! [SV284: $i,SV247: $i] :
( ( ( in @ SV247 @ SV284 )
= $false )
| ( ( subset @ SV247 @ ( union @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1712,plain,
! [SV285: $i,SV248: $i] :
( ( ( in @ SV248 @ SV285 )
= $false )
| ( ( ~ ( in @ SV285 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1713,plain,
! [SV288: $i,SV252: $i] :
( ( ( ~ ( relation @ SV252 ) )
= $true )
| ( ( ~ ( relation @ SV288 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV252 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1714,plain,
! [SV289: $i,SV253: $i] :
( ( ( in @ SV253 @ SV289 )
= $false )
| ( ( element @ SV253 @ SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1715,plain,
! [SV290: $i,SV254: $i] :
( ( ( element @ SV254 @ SV290 )
= $false )
| ( ( ( empty @ SV290 )
| ( in @ SV254 @ SV290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1716,plain,
! [SV255: $i,SV302: $i,SV291: $i] :
( ( ( ~ ( element @ SV291 @ ( powerset @ SV302 ) )
| ~ ( in @ SV255 @ SV291 ) )
= $true )
| ( ( element @ SV255 @ SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1717,plain,
! [SV256: $i,SV303: $i,SV292: $i] :
( ( ( ~ ( element @ SV292 @ ( powerset @ SV303 ) )
| ~ ( in @ SV256 @ SV292 ) )
= $true )
| ( ( ~ ( empty @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1718,plain,
! [SV257: $i,SV293: $i] :
( ( ( empty @ SV293 )
= $false )
| ( ( ~ ( in @ SV257 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1719,plain,
! [SV304: $i] :
( ( ( in @ ( sK29_B @ SV304 ) @ SV304 )
| ( SV304 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1720,plain,
! [SV305: $i] :
( ( ( SV305 != empty_set )
| ! [SY2503: $i] :
~ ( in @ SY2503 @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1721,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)],[1650]) ).
thf(1722,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)],[1651]) ).
thf(1723,plain,
! [SV306: $i] :
( ( ! [SY2504: $i] :
( ~ ( ~ ( ( ( sK30_C @ SY2504 @ SV306 )
!= SV306 )
| ~ ( in @ ( sK30_C @ SY2504 @ SV306 ) @ SY2504 ) )
| ~ ( ( ( sK30_C @ SY2504 @ SV306 )
= SV306 )
| ( in @ ( sK30_C @ SY2504 @ SV306 ) @ SY2504 ) ) )
| ( SY2504
= ( singleton @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1724,plain,
! [SV307: $i] :
( ( ! [SY2505: $i] :
( ( SY2505
!= ( singleton @ SV307 ) )
| ~ ( ~ ! [SY2506: $i] :
( ( SY2506 != SV307 )
| ( in @ SY2506 @ SY2505 ) )
| ~ ! [SY2507: $i] :
( ~ ( in @ SY2507 @ SY2505 )
| ( SY2507 = SV307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1725,plain,
! [SV308: $i] :
( ( ! [SY2508: $i] :
( ( disjoint @ SV308 @ SY2508 )
| ~ ( ~ ( in @ ( sK38_C @ SY2508 @ SV308 ) @ SV308 )
| ~ ( in @ ( sK38_C @ SY2508 @ SV308 ) @ SY2508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1726,plain,
! [SV309: $i] :
( ( ! [SY2509: $i] :
( ! [SY2510: $i] :
( ~ ( in @ SY2510 @ SV309 )
| ~ ( in @ SY2510 @ SY2509 ) )
| ~ ( disjoint @ SV309 @ SY2509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1727,plain,
! [SV310: $i] :
( ( ! [SY2511: $i] :
( ~ ( ~ ( ! [SY2512: $i] :
( ~ ( in @ ( sK14_C @ SY2511 @ SV310 ) @ SY2512 )
| ~ ( in @ SY2512 @ SV310 ) )
| ~ ( in @ ( sK14_C @ SY2511 @ SV310 ) @ SY2511 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SY2511 @ SV310 ) @ ( sK15_SY2048 @ SY2511 @ SV310 ) )
| ~ ( in @ ( sK15_SY2048 @ SY2511 @ SV310 ) @ SV310 ) )
| ( in @ ( sK14_C @ SY2511 @ SV310 ) @ SY2511 ) ) )
| ( SY2511
= ( union @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1728,plain,
! [SV311: $i] :
( ( ! [SY2513: $i] :
( ( SY2513
!= ( union @ SV311 ) )
| ~ ( ~ ! [SY2514: $i] :
( ! [SY2515: $i] :
( ~ ( in @ SY2514 @ SY2515 )
| ~ ( in @ SY2515 @ SV311 ) )
| ( in @ SY2514 @ SY2513 ) )
| ~ ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SY2513 )
| ~ ( ~ ( in @ SY2516 @ ( sK13_D @ SY2516 @ SY2513 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SY2516 @ SY2513 @ SV311 ) @ SV311 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1729,plain,
! [SV258: $i,SV294: $i] :
( ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2482: $i] :
( ~ ( element @ SY2482 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SY2482
= ( complements_of_subsets @ SV258 @ SV294 ) ) )
| ~ ! [SY2483: $i] :
( ~ ( element @ SY2483 @ ( powerset @ ( powerset @ SV258 ) ) )
| ( SY2483
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2484: $i] :
( ~ ( element @ SY2484 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2484 @ SY2483 )
| ( in @ ( subset_complement @ SV258 @ SY2484 ) @ SV294 ) )
| ~ ! [SY2485: $i] :
( ~ ( element @ SY2485 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2485 ) @ SV294 )
| ( in @ SY2485 @ SY2483 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1730,plain,
! [SV259: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV259 )
| ~ ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV295 ) )
= $false )
| ( ( element @ SV259 @ ( powerset @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1731,plain,
! [SV260: $i] :
( ( ! [SY2386: $i,SY2387: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2386 )
| ~ ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) )
| ~ ( ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2386 )
| ( in @ ( sK19_D @ SY2387 @ SY2386 @ SV260 ) @ SY2387 ) ) ) )
| ( SY2387
= ( set_intersection2 @ SV260 @ SY2386 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1732,plain,
! [SV260: $i] :
( ( ! [SY2388: $i,SY2389: $i] :
( ( SY2389
!= ( set_intersection2 @ SV260 @ SY2388 ) )
| ~ ( ~ ! [SY2390: $i] :
( ~ ( in @ SY2390 @ SV260 )
| ~ ( in @ SY2390 @ SY2388 )
| ( in @ SY2390 @ SY2389 ) )
| ~ ~ ( ~ ! [SY2391: $i] :
( ~ ( in @ SY2391 @ SY2389 )
| ( in @ SY2391 @ SV260 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2389 )
| ( in @ SX3 @ SY2388 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1733,plain,
! [SV261: $i] :
( ( ( ~ ! [SY2393: $i] :
( ~ ( ~ ( ! [SY2394: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ SY2394 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ ( sK18_SY2050 @ SY2393 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) ) )
| ( SY2393
= ( relation_dom @ SV261 ) ) )
| ~ ! [SY2395: $i] :
( ( SY2395
!= ( relation_dom @ SV261 ) )
| ~ ( ~ ! [SY2396: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2396 @ SY2397 ) @ SV261 )
| ( in @ SY2396 @ SY2395 ) )
| ~ ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SY2395 )
| ( in @ ( ordered_pair @ SY2398 @ ( sK16_D @ SY2398 @ SY2395 @ SV261 ) ) @ SV261 ) ) ) ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1734,plain,
! [SV262: $i] :
( ( ! [SY2399: $i,SY2400: $i] :
( ~ ( in @ SV262 @ SY2400 )
| ~ ( in @ SY2399 @ SY2400 )
| ( subset @ ( unordered_pair @ SV262 @ SY2399 ) @ SY2400 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1735,plain,
! [SV262: $i] :
( ( ~ ( ~ ! [SY2401: $i,SY2402: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2401 ) @ SY2402 )
| ( in @ SV262 @ SY2402 ) )
| ~ ! [SY2403: $i,SY2404: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2403 ) @ SY2404 )
| ( in @ SY2403 @ SY2404 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1736,plain,
! [SV312: $i] :
( ( ! [SY2517: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SY2517 @ SV312 ) @ SY2517 )
| ~ ( subset @ ( sK28_C @ SY2517 @ SV312 ) @ SV312 ) )
| ~ ( ( in @ ( sK28_C @ SY2517 @ SV312 ) @ SY2517 )
| ( subset @ ( sK28_C @ SY2517 @ SV312 ) @ SV312 ) ) )
| ( SY2517
= ( powerset @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1737,plain,
! [SV313: $i] :
( ( ! [SY2518: $i] :
( ( SY2518
!= ( powerset @ SV313 ) )
| ~ ( ~ ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SY2518 )
| ( subset @ SY2519 @ SV313 ) )
| ~ ! [SY2520: $i] :
( ~ ( subset @ SY2520 @ SV313 )
| ( in @ SY2520 @ SY2518 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1738,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1667]) ).
thf(1739,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)],[1668]) ).
thf(1740,plain,
! [SV263: $i] :
( ( ! [SY2405: $i,SY2406: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
!= SY2405 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2406 @ SY2405 @ SV263 ) @ SY2406 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
= SV263 )
| ( ( sK27_D @ SY2406 @ SY2405 @ SV263 )
= SY2405 ) ) )
| ( SY2406
= ( unordered_pair @ SV263 @ SY2405 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1741,plain,
! [SV263: $i] :
( ( ! [SY2407: $i,SY2408: $i] :
( ( SY2408
!= ( unordered_pair @ SV263 @ SY2407 ) )
| ~ ( ~ ! [SY2409: $i] :
( ~ ( in @ SY2409 @ SY2408 )
| ( SY2409 = SV263 )
| ( SY2409 = SY2407 ) )
| ~ ~ ( ~ ! [SY2410: $i] :
( ( SY2410 != SV263 )
| ( in @ SY2410 @ SY2408 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY2407 )
| ( in @ SX3 @ SY2408 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1742,plain,
! [SV314: $i] :
( ( ! [SY2521: $i] :
( ~ ( in @ SV314 @ SY2521 )
| ( subset @ ( singleton @ SV314 ) @ SY2521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1743,plain,
! [SV315: $i] :
( ( ! [SY2522: $i] :
( ~ ( subset @ ( singleton @ SV315 ) @ SY2522 )
| ( in @ SV315 @ SY2522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1744,plain,
! [SV264: $i] :
( ( ! [SY2412: $i,SY2413: $i] :
( ~ ( relation @ SY2413 )
| ~ ( in @ ( ordered_pair @ SV264 @ SY2412 ) @ SY2413 )
| ( in @ SV264 @ ( relation_dom @ SY2413 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1745,plain,
! [SV264: $i] :
( ( ! [SY2414: $i,SY2415: $i] :
( ~ ( relation @ SY2415 )
| ~ ( in @ ( ordered_pair @ SV264 @ SY2414 ) @ SY2415 )
| ( in @ SY2414 @ ( relation_rng @ SY2415 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1746,plain,
! [SV316: $i] :
( ( ! [SY2523: $i] :
( ~ ( in @ SV316 @ SY2523 )
| ( subset @ ( singleton @ SV316 ) @ SY2523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1747,plain,
! [SV317: $i] :
( ( ! [SY2524: $i] :
( ~ ( subset @ ( singleton @ SV317 ) @ SY2524 )
| ( in @ SV317 @ SY2524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1748,plain,
! [SV265: $i] :
( ( ( ~ ! [SY2416: $i] :
( ~ ( ~ ( ! [SY2417: $i] :
~ ( in @ ( ordered_pair @ SY2417 @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2416 @ SV265 ) @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) ) )
| ( SY2416
= ( relation_rng @ SV265 ) ) )
| ~ ! [SY2418: $i] :
( ( SY2418
!= ( relation_rng @ SV265 ) )
| ~ ( ~ ! [SY2419: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2419 ) @ SV265 )
| ( in @ SY2419 @ SY2418 ) )
| ~ ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SY2418 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2421 @ SY2418 @ SV265 ) @ SY2421 ) @ SV265 ) ) ) ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1749,plain,
! [SV266: $i,SV296: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) )
| ~ ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) ) )
= $false )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1750,plain,
! [SV267: $i] :
( ( ! [SY2423: $i] :
( ~ ( subset @ SY2423 @ ( sK4_B @ SV267 ) )
| ( are_equipotent @ SY2423 @ ( sK4_B @ SV267 ) )
| ( in @ SY2423 @ ( sK4_B @ SV267 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1751,plain,
! [SV267: $i] :
( ( ~ ( ~ ! [SY2424: $i] :
( ~ ( ~ ! [SY2425: $i] :
( ~ ( subset @ SY2425 @ SY2424 )
| ( in @ SY2425 @ ( sK5_SY2040 @ SY2424 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2424 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SY2424 @ ( sK4_B @ SV267 ) ) )
| ~ ~ ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1752,plain,
! [SV297: $i,SV268: $i] :
( ( ~ ! [SY2486: $i,SY2487: $i] :
( ~ ( in @ SV268 @ SY2486 )
| ~ ( in @ SV297 @ SY2487 )
| ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2486 @ SY2487 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1753,plain,
! [SV297: $i,SV268: $i] :
( ( ~ ~ ( ~ ! [SY2488: $i] :
( ! [SY2489: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2488 @ SY2489 ) )
| ( in @ SV268 @ SY2488 ) )
| ~ ! [SY2490: $i,SY2491: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2490 @ SY2491 ) )
| ( in @ SV297 @ SY2491 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1754,plain,
! [SV318: $i] :
( ( ~ ( ~ ! [SY2525: $i,SY2526: $i] :
( ( sK36_B @ SV318 )
!= ( ordered_pair @ SY2525 @ SY2526 ) )
| ~ ( in @ ( sK36_B @ SV318 ) @ SV318 ) )
| ( relation @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1755,plain,
! [SV319: $i] :
( ( ~ ( relation @ SV319 )
| ! [SY2527: $i] :
( ( SY2527
= ( ordered_pair @ ( sK34_C @ SY2527 @ SV319 ) @ ( sK35_SY2059 @ SY2527 @ SV319 ) ) )
| ~ ( in @ SY2527 @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1756,plain,
! [SV320: $i] :
( ( ! [SY2528: $i] :
( ( ( set_difference @ SV320 @ ( singleton @ SY2528 ) )
!= SV320 )
| ~ ( in @ SY2528 @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1757,plain,
! [SV321: $i] :
( ( ! [SY2529: $i] :
( ( in @ SY2529 @ SV321 )
| ( ( set_difference @ SV321 @ ( singleton @ SY2529 ) )
= SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1758,plain,
! [SV298: $i,SV269: $i] :
( ( ~ ! [SY2492: $i] :
( ! [SY2493: $i] :
( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SY2492 @ SY2493 ) )
| ( SV269 = SY2492 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1759,plain,
! [SV298: $i,SV269: $i] :
( ( ~ ! [SY2494: $i,SY2495: $i] :
( ( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SY2494 @ SY2495 ) )
| ( SV298 = SY2495 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1760,plain,
! [SV270: $i] :
( ( ! [SY2440: $i,SY2441: $i] :
( ~ ( ~ ( ! [SY2442: $i,SY2443: $i] :
( ~ ( in @ SY2442 @ SV270 )
| ~ ( in @ SY2443 @ SY2440 )
| ( ( sK23_D @ SY2441 @ SY2440 @ SV270 )
!= ( ordered_pair @ SY2442 @ SY2443 ) ) )
| ~ ( in @ ( sK23_D @ SY2441 @ SY2440 @ SV270 ) @ SY2441 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2441 @ SY2440 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SY2441 @ SY2440 @ SV270 ) @ SY2440 ) )
| ( ( sK23_D @ SY2441 @ SY2440 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2441 @ SY2440 @ SV270 ) @ ( sK25_SY2056 @ SY2441 @ SY2440 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SY2441 @ SY2440 @ SV270 ) @ SY2441 ) ) )
| ( SY2441
= ( cartesian_product2 @ SV270 @ SY2440 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1761,plain,
! [SV270: $i] :
( ( ! [SY2444: $i,SY2445: $i] :
( ( SY2445
!= ( cartesian_product2 @ SV270 @ SY2444 ) )
| ~ ( ~ ! [SY2446: $i] :
( ! [SY2447: $i,SY2448: $i] :
( ~ ( in @ SY2447 @ SV270 )
| ~ ( in @ SY2448 @ SY2444 )
| ( SY2446
!= ( ordered_pair @ SY2447 @ SY2448 ) ) )
| ( in @ SY2446 @ SY2445 ) )
| ~ ! [SY2449: $i] :
( ~ ( in @ SY2449 @ SY2445 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ SY2444 ) )
| ( SY2449
!= ( ordered_pair @ ( sK21_E @ SY2449 @ SY2445 @ SY2444 @ SV270 ) @ ( sK22_SY2051 @ SY2449 @ SY2445 @ SY2444 @ SV270 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1762,plain,
! [SV271: $i] :
( ( ! [SY2450: $i,SY2451: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ~ ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2450 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2451 )
| ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SY2451 @ SY2450 @ SV271 ) @ SY2450 ) ) )
| ( SY2451
= ( set_union2 @ SV271 @ SY2450 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1763,plain,
! [SV271: $i] :
( ( ! [SY2452: $i,SY2453: $i] :
( ( SY2453
!= ( set_union2 @ SV271 @ SY2452 ) )
| ~ ( ~ ! [SY2454: $i] :
( ~ ( in @ SY2454 @ SY2453 )
| ( in @ SY2454 @ SV271 )
| ( in @ SY2454 @ SY2452 ) )
| ~ ~ ( ~ ! [SY2455: $i] :
( ~ ( in @ SY2455 @ SV271 )
| ( in @ SY2455 @ SY2453 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2452 )
| ( in @ SX3 @ SY2453 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1764,plain,
! [SV272: $i] :
( ( ! [SY2457: $i] :
( ~ ( subset @ SY2457 @ ( sK39_B @ SV272 ) )
| ( are_equipotent @ SY2457 @ ( sK39_B @ SV272 ) )
| ( in @ SY2457 @ ( sK39_B @ SV272 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1765,plain,
! [SV272: $i] :
( ( ~ ( ~ ! [SY2458: $i] :
( ~ ( in @ SY2458 @ ( sK39_B @ SV272 ) )
| ( in @ ( powerset @ SY2458 ) @ ( sK39_B @ SV272 ) ) )
| ~ ~ ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) )
| ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1766,plain,
! [SV273: $i] :
( ( ( ~ ! [SY2461: $i] :
( ~ ( relation @ SY2461 )
| ~ ( subset @ SV273 @ SY2461 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SY2461 ) ) )
| ~ ! [SY2462: $i] :
( ~ ( relation @ SY2462 )
| ~ ( subset @ SV273 @ SY2462 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SY2462 ) ) ) )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1767,plain,
! [SV299: $i,SV274: $i] :
( ( ~ ! [SY2496: $i,SY2497: $i] :
( ~ ( in @ SV274 @ SY2496 )
| ~ ( in @ SV299 @ SY2497 )
| ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2496 @ SY2497 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1768,plain,
! [SV299: $i,SV274: $i] :
( ( ~ ~ ( ~ ! [SY2498: $i] :
( ! [SY2499: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2498 @ SY2499 ) )
| ( in @ SV274 @ SY2498 ) )
| ~ ! [SY2500: $i,SY2501: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2500 @ SY2501 ) )
| ( in @ SV299 @ SY2501 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1769,plain,
! [SV322: $i] :
( ( ! [SY2530: $i] :
( ( disjoint @ SV322 @ SY2530 )
| ( in @ ( sK37_C @ SY2530 @ SV322 ) @ ( set_intersection2 @ SV322 @ SY2530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1770,plain,
! [SV323: $i] :
( ( ! [SY2531: $i] :
( ! [SY2532: $i] :
~ ( in @ SY2532 @ ( set_intersection2 @ SV323 @ SY2531 ) )
| ~ ( disjoint @ SV323 @ SY2531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(1771,plain,
! [SV324: $i] :
( ( ! [SY2533: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SY2533 @ SV324 ) @ SV324 )
| ~ ~ ( in @ ( sK20_C @ SY2533 @ SV324 ) @ SY2533 ) )
| ( subset @ SV324 @ SY2533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1772,plain,
! [SV325: $i] :
( ( ! [SY2534: $i] :
( ~ ( subset @ SV325 @ SY2534 )
| ! [SY2535: $i] :
( ~ ( in @ SY2535 @ SV325 )
| ( in @ SY2535 @ SY2534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(1773,plain,
! [SV275: $i] :
( ( ! [SY2470: $i,SY2471: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2470 )
| ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2470 )
| ( in @ ( sK12_D @ SY2471 @ SY2470 @ SV275 ) @ SY2471 ) ) ) )
| ( SY2471
= ( set_difference @ SV275 @ SY2470 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1774,plain,
! [SV275: $i] :
( ( ! [SY2472: $i,SY2473: $i] :
( ( SY2473
!= ( set_difference @ SV275 @ SY2472 ) )
| ~ ( ~ ! [SY2474: $i] :
( ~ ( in @ SY2474 @ SV275 )
| ( in @ SY2474 @ SY2472 )
| ( in @ SY2474 @ SY2473 ) )
| ~ ~ ( ~ ! [SY2475: $i] :
( ~ ( in @ SY2475 @ SY2473 )
| ( in @ SY2475 @ SV275 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2473 )
| ~ ( in @ SX3 @ SY2472 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1775,plain,
! [SV277: $i,SV238: $i] :
( ( ( in @ SV238 @ SV277 )
= $false )
| ( ( disjoint @ ( singleton @ SV238 ) @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1776,plain,
! [SV240: $i,SV279: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ SV279 )
| ( in @ SV326 @ SV240 ) )
= $true )
| ( ( element @ SV279 @ ( powerset @ SV240 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1777,plain,
! [SV280: $i,SV241: $i,SV327: $i] :
( ( ( ( in @ SV327 @ SV241 )
| ( subset @ SV241 @ ( set_difference @ SV280 @ ( singleton @ SV327 ) ) ) )
= $true )
| ( ( subset @ SV241 @ SV280 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(1778,plain,
! [SV245: $i,SV300: $i] :
( ( ( element @ SV300 @ ( powerset @ SV245 ) )
= $false )
| ( ( ! [SY2502: $i] :
( ~ ( element @ SY2502 @ SV245 )
| ( in @ SY2502 @ SV300 )
| ( in @ SY2502 @ ( subset_complement @ SV245 @ SV300 ) ) ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1779,plain,
! [SV283: $i,SV246: $i,SV301: $i] :
( ( ( element @ SV301 @ ( powerset @ SV246 ) )
= $false )
| ( ( ~ ( in @ SV283 @ ( subset_complement @ SV246 @ SV301 ) )
| ~ ( in @ SV283 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1780,plain,
! [SV248: $i,SV285: $i] :
( ( ( in @ SV285 @ SV248 )
= $false )
| ( ( in @ SV248 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1781,plain,
! [SV288: $i,SV252: $i] :
( ( ( relation @ SV252 )
= $false )
| ( ( ~ ( relation @ SV288 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV252 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1782,plain,
! [SV254: $i,SV290: $i] :
( ( ( empty @ SV290 )
= $true )
| ( ( in @ SV254 @ SV290 )
= $true )
| ( ( element @ SV254 @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(1783,plain,
! [SV255: $i,SV302: $i,SV291: $i] :
( ( ( ~ ( element @ SV291 @ ( powerset @ SV302 ) ) )
= $true )
| ( ( ~ ( in @ SV255 @ SV291 ) )
= $true )
| ( ( element @ SV255 @ SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(1784,plain,
! [SV256: $i,SV303: $i,SV292: $i] :
( ( ( ~ ( element @ SV292 @ ( powerset @ SV303 ) ) )
= $true )
| ( ( ~ ( in @ SV256 @ SV292 ) )
= $true )
| ( ( ~ ( empty @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1785,plain,
! [SV293: $i,SV257: $i] :
( ( ( in @ SV257 @ SV293 )
= $false )
| ( ( empty @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1786,plain,
! [SV304: $i] :
( ( ( in @ ( sK29_B @ SV304 ) @ SV304 )
= $true )
| ( ( SV304 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1787,plain,
! [SV305: $i] :
( ( ( ( SV305 != empty_set ) )
= $true )
| ( ( ! [SY2503: $i] :
~ ( in @ SY2503 @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1788,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1721]) ).
thf(1789,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1721]) ).
thf(1790,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1791,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1792,plain,
! [SV306: $i,SV328: $i] :
( ( ~ ( ~ ( ( ( sK30_C @ SV328 @ SV306 )
!= SV306 )
| ~ ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) )
| ~ ( ( ( sK30_C @ SV328 @ SV306 )
= SV306 )
| ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) ) )
| ( SV328
= ( singleton @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(1793,plain,
! [SV307: $i,SV329: $i] :
( ( ( SV329
!= ( singleton @ SV307 ) )
| ~ ( ~ ! [SY2536: $i] :
( ( SY2536 != SV307 )
| ( in @ SY2536 @ SV329 ) )
| ~ ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV329 )
| ( SY2537 = SV307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(1794,plain,
! [SV330: $i,SV308: $i] :
( ( ( disjoint @ SV308 @ SV330 )
| ~ ( ~ ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV308 )
| ~ ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(1795,plain,
! [SV331: $i,SV309: $i] :
( ( ! [SY2538: $i] :
( ~ ( in @ SY2538 @ SV309 )
| ~ ( in @ SY2538 @ SV331 ) )
| ~ ( disjoint @ SV309 @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1796,plain,
! [SV310: $i,SV332: $i] :
( ( ~ ( ~ ( ! [SY2539: $i] :
( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SY2539 )
| ~ ( in @ SY2539 @ SV310 ) )
| ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) )
| ~ ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 ) )
| ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) ) )
| ( SV332
= ( union @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(1797,plain,
! [SV311: $i,SV333: $i] :
( ( ( SV333
!= ( union @ SV311 ) )
| ~ ( ~ ! [SY2540: $i] :
( ! [SY2515: $i] :
( ~ ( in @ SY2540 @ SY2515 )
| ~ ( in @ SY2515 @ SV311 ) )
| ( in @ SY2540 @ SV333 ) )
| ~ ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV333 )
| ~ ( ~ ( in @ SY2542 @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) @ SV311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(1798,plain,
! [SV294: $i,SV258: $i] :
( ( ( ~ ! [SY2482: $i] :
( ~ ( element @ SY2482 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SY2482
= ( complements_of_subsets @ SV258 @ SV294 ) ) )
| ~ ! [SY2483: $i] :
( ~ ( element @ SY2483 @ ( powerset @ ( powerset @ SV258 ) ) )
| ( SY2483
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2484: $i] :
( ~ ( element @ SY2484 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2484 @ SY2483 )
| ( in @ ( subset_complement @ SV258 @ SY2484 ) @ SV294 ) )
| ~ ! [SY2485: $i] :
( ~ ( element @ SY2485 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2485 ) @ SV294 )
| ( in @ SY2485 @ SY2483 ) ) ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1799,plain,
! [SV259: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV259 ) )
= $false )
| ( ( element @ SV259 @ ( powerset @ SV295 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1800,plain,
! [SV259: $i,SV295: $i] :
( ( ( ~ ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV295 ) )
= $false )
| ( ( element @ SV259 @ ( powerset @ SV295 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1801,plain,
! [SV260: $i,SV334: $i] :
( ( ! [SY2543: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY2543 @ SV334 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SY2543 @ SV334 @ SV260 ) @ SV334 )
| ~ ( in @ ( sK19_D @ SY2543 @ SV334 @ SV260 ) @ SY2543 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY2543 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SY2543 @ SV334 @ SV260 ) @ SY2543 ) )
| ~ ( ( in @ ( sK19_D @ SY2543 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SY2543 @ SV334 @ SV260 ) @ SY2543 ) ) ) )
| ( SY2543
= ( set_intersection2 @ SV260 @ SV334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1802,plain,
! [SV335: $i,SV260: $i] :
( ( ! [SY2544: $i] :
( ( SY2544
!= ( set_intersection2 @ SV260 @ SV335 ) )
| ~ ( ~ ! [SY2545: $i] :
( ~ ( in @ SY2545 @ SV260 )
| ~ ( in @ SY2545 @ SV335 )
| ( in @ SY2545 @ SY2544 ) )
| ~ ~ ( ~ ! [SY2391: $i] :
( ~ ( in @ SY2391 @ SY2544 )
| ( in @ SY2391 @ SV260 ) )
| ~ ! [SY2547: $i] :
( ~ ( in @ SY2547 @ SY2544 )
| ( in @ SY2547 @ SV335 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(1803,plain,
! [SV261: $i] :
( ( ( ~ ! [SY2393: $i] :
( ~ ( ~ ( ! [SY2394: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ SY2394 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ ( sK18_SY2050 @ SY2393 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) ) )
| ( SY2393
= ( relation_dom @ SV261 ) ) ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1804,plain,
! [SV261: $i] :
( ( ( ~ ! [SY2395: $i] :
( ( SY2395
!= ( relation_dom @ SV261 ) )
| ~ ( ~ ! [SY2396: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2396 @ SY2397 ) @ SV261 )
| ( in @ SY2396 @ SY2395 ) )
| ~ ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SY2395 )
| ( in @ ( ordered_pair @ SY2398 @ ( sK16_D @ SY2398 @ SY2395 @ SV261 ) ) @ SV261 ) ) ) ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1805,plain,
! [SV336: $i,SV262: $i] :
( ( ! [SY2548: $i] :
( ~ ( in @ SV262 @ SY2548 )
| ~ ( in @ SV336 @ SY2548 )
| ( subset @ ( unordered_pair @ SV262 @ SV336 ) @ SY2548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(1806,plain,
! [SV262: $i] :
( ( ~ ! [SY2401: $i,SY2402: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2401 ) @ SY2402 )
| ( in @ SV262 @ SY2402 ) )
| ~ ! [SY2403: $i,SY2404: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2403 ) @ SY2404 )
| ( in @ SY2403 @ SY2404 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1807,plain,
! [SV312: $i,SV337: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ~ ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) )
| ~ ( ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) ) )
| ( SV337
= ( powerset @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(1808,plain,
! [SV313: $i,SV338: $i] :
( ( ( SV338
!= ( powerset @ SV313 ) )
| ~ ( ~ ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV338 )
| ( subset @ SY2549 @ SV313 ) )
| ~ ! [SY2550: $i] :
( ~ ( subset @ SY2550 @ SV313 )
| ( in @ SY2550 @ SV338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(1809,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1810,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1738]) ).
thf(1811,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1739]) ).
thf(1812,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1739]) ).
thf(1813,plain,
! [SV263: $i,SV339: $i] :
( ( ! [SY2551: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY2551 @ SV339 @ SV263 ) @ SY2551 )
| ( ( sK27_D @ SY2551 @ SV339 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY2551 @ SV339 @ SV263 ) @ SY2551 )
| ( ( sK27_D @ SY2551 @ SV339 @ SV263 )
!= SV339 ) ) )
| ~ ( ( in @ ( sK27_D @ SY2551 @ SV339 @ SV263 ) @ SY2551 )
| ( ( sK27_D @ SY2551 @ SV339 @ SV263 )
= SV263 )
| ( ( sK27_D @ SY2551 @ SV339 @ SV263 )
= SV339 ) ) )
| ( SY2551
= ( unordered_pair @ SV263 @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(1814,plain,
! [SV340: $i,SV263: $i] :
( ( ! [SY2552: $i] :
( ( SY2552
!= ( unordered_pair @ SV263 @ SV340 ) )
| ~ ( ~ ! [SY2553: $i] :
( ~ ( in @ SY2553 @ SY2552 )
| ( SY2553 = SV263 )
| ( SY2553 = SV340 ) )
| ~ ~ ( ~ ! [SY2410: $i] :
( ( SY2410 != SV263 )
| ( in @ SY2410 @ SY2552 ) )
| ~ ! [SY2555: $i] :
( ( SY2555 != SV340 )
| ( in @ SY2555 @ SY2552 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1815,plain,
! [SV341: $i,SV314: $i] :
( ( ~ ( in @ SV314 @ SV341 )
| ( subset @ ( singleton @ SV314 ) @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1816,plain,
! [SV342: $i,SV315: $i] :
( ( ~ ( subset @ ( singleton @ SV315 ) @ SV342 )
| ( in @ SV315 @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(1817,plain,
! [SV343: $i,SV264: $i] :
( ( ! [SY2556: $i] :
( ~ ( relation @ SY2556 )
| ~ ( in @ ( ordered_pair @ SV264 @ SV343 ) @ SY2556 )
| ( in @ SV264 @ ( relation_dom @ SY2556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1818,plain,
! [SV344: $i,SV264: $i] :
( ( ! [SY2557: $i] :
( ~ ( relation @ SY2557 )
| ~ ( in @ ( ordered_pair @ SV264 @ SV344 ) @ SY2557 )
| ( in @ SV344 @ ( relation_rng @ SY2557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(1819,plain,
! [SV345: $i,SV316: $i] :
( ( ~ ( in @ SV316 @ SV345 )
| ( subset @ ( singleton @ SV316 ) @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(1820,plain,
! [SV346: $i,SV317: $i] :
( ( ~ ( subset @ ( singleton @ SV317 ) @ SV346 )
| ( in @ SV317 @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(1821,plain,
! [SV265: $i] :
( ( ( ~ ! [SY2416: $i] :
( ~ ( ~ ( ! [SY2417: $i] :
~ ( in @ ( ordered_pair @ SY2417 @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2416 @ SV265 ) @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) ) )
| ( SY2416
= ( relation_rng @ SV265 ) ) ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1822,plain,
! [SV265: $i] :
( ( ( ~ ! [SY2418: $i] :
( ( SY2418
!= ( relation_rng @ SV265 ) )
| ~ ( ~ ! [SY2419: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2419 ) @ SV265 )
| ( in @ SY2419 @ SY2418 ) )
| ~ ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SY2418 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2421 @ SY2418 @ SV265 ) @ SY2421 ) @ SV265 ) ) ) ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1823,plain,
! [SV266: $i,SV296: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) ) )
= $false )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1824,plain,
! [SV266: $i,SV296: $i] :
( ( ( ~ ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) ) )
= $false )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1825,plain,
! [SV267: $i,SV347: $i] :
( ( ~ ( subset @ SV347 @ ( sK4_B @ SV267 ) )
| ( are_equipotent @ SV347 @ ( sK4_B @ SV267 ) )
| ( in @ SV347 @ ( sK4_B @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1826,plain,
! [SV267: $i] :
( ( ~ ! [SY2424: $i] :
( ~ ( ~ ! [SY2425: $i] :
( ~ ( subset @ SY2425 @ SY2424 )
| ( in @ SY2425 @ ( sK5_SY2040 @ SY2424 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2424 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SY2424 @ ( sK4_B @ SV267 ) ) )
| ~ ~ ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1827,plain,
! [SV297: $i,SV268: $i] :
( ( ! [SY2486: $i,SY2487: $i] :
( ~ ( in @ SV268 @ SY2486 )
| ~ ( in @ SV297 @ SY2487 )
| ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2486 @ SY2487 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1828,plain,
! [SV297: $i,SV268: $i] :
( ( ~ ( ~ ! [SY2488: $i] :
( ! [SY2489: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2488 @ SY2489 ) )
| ( in @ SV268 @ SY2488 ) )
| ~ ! [SY2490: $i,SY2491: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2490 @ SY2491 ) )
| ( in @ SV297 @ SY2491 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1829,plain,
! [SV318: $i] :
( ( ( ~ ( ~ ! [SY2525: $i,SY2526: $i] :
( ( sK36_B @ SV318 )
!= ( ordered_pair @ SY2525 @ SY2526 ) )
| ~ ( in @ ( sK36_B @ SV318 ) @ SV318 ) ) )
= $true )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1830,plain,
! [SV319: $i] :
( ( ( ~ ( relation @ SV319 ) )
= $true )
| ( ( ! [SY2527: $i] :
( ( SY2527
= ( ordered_pair @ ( sK34_C @ SY2527 @ SV319 ) @ ( sK35_SY2059 @ SY2527 @ SV319 ) ) )
| ~ ( in @ SY2527 @ SV319 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1831,plain,
! [SV348: $i,SV320: $i] :
( ( ( ( set_difference @ SV320 @ ( singleton @ SV348 ) )
!= SV320 )
| ~ ( in @ SV348 @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(1832,plain,
! [SV321: $i,SV349: $i] :
( ( ( in @ SV349 @ SV321 )
| ( ( set_difference @ SV321 @ ( singleton @ SV349 ) )
= SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(1833,plain,
! [SV298: $i,SV269: $i] :
( ( ! [SY2492: $i] :
( ! [SY2493: $i] :
( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SY2492 @ SY2493 ) )
| ( SV269 = SY2492 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(1834,plain,
! [SV298: $i,SV269: $i] :
( ( ! [SY2494: $i,SY2495: $i] :
( ( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SY2494 @ SY2495 ) )
| ( SV298 = SY2495 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1835,plain,
! [SV350: $i,SV270: $i] :
( ( ! [SY2558: $i] :
( ~ ( ~ ( ! [SY2559: $i,SY2560: $i] :
( ~ ( in @ SY2559 @ SV270 )
| ~ ( in @ SY2560 @ SV350 )
| ( ( sK23_D @ SY2558 @ SV350 @ SV270 )
!= ( ordered_pair @ SY2559 @ SY2560 ) ) )
| ~ ( in @ ( sK23_D @ SY2558 @ SV350 @ SV270 ) @ SY2558 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SY2558 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SY2558 @ SV350 @ SV270 ) @ SV350 ) )
| ( ( sK23_D @ SY2558 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SY2558 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SY2558 @ SV350 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SY2558 @ SV350 @ SV270 ) @ SY2558 ) ) )
| ( SY2558
= ( cartesian_product2 @ SV270 @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(1836,plain,
! [SV351: $i,SV270: $i] :
( ( ! [SY2561: $i] :
( ( SY2561
!= ( cartesian_product2 @ SV270 @ SV351 ) )
| ~ ( ~ ! [SY2562: $i] :
( ! [SY2563: $i,SY2564: $i] :
( ~ ( in @ SY2563 @ SV270 )
| ~ ( in @ SY2564 @ SV351 )
| ( SY2562
!= ( ordered_pair @ SY2563 @ SY2564 ) ) )
| ( in @ SY2562 @ SY2561 ) )
| ~ ! [SY2565: $i] :
( ~ ( in @ SY2565 @ SY2561 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2565 @ SY2561 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2565 @ SY2561 @ SV351 @ SV270 ) @ SV351 ) )
| ( SY2565
!= ( ordered_pair @ ( sK21_E @ SY2565 @ SY2561 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SY2565 @ SY2561 @ SV351 @ SV270 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1837,plain,
! [SV271: $i,SV352: $i] :
( ( ! [SY2566: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY2566 @ SV352 @ SV271 ) @ SY2566 )
| ~ ( in @ ( sK26_D @ SY2566 @ SV352 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY2566 @ SV352 @ SV271 ) @ SY2566 )
| ~ ( in @ ( sK26_D @ SY2566 @ SV352 @ SV271 ) @ SV352 ) ) )
| ~ ( ( in @ ( sK26_D @ SY2566 @ SV352 @ SV271 ) @ SY2566 )
| ( in @ ( sK26_D @ SY2566 @ SV352 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SY2566 @ SV352 @ SV271 ) @ SV352 ) ) )
| ( SY2566
= ( set_union2 @ SV271 @ SV352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1838,plain,
! [SV353: $i,SV271: $i] :
( ( ! [SY2567: $i] :
( ( SY2567
!= ( set_union2 @ SV271 @ SV353 ) )
| ~ ( ~ ! [SY2568: $i] :
( ~ ( in @ SY2568 @ SY2567 )
| ( in @ SY2568 @ SV271 )
| ( in @ SY2568 @ SV353 ) )
| ~ ~ ( ~ ! [SY2455: $i] :
( ~ ( in @ SY2455 @ SV271 )
| ( in @ SY2455 @ SY2567 ) )
| ~ ! [SY2570: $i] :
( ~ ( in @ SY2570 @ SV353 )
| ( in @ SY2570 @ SY2567 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(1839,plain,
! [SV272: $i,SV354: $i] :
( ( ~ ( subset @ SV354 @ ( sK39_B @ SV272 ) )
| ( are_equipotent @ SV354 @ ( sK39_B @ SV272 ) )
| ( in @ SV354 @ ( sK39_B @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(1840,plain,
! [SV272: $i] :
( ( ~ ! [SY2458: $i] :
( ~ ( in @ SY2458 @ ( sK39_B @ SV272 ) )
| ( in @ ( powerset @ SY2458 ) @ ( sK39_B @ SV272 ) ) )
| ~ ~ ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) )
| ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1841,plain,
! [SV273: $i] :
( ( ( ~ ! [SY2461: $i] :
( ~ ( relation @ SY2461 )
| ~ ( subset @ SV273 @ SY2461 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SY2461 ) ) ) )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1842,plain,
! [SV273: $i] :
( ( ( ~ ! [SY2462: $i] :
( ~ ( relation @ SY2462 )
| ~ ( subset @ SV273 @ SY2462 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SY2462 ) ) ) )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1843,plain,
! [SV299: $i,SV274: $i] :
( ( ! [SY2496: $i,SY2497: $i] :
( ~ ( in @ SV274 @ SY2496 )
| ~ ( in @ SV299 @ SY2497 )
| ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2496 @ SY2497 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1844,plain,
! [SV299: $i,SV274: $i] :
( ( ~ ( ~ ! [SY2498: $i] :
( ! [SY2499: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2498 @ SY2499 ) )
| ( in @ SV274 @ SY2498 ) )
| ~ ! [SY2500: $i,SY2501: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2500 @ SY2501 ) )
| ( in @ SV299 @ SY2501 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1845,plain,
! [SV355: $i,SV322: $i] :
( ( ( disjoint @ SV322 @ SV355 )
| ( in @ ( sK37_C @ SV355 @ SV322 ) @ ( set_intersection2 @ SV322 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(1846,plain,
! [SV356: $i,SV323: $i] :
( ( ! [SY2571: $i] :
~ ( in @ SY2571 @ ( set_intersection2 @ SV323 @ SV356 ) )
| ~ ( disjoint @ SV323 @ SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(1847,plain,
! [SV324: $i,SV357: $i] :
( ( ~ ( ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV324 )
| ~ ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV357 ) )
| ( subset @ SV324 @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(1848,plain,
! [SV358: $i,SV325: $i] :
( ( ~ ( subset @ SV325 @ SV358 )
| ! [SY2572: $i] :
( ~ ( in @ SY2572 @ SV325 )
| ( in @ SY2572 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1849,plain,
! [SV275: $i,SV359: $i] :
( ( ! [SY2573: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY2573 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2573 @ SV359 @ SV275 ) @ SV359 )
| ~ ( in @ ( sK12_D @ SY2573 @ SV359 @ SV275 ) @ SY2573 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY2573 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SY2573 @ SV359 @ SV275 ) @ SY2573 ) )
| ~ ( ~ ( in @ ( sK12_D @ SY2573 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SY2573 @ SV359 @ SV275 ) @ SY2573 ) ) ) )
| ( SY2573
= ( set_difference @ SV275 @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(1850,plain,
! [SV360: $i,SV275: $i] :
( ( ! [SY2574: $i] :
( ( SY2574
!= ( set_difference @ SV275 @ SV360 ) )
| ~ ( ~ ! [SY2575: $i] :
( ~ ( in @ SY2575 @ SV275 )
| ( in @ SY2575 @ SV360 )
| ( in @ SY2575 @ SY2574 ) )
| ~ ~ ( ~ ! [SY2475: $i] :
( ~ ( in @ SY2475 @ SY2574 )
| ( in @ SY2475 @ SV275 ) )
| ~ ! [SY2577: $i] :
( ~ ( in @ SY2577 @ SY2574 )
| ~ ( in @ SY2577 @ SV360 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(1851,plain,
! [SV240: $i,SV279: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ SV279 ) )
= $true )
| ( ( in @ SV326 @ SV240 )
= $true )
| ( ( element @ SV279 @ ( powerset @ SV240 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1776]) ).
thf(1852,plain,
! [SV280: $i,SV241: $i,SV327: $i] :
( ( ( in @ SV327 @ SV241 )
= $true )
| ( ( subset @ SV241 @ ( set_difference @ SV280 @ ( singleton @ SV327 ) ) )
= $true )
| ( ( subset @ SV241 @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1853,plain,
! [SV300: $i,SV245: $i,SV361: $i] :
( ( ( ~ ( element @ SV361 @ SV245 )
| ( in @ SV361 @ SV300 )
| ( in @ SV361 @ ( subset_complement @ SV245 @ SV300 ) ) )
= $true )
| ( ( element @ SV300 @ ( powerset @ SV245 ) )
= $false )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(1854,plain,
! [SV301: $i,SV246: $i,SV283: $i] :
( ( ( ~ ( in @ SV283 @ ( subset_complement @ SV246 @ SV301 ) ) )
= $true )
| ( ( ~ ( in @ SV283 @ SV301 ) )
= $true )
| ( ( element @ SV301 @ ( powerset @ SV246 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1855,plain,
! [SV252: $i,SV288: $i] :
( ( ( relation @ SV288 )
= $false )
| ( ( relation @ SV252 )
= $false )
| ( ( relation @ ( set_union2 @ SV252 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1856,plain,
! [SV255: $i,SV302: $i,SV291: $i] :
( ( ( element @ SV291 @ ( powerset @ SV302 ) )
= $false )
| ( ( ~ ( in @ SV255 @ SV291 ) )
= $true )
| ( ( element @ SV255 @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1857,plain,
! [SV256: $i,SV303: $i,SV292: $i] :
( ( ( element @ SV292 @ ( powerset @ SV303 ) )
= $false )
| ( ( ~ ( in @ SV256 @ SV292 ) )
= $true )
| ( ( ~ ( empty @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1858,plain,
! [SV305: $i] :
( ( ( SV305 = empty_set )
= $false )
| ( ( ! [SY2503: $i] :
~ ( in @ SY2503 @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1859,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1860,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1789]) ).
thf(1861,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1862,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1863,plain,
! [SV306: $i,SV328: $i] :
( ( ( ~ ( ~ ( ( ( sK30_C @ SV328 @ SV306 )
!= SV306 )
| ~ ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) )
| ~ ( ( ( sK30_C @ SV328 @ SV306 )
= SV306 )
| ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) ) ) )
= $true )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(1864,plain,
! [SV307: $i,SV329: $i] :
( ( ( ( SV329
!= ( singleton @ SV307 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2536: $i] :
( ( SY2536 != SV307 )
| ( in @ SY2536 @ SV329 ) )
| ~ ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV329 )
| ( SY2537 = SV307 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1865,plain,
! [SV330: $i,SV308: $i] :
( ( ( disjoint @ SV308 @ SV330 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV308 )
| ~ ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV330 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1866,plain,
! [SV331: $i,SV309: $i] :
( ( ( ! [SY2538: $i] :
( ~ ( in @ SY2538 @ SV309 )
| ~ ( in @ SY2538 @ SV331 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV309 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(1867,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( ~ ( ! [SY2539: $i] :
( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SY2539 )
| ~ ( in @ SY2539 @ SV310 ) )
| ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) )
| ~ ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 ) )
| ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) ) ) )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1868,plain,
! [SV311: $i,SV333: $i] :
( ( ( ( SV333
!= ( union @ SV311 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2540: $i] :
( ! [SY2515: $i] :
( ~ ( in @ SY2540 @ SY2515 )
| ~ ( in @ SY2515 @ SV311 ) )
| ( in @ SY2540 @ SV333 ) )
| ~ ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV333 )
| ~ ( ~ ( in @ SY2542 @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) @ SV311 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(1869,plain,
! [SV294: $i,SV258: $i] :
( ( ( ~ ! [SY2482: $i] :
( ~ ( element @ SY2482 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SY2482
= ( complements_of_subsets @ SV258 @ SV294 ) ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1870,plain,
! [SV294: $i,SV258: $i] :
( ( ( ~ ! [SY2483: $i] :
( ~ ( element @ SY2483 @ ( powerset @ ( powerset @ SV258 ) ) )
| ( SY2483
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2484: $i] :
( ~ ( element @ SY2484 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2484 @ SY2483 )
| ( in @ ( subset_complement @ SV258 @ SY2484 ) @ SV294 ) )
| ~ ! [SY2485: $i] :
( ~ ( element @ SY2485 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2485 ) @ SV294 )
| ( in @ SY2485 @ SY2483 ) ) ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1871,plain,
! [SV259: $i,SV295: $i] :
( ( ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV259 )
= $true )
| ( ( element @ SV259 @ ( powerset @ SV295 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1872,plain,
! [SV259: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV295 ) )
= $true )
| ( ( element @ SV259 @ ( powerset @ SV295 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1873,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) ) )
| ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(1874,plain,
! [SV335: $i,SV260: $i,SV363: $i] :
( ( ( SV363
!= ( set_intersection2 @ SV260 @ SV335 ) )
| ~ ( ~ ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV260 )
| ~ ( in @ SY2578 @ SV335 )
| ( in @ SY2578 @ SV363 ) )
| ~ ~ ( ~ ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) )
| ~ ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(1875,plain,
! [SV261: $i] :
( ( ( ! [SY2393: $i] :
( ~ ( ~ ( ! [SY2394: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ SY2394 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY2393 @ SV261 ) @ ( sK18_SY2050 @ SY2393 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SY2393 @ SV261 ) @ SY2393 ) ) )
| ( SY2393
= ( relation_dom @ SV261 ) ) ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1876,plain,
! [SV261: $i] :
( ( ( ! [SY2395: $i] :
( ( SY2395
!= ( relation_dom @ SV261 ) )
| ~ ( ~ ! [SY2396: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2396 @ SY2397 ) @ SV261 )
| ( in @ SY2396 @ SY2395 ) )
| ~ ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SY2395 )
| ( in @ ( ordered_pair @ SY2398 @ ( sK16_D @ SY2398 @ SY2395 @ SV261 ) ) @ SV261 ) ) ) ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1877,plain,
! [SV336: $i,SV364: $i,SV262: $i] :
( ( ~ ( in @ SV262 @ SV364 )
| ~ ( in @ SV336 @ SV364 )
| ( subset @ ( unordered_pair @ SV262 @ SV336 ) @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(1878,plain,
! [SV262: $i] :
( ( ~ ! [SY2401: $i,SY2402: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2401 ) @ SY2402 )
| ( in @ SV262 @ SY2402 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1806]) ).
thf(1879,plain,
! [SV262: $i] :
( ( ~ ! [SY2403: $i,SY2404: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2403 ) @ SY2404 )
| ( in @ SY2403 @ SY2404 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1806]) ).
thf(1880,plain,
! [SV312: $i,SV337: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ~ ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) )
| ~ ( ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) ) ) )
= $true )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1881,plain,
! [SV313: $i,SV338: $i] :
( ( ( ( SV338
!= ( powerset @ SV313 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV338 )
| ( subset @ SY2549 @ SV313 ) )
| ~ ! [SY2550: $i] :
( ~ ( subset @ SY2550 @ SV313 )
| ( in @ SY2550 @ SV338 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(1882,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY2057 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1883,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1810]) ).
thf(1884,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1885,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1886,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) ) )
| ~ ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV263 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV339 ) ) )
| ( SV365
= ( unordered_pair @ SV263 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(1887,plain,
! [SV340: $i,SV263: $i,SV366: $i] :
( ( ( SV366
!= ( unordered_pair @ SV263 @ SV340 ) )
| ~ ( ~ ! [SY2581: $i] :
( ~ ( in @ SY2581 @ SV366 )
| ( SY2581 = SV263 )
| ( SY2581 = SV340 ) )
| ~ ~ ( ~ ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) )
| ~ ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(1888,plain,
! [SV341: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ SV341 ) )
= $true )
| ( ( subset @ ( singleton @ SV314 ) @ SV341 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(1889,plain,
! [SV342: $i,SV315: $i] :
( ( ( ~ ( subset @ ( singleton @ SV315 ) @ SV342 ) )
= $true )
| ( ( in @ SV315 @ SV342 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1890,plain,
! [SV343: $i,SV264: $i,SV367: $i] :
( ( ~ ( relation @ SV367 )
| ~ ( in @ ( ordered_pair @ SV264 @ SV343 ) @ SV367 )
| ( in @ SV264 @ ( relation_dom @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(1891,plain,
! [SV344: $i,SV264: $i,SV368: $i] :
( ( ~ ( relation @ SV368 )
| ~ ( in @ ( ordered_pair @ SV264 @ SV344 ) @ SV368 )
| ( in @ SV344 @ ( relation_rng @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(1892,plain,
! [SV345: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ SV345 ) )
= $true )
| ( ( subset @ ( singleton @ SV316 ) @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(1893,plain,
! [SV346: $i,SV317: $i] :
( ( ( ~ ( subset @ ( singleton @ SV317 ) @ SV346 ) )
= $true )
| ( ( in @ SV317 @ SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1894,plain,
! [SV265: $i] :
( ( ( ! [SY2416: $i] :
( ~ ( ~ ( ! [SY2417: $i] :
~ ( in @ ( ordered_pair @ SY2417 @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SY2416 @ SV265 ) @ ( sK10_C @ SY2416 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SY2416 @ SV265 ) @ SY2416 ) ) )
| ( SY2416
= ( relation_rng @ SV265 ) ) ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1895,plain,
! [SV265: $i] :
( ( ( ! [SY2418: $i] :
( ( SY2418
!= ( relation_rng @ SV265 ) )
| ~ ( ~ ! [SY2419: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2419 ) @ SV265 )
| ( in @ SY2419 @ SY2418 ) )
| ~ ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SY2418 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2421 @ SY2418 @ SV265 ) @ SY2421 ) @ SV265 ) ) ) ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1896,plain,
! [SV266: $i,SV296: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) )
= $true )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1897,plain,
! [SV266: $i,SV296: $i] :
( ( ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
| ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) )
= $true )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(1898,plain,
! [SV267: $i,SV347: $i] :
( ( ( ~ ( subset @ SV347 @ ( sK4_B @ SV267 ) )
| ( are_equipotent @ SV347 @ ( sK4_B @ SV267 ) ) )
= $true )
| ( ( in @ SV347 @ ( sK4_B @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1899,plain,
! [SV267: $i] :
( ( ~ ! [SY2424: $i] :
( ~ ( ~ ! [SY2425: $i] :
( ~ ( subset @ SY2425 @ SY2424 )
| ( in @ SY2425 @ ( sK5_SY2040 @ SY2424 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2424 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SY2424 @ ( sK4_B @ SV267 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1900,plain,
! [SV267: $i] :
( ( ~ ~ ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1901,plain,
! [SV297: $i,SV369: $i,SV268: $i] :
( ( ! [SY2584: $i] :
( ~ ( in @ SV268 @ SV369 )
| ~ ( in @ SV297 @ SY2584 )
| ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV369 @ SY2584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(1902,plain,
! [SV297: $i,SV268: $i] :
( ( ~ ! [SY2488: $i] :
( ! [SY2489: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2488 @ SY2489 ) )
| ( in @ SV268 @ SY2488 ) )
| ~ ! [SY2490: $i,SY2491: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2490 @ SY2491 ) )
| ( in @ SV297 @ SY2491 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(1903,plain,
! [SV318: $i] :
( ( ( ~ ! [SY2525: $i,SY2526: $i] :
( ( sK36_B @ SV318 )
!= ( ordered_pair @ SY2525 @ SY2526 ) )
| ~ ( in @ ( sK36_B @ SV318 ) @ SV318 ) )
= $false )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1904,plain,
! [SV319: $i] :
( ( ( relation @ SV319 )
= $false )
| ( ( ! [SY2527: $i] :
( ( SY2527
= ( ordered_pair @ ( sK34_C @ SY2527 @ SV319 ) @ ( sK35_SY2059 @ SY2527 @ SV319 ) ) )
| ~ ( in @ SY2527 @ SV319 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1905,plain,
! [SV348: $i,SV320: $i] :
( ( ( ( ( set_difference @ SV320 @ ( singleton @ SV348 ) )
!= SV320 ) )
= $true )
| ( ( ~ ( in @ SV348 @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(1906,plain,
! [SV321: $i,SV349: $i] :
( ( ( in @ SV349 @ SV321 )
= $true )
| ( ( ( set_difference @ SV321 @ ( singleton @ SV349 ) )
= SV321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(1907,plain,
! [SV370: $i,SV298: $i,SV269: $i] :
( ( ! [SY2585: $i] :
( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SV370 @ SY2585 ) )
| ( SV269 = SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(1908,plain,
! [SV371: $i,SV298: $i,SV269: $i] :
( ( ! [SY2586: $i] :
( ( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SV371 @ SY2586 ) )
| ( SV298 = SY2586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(1909,plain,
! [SV372: $i,SV350: $i,SV270: $i] :
( ( ~ ( ~ ( ! [SY2587: $i,SY2588: $i] :
( ~ ( in @ SY2587 @ SV270 )
| ~ ( in @ SY2588 @ SV350 )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SY2587 @ SY2588 ) ) )
| ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) ) )
| ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(1910,plain,
! [SV351: $i,SV270: $i,SV373: $i] :
( ( ( SV373
!= ( cartesian_product2 @ SV270 @ SV351 ) )
| ~ ( ~ ! [SY2589: $i] :
( ! [SY2563: $i,SY2564: $i] :
( ~ ( in @ SY2563 @ SV270 )
| ~ ( in @ SY2564 @ SV351 )
| ( SY2589
!= ( ordered_pair @ SY2563 @ SY2564 ) ) )
| ( in @ SY2589 @ SV373 ) )
| ~ ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV373 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SY2592
!= ( ordered_pair @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(1911,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) )
| ~ ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) )
| ( SV374
= ( set_union2 @ SV271 @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(1912,plain,
! [SV353: $i,SV271: $i,SV375: $i] :
( ( ( SV375
!= ( set_union2 @ SV271 @ SV353 ) )
| ~ ( ~ ! [SY2593: $i] :
( ~ ( in @ SY2593 @ SV375 )
| ( in @ SY2593 @ SV271 )
| ( in @ SY2593 @ SV353 ) )
| ~ ~ ( ~ ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) )
| ~ ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(1913,plain,
! [SV272: $i,SV354: $i] :
( ( ( ~ ( subset @ SV354 @ ( sK39_B @ SV272 ) )
| ( are_equipotent @ SV354 @ ( sK39_B @ SV272 ) ) )
= $true )
| ( ( in @ SV354 @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(1914,plain,
! [SV272: $i] :
( ( ~ ! [SY2458: $i] :
( ~ ( in @ SY2458 @ ( sK39_B @ SV272 ) )
| ( in @ ( powerset @ SY2458 ) @ ( sK39_B @ SV272 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1915,plain,
! [SV272: $i] :
( ( ~ ~ ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) )
| ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1916,plain,
! [SV273: $i] :
( ( ( ! [SY2461: $i] :
( ~ ( relation @ SY2461 )
| ~ ( subset @ SV273 @ SY2461 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SY2461 ) ) ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(1917,plain,
! [SV273: $i] :
( ( ( ! [SY2462: $i] :
( ~ ( relation @ SY2462 )
| ~ ( subset @ SV273 @ SY2462 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SY2462 ) ) ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(1918,plain,
! [SV299: $i,SV376: $i,SV274: $i] :
( ( ! [SY2596: $i] :
( ~ ( in @ SV274 @ SV376 )
| ~ ( in @ SV299 @ SY2596 )
| ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV376 @ SY2596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(1919,plain,
! [SV299: $i,SV274: $i] :
( ( ~ ! [SY2498: $i] :
( ! [SY2499: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2498 @ SY2499 ) )
| ( in @ SV274 @ SY2498 ) )
| ~ ! [SY2500: $i,SY2501: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2500 @ SY2501 ) )
| ( in @ SV299 @ SY2501 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1920,plain,
! [SV355: $i,SV322: $i] :
( ( ( disjoint @ SV322 @ SV355 )
= $true )
| ( ( in @ ( sK37_C @ SV355 @ SV322 ) @ ( set_intersection2 @ SV322 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1921,plain,
! [SV356: $i,SV323: $i] :
( ( ( ! [SY2571: $i] :
~ ( in @ SY2571 @ ( set_intersection2 @ SV323 @ SV356 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV323 @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1922,plain,
! [SV324: $i,SV357: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV324 )
| ~ ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV357 ) ) )
= $true )
| ( ( subset @ SV324 @ SV357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(1923,plain,
! [SV358: $i,SV325: $i] :
( ( ( ~ ( subset @ SV325 @ SV358 ) )
= $true )
| ( ( ! [SY2572: $i] :
( ~ ( in @ SY2572 @ SV325 )
| ( in @ SY2572 @ SV358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(1924,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) ) )
| ( SV377
= ( set_difference @ SV275 @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(1925,plain,
! [SV360: $i,SV275: $i,SV378: $i] :
( ( ( SV378
!= ( set_difference @ SV275 @ SV360 ) )
| ~ ( ~ ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV275 )
| ( in @ SY2597 @ SV360 )
| ( in @ SY2597 @ SV378 ) )
| ~ ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) )
| ~ ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(1926,plain,
! [SV240: $i,SV279: $i,SV326: $i] :
( ( ( in @ SV326 @ SV279 )
= $false )
| ( ( in @ SV326 @ SV240 )
= $true )
| ( ( element @ SV279 @ ( powerset @ SV240 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1927,plain,
! [SV300: $i,SV245: $i,SV361: $i] :
( ( ( ~ ( element @ SV361 @ SV245 ) )
= $true )
| ( ( ( in @ SV361 @ SV300 )
| ( in @ SV361 @ ( subset_complement @ SV245 @ SV300 ) ) )
= $true )
| ( ( element @ SV300 @ ( powerset @ SV245 ) )
= $false )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(1928,plain,
! [SV301: $i,SV246: $i,SV283: $i] :
( ( ( in @ SV283 @ ( subset_complement @ SV246 @ SV301 ) )
= $false )
| ( ( ~ ( in @ SV283 @ SV301 ) )
= $true )
| ( ( element @ SV301 @ ( powerset @ SV246 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1929,plain,
! [SV302: $i,SV291: $i,SV255: $i] :
( ( ( in @ SV255 @ SV291 )
= $false )
| ( ( element @ SV291 @ ( powerset @ SV302 ) )
= $false )
| ( ( element @ SV255 @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1930,plain,
! [SV303: $i,SV292: $i,SV256: $i] :
( ( ( in @ SV256 @ SV292 )
= $false )
| ( ( element @ SV292 @ ( powerset @ SV303 ) )
= $false )
| ( ( ~ ( empty @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1931,plain,
! [SV305: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(1932,plain,
! [SV380: $i] :
( ( ( empty @ SV380 )
| ! [SY2600: $i] :
( ~ ( element @ SY2600 @ SV380 )
| ( in @ SY2600 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(1933,plain,
! [SV381: $i] :
( ( ( empty @ SV381 )
| ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV381 )
| ( element @ SY2601 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(1934,plain,
! [SV382: $i] :
( ( ~ ( empty @ SV382 )
| ! [SY2602: $i] :
( ~ ( element @ SY2602 @ SV382 )
| ( empty @ SY2602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(1935,plain,
! [SV383: $i] :
( ( ~ ( empty @ SV383 )
| ! [SY2603: $i] :
( ~ ( empty @ SY2603 )
| ( element @ SY2603 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1936,plain,
! [SV306: $i,SV328: $i] :
( ( ( ~ ( ( ( sK30_C @ SV328 @ SV306 )
!= SV306 )
| ~ ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) )
| ~ ( ( ( sK30_C @ SV328 @ SV306 )
= SV306 )
| ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) ) )
= $false )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(1937,plain,
! [SV307: $i,SV329: $i] :
( ( ( SV329
= ( singleton @ SV307 ) )
= $false )
| ( ( ~ ( ~ ! [SY2536: $i] :
( ( SY2536 != SV307 )
| ( in @ SY2536 @ SV329 ) )
| ~ ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV329 )
| ( SY2537 = SV307 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1938,plain,
! [SV308: $i,SV330: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV308 )
| ~ ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV330 ) )
= $false )
| ( ( disjoint @ SV308 @ SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1939,plain,
! [SV331: $i,SV309: $i,SV384: $i] :
( ( ( ~ ( in @ SV384 @ SV309 )
| ~ ( in @ SV384 @ SV331 ) )
= $true )
| ( ( ~ ( disjoint @ SV309 @ SV331 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(1940,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( ! [SY2539: $i] :
( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SY2539 )
| ~ ( in @ SY2539 @ SV310 ) )
| ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
| ~ ( ~ ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) )
| ~ ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 ) )
| ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) ) )
= $false )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1941,plain,
! [SV311: $i,SV333: $i] :
( ( ( SV333
= ( union @ SV311 ) )
= $false )
| ( ( ~ ( ~ ! [SY2540: $i] :
( ! [SY2515: $i] :
( ~ ( in @ SY2540 @ SY2515 )
| ~ ( in @ SY2515 @ SV311 ) )
| ( in @ SY2540 @ SV333 ) )
| ~ ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV333 )
| ~ ( ~ ( in @ SY2542 @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) @ SV311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1942,plain,
! [SV294: $i,SV258: $i] :
( ( ( ! [SY2482: $i] :
( ~ ( element @ SY2482 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) @ SY2482 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SY2482 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SY2482
= ( complements_of_subsets @ SV258 @ SV294 ) ) ) )
= $true )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1869]) ).
thf(1943,plain,
! [SV294: $i,SV258: $i] :
( ( ( ! [SY2483: $i] :
( ~ ( element @ SY2483 @ ( powerset @ ( powerset @ SV258 ) ) )
| ( SY2483
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2484: $i] :
( ~ ( element @ SY2484 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2484 @ SY2483 )
| ( in @ ( subset_complement @ SV258 @ SY2484 ) @ SV294 ) )
| ~ ! [SY2485: $i] :
( ~ ( element @ SY2485 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2485 ) @ SV294 )
| ( in @ SY2485 @ SY2483 ) ) ) ) )
= $true )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1870]) ).
thf(1944,plain,
! [SV259: $i,SV295: $i] :
( ( ( in @ ( sK40_C @ SV295 @ SV259 ) @ SV295 )
= $false )
| ( ( element @ SV259 @ ( powerset @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1945,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) ) ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(1946,plain,
! [SV335: $i,SV260: $i,SV363: $i] :
( ( ( ( SV363
!= ( set_intersection2 @ SV260 @ SV335 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV260 )
| ~ ( in @ SY2578 @ SV335 )
| ( in @ SY2578 @ SV363 ) )
| ~ ~ ( ~ ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) )
| ~ ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(1947,plain,
! [SV261: $i,SV385: $i] :
( ( ( ~ ( ~ ( ! [SY2604: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SY2604 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ ( sK18_SY2050 @ SV385 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) ) )
| ( SV385
= ( relation_dom @ SV261 ) ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(1948,plain,
! [SV261: $i,SV386: $i] :
( ( ( ( SV386
!= ( relation_dom @ SV261 ) )
| ~ ( ~ ! [SY2605: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2605 @ SY2397 ) @ SV261 )
| ( in @ SY2605 @ SV386 ) )
| ~ ! [SY2607: $i] :
( ~ ( in @ SY2607 @ SV386 )
| ( in @ ( ordered_pair @ SY2607 @ ( sK16_D @ SY2607 @ SV386 @ SV261 ) ) @ SV261 ) ) ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(1949,plain,
! [SV336: $i,SV364: $i,SV262: $i] :
( ( ( ~ ( in @ SV262 @ SV364 )
| ~ ( in @ SV336 @ SV364 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV262 @ SV336 ) @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(1950,plain,
! [SV262: $i] :
( ( ! [SY2401: $i,SY2402: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2401 ) @ SY2402 )
| ( in @ SV262 @ SY2402 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1951,plain,
! [SV262: $i] :
( ( ! [SY2403: $i,SY2404: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SY2403 ) @ SY2404 )
| ( in @ SY2403 @ SY2404 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1879]) ).
thf(1952,plain,
! [SV312: $i,SV337: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ~ ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) )
| ~ ( ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) ) )
= $false )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(1953,plain,
! [SV313: $i,SV338: $i] :
( ( ( SV338
= ( powerset @ SV313 ) )
= $false )
| ( ( ~ ( ~ ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV338 )
| ( subset @ SY2549 @ SV313 ) )
| ~ ! [SY2550: $i] :
( ~ ( subset @ SY2550 @ SV313 )
| ( in @ SY2550 @ SV338 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(1954,plain,
! [SV387: $i] :
( ( ( SV387 = empty_set )
| ! [SY2608: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SY2608 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SY2608 @ SV387 ) @ ( sK33_SY2057 @ SY2608 @ SV387 ) ) )
| ~ ( in @ ( sK32_C @ SY2608 @ SV387 ) @ SY2608 ) )
| ~ ( ! [SY2609: $i] :
( ~ ( in @ SY2609 @ SV387 )
| ( in @ ( sK32_C @ SY2608 @ SV387 ) @ SY2609 ) )
| ( in @ ( sK32_C @ SY2608 @ SV387 ) @ SY2608 ) ) )
| ( SY2608
= ( set_meet @ SV387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(1955,plain,
! [SV388: $i] :
( ( ( SV388 = empty_set )
| ! [SY2610: $i] :
( ( SY2610
!= ( set_meet @ SV388 ) )
| ~ ( ~ ! [SY2611: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2611 @ SY2610 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SY2611 @ ( sK31_D @ SY2611 @ SY2610 @ SV388 ) ) )
| ( in @ SY2611 @ SY2610 ) )
| ~ ! [SY2612: $i] :
( ~ ( in @ SY2612 @ SY2610 )
| ! [SY2613: $i] :
( ~ ( in @ SY2613 @ SV388 )
| ( in @ SY2612 @ SY2613 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(1956,plain,
! [SV389: $i] :
( ( ( SV389 != empty_set )
| ! [SY2614: $i] :
( ( SY2614
!= ( set_meet @ SV389 ) )
| ( SY2614 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(1957,plain,
! [SV390: $i] :
( ( ( SV390 != empty_set )
| ! [SY2615: $i] :
( ( SY2615 != empty_set )
| ( SY2615
= ( set_meet @ SV390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(1958,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) ) )
| ~ ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV263 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV339 ) ) ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(1959,plain,
! [SV340: $i,SV263: $i,SV366: $i] :
( ( ( ( SV366
!= ( unordered_pair @ SV263 @ SV340 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2581: $i] :
( ~ ( in @ SY2581 @ SV366 )
| ( SY2581 = SV263 )
| ( SY2581 = SV340 ) )
| ~ ~ ( ~ ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) )
| ~ ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(1960,plain,
! [SV341: $i,SV314: $i] :
( ( ( in @ SV314 @ SV341 )
= $false )
| ( ( subset @ ( singleton @ SV314 ) @ SV341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1961,plain,
! [SV342: $i,SV315: $i] :
( ( ( subset @ ( singleton @ SV315 ) @ SV342 )
= $false )
| ( ( in @ SV315 @ SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1962,plain,
! [SV343: $i,SV264: $i,SV367: $i] :
( ( ( ~ ( relation @ SV367 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV264 @ SV343 ) @ SV367 )
| ( in @ SV264 @ ( relation_dom @ SV367 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(1963,plain,
! [SV344: $i,SV264: $i,SV368: $i] :
( ( ( ~ ( relation @ SV368 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV264 @ SV344 ) @ SV368 )
| ( in @ SV344 @ ( relation_rng @ SV368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(1964,plain,
! [SV345: $i,SV316: $i] :
( ( ( in @ SV316 @ SV345 )
= $false )
| ( ( subset @ ( singleton @ SV316 ) @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(1965,plain,
! [SV346: $i,SV317: $i] :
( ( ( subset @ ( singleton @ SV317 ) @ SV346 )
= $false )
| ( ( in @ SV317 @ SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1966,plain,
! [SV265: $i,SV391: $i] :
( ( ( ~ ( ~ ( ! [SY2616: $i] :
~ ( in @ ( ordered_pair @ SY2616 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV391 @ SV265 ) @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) ) )
| ( SV391
= ( relation_rng @ SV265 ) ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(1967,plain,
! [SV265: $i,SV392: $i] :
( ( ( ( SV392
!= ( relation_rng @ SV265 ) )
| ~ ( ~ ! [SY2617: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2617 ) @ SV265 )
| ( in @ SY2617 @ SV392 ) )
| ~ ! [SY2619: $i] :
( ~ ( in @ SY2619 @ SV392 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2619 @ SV392 @ SV265 ) @ SY2619 ) @ SV265 ) ) ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(1968,plain,
! [SV266: $i,SV296: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 ) )
= $true )
| ( ( ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) )
= $true )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1896]) ).
thf(1969,plain,
! [SV266: $i,SV296: $i] :
( ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
= $true )
| ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 )
= $true )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(1970,plain,
! [SV267: $i,SV347: $i] :
( ( ( ~ ( subset @ SV347 @ ( sK4_B @ SV267 ) ) )
= $true )
| ( ( are_equipotent @ SV347 @ ( sK4_B @ SV267 ) )
= $true )
| ( ( in @ SV347 @ ( sK4_B @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(1971,plain,
! [SV267: $i] :
( ( ! [SY2424: $i] :
( ~ ( ~ ! [SY2425: $i] :
( ~ ( subset @ SY2425 @ SY2424 )
| ( in @ SY2425 @ ( sK5_SY2040 @ SY2424 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SY2424 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SY2424 @ ( sK4_B @ SV267 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1972,plain,
! [SV267: $i] :
( ( ~ ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(1973,plain,
! [SV393: $i,SV297: $i,SV369: $i,SV268: $i] :
( ( ~ ( in @ SV268 @ SV369 )
| ~ ( in @ SV297 @ SV393 )
| ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV369 @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(1974,plain,
! [SV297: $i,SV268: $i] :
( ( ~ ! [SY2488: $i] :
( ! [SY2489: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2488 @ SY2489 ) )
| ( in @ SV268 @ SY2488 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1902]) ).
thf(1975,plain,
! [SV297: $i,SV268: $i] :
( ( ~ ! [SY2490: $i,SY2491: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2490 @ SY2491 ) )
| ( in @ SV297 @ SY2491 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1902]) ).
thf(1976,plain,
! [SV318: $i] :
( ( ( ~ ! [SY2525: $i,SY2526: $i] :
( ( sK36_B @ SV318 )
!= ( ordered_pair @ SY2525 @ SY2526 ) ) )
= $false )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1903]) ).
thf(1977,plain,
! [SV318: $i] :
( ( ( ~ ( in @ ( sK36_B @ SV318 ) @ SV318 ) )
= $false )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1903]) ).
thf(1978,plain,
! [SV319: $i,SV394: $i] :
( ( ( ( SV394
= ( ordered_pair @ ( sK34_C @ SV394 @ SV319 ) @ ( sK35_SY2059 @ SV394 @ SV319 ) ) )
| ~ ( in @ SV394 @ SV319 ) )
= $true )
| ( ( relation @ SV319 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(1979,plain,
! [SV348: $i,SV320: $i] :
( ( ( ( set_difference @ SV320 @ ( singleton @ SV348 ) )
= SV320 )
= $false )
| ( ( ~ ( in @ SV348 @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1980,plain,
! [SV370: $i,SV298: $i,SV269: $i] :
( ( ( ! [SY2585: $i] :
( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SV370 @ SY2585 ) ) )
= $true )
| ( ( SV269 = SV370 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(1981,plain,
! [SV395: $i,SV371: $i,SV298: $i,SV269: $i] :
( ( ( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SV371 @ SV395 ) )
| ( SV298 = SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(1982,plain,
! [SV372: $i,SV350: $i,SV270: $i] :
( ( ( ~ ( ~ ( ! [SY2587: $i,SY2588: $i] :
( ~ ( in @ SY2587 @ SV270 )
| ~ ( in @ SY2588 @ SV350 )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SY2587 @ SY2588 ) ) )
| ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) ) ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(1983,plain,
! [SV351: $i,SV270: $i,SV373: $i] :
( ( ( ( SV373
!= ( cartesian_product2 @ SV270 @ SV351 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2589: $i] :
( ! [SY2563: $i,SY2564: $i] :
( ~ ( in @ SY2563 @ SV270 )
| ~ ( in @ SY2564 @ SV351 )
| ( SY2589
!= ( ordered_pair @ SY2563 @ SY2564 ) ) )
| ( in @ SY2589 @ SV373 ) )
| ~ ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV373 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SY2592
!= ( ordered_pair @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(1984,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) )
| ~ ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1985,plain,
! [SV353: $i,SV271: $i,SV375: $i] :
( ( ( ( SV375
!= ( set_union2 @ SV271 @ SV353 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2593: $i] :
( ~ ( in @ SY2593 @ SV375 )
| ( in @ SY2593 @ SV271 )
| ( in @ SY2593 @ SV353 ) )
| ~ ~ ( ~ ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) )
| ~ ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(1986,plain,
! [SV272: $i,SV354: $i] :
( ( ( ~ ( subset @ SV354 @ ( sK39_B @ SV272 ) ) )
= $true )
| ( ( are_equipotent @ SV354 @ ( sK39_B @ SV272 ) )
= $true )
| ( ( in @ SV354 @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(1987,plain,
! [SV272: $i] :
( ( ! [SY2458: $i] :
( ~ ( in @ SY2458 @ ( sK39_B @ SV272 ) )
| ( in @ ( powerset @ SY2458 ) @ ( sK39_B @ SV272 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(1988,plain,
! [SV272: $i] :
( ( ~ ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) )
| ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(1989,plain,
! [SV273: $i,SV396: $i] :
( ( ( ~ ( relation @ SV396 )
| ~ ( subset @ SV273 @ SV396 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SV396 ) ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(1990,plain,
! [SV273: $i,SV397: $i] :
( ( ( ~ ( relation @ SV397 )
| ~ ( subset @ SV273 @ SV397 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SV397 ) ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(1991,plain,
! [SV398: $i,SV299: $i,SV376: $i,SV274: $i] :
( ( ~ ( in @ SV274 @ SV376 )
| ~ ( in @ SV299 @ SV398 )
| ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV376 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(1992,plain,
! [SV299: $i,SV274: $i] :
( ( ~ ! [SY2498: $i] :
( ! [SY2499: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2498 @ SY2499 ) )
| ( in @ SV274 @ SY2498 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(1993,plain,
! [SV299: $i,SV274: $i] :
( ( ~ ! [SY2500: $i,SY2501: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2500 @ SY2501 ) )
| ( in @ SV299 @ SY2501 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(1994,plain,
! [SV356: $i,SV323: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ ( set_intersection2 @ SV323 @ SV356 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV323 @ SV356 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(1995,plain,
! [SV324: $i,SV357: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV324 )
| ~ ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV357 ) )
= $false )
| ( ( subset @ SV324 @ SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1996,plain,
! [SV358: $i,SV325: $i] :
( ( ( subset @ SV325 @ SV358 )
= $false )
| ( ( ! [SY2572: $i] :
( ~ ( in @ SY2572 @ SV325 )
| ( in @ SY2572 @ SV358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(1997,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) ) ) )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(1998,plain,
! [SV360: $i,SV275: $i,SV378: $i] :
( ( ( ( SV378
!= ( set_difference @ SV275 @ SV360 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV275 )
| ( in @ SY2597 @ SV360 )
| ( in @ SY2597 @ SV378 ) )
| ~ ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) )
| ~ ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(1999,plain,
! [SV300: $i,SV245: $i,SV361: $i] :
( ( ( element @ SV361 @ SV245 )
= $false )
| ( ( ( in @ SV361 @ SV300 )
| ( in @ SV361 @ ( subset_complement @ SV245 @ SV300 ) ) )
= $true )
| ( ( element @ SV300 @ ( powerset @ SV245 ) )
= $false )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(2000,plain,
! [SV246: $i,SV301: $i,SV283: $i] :
( ( ( in @ SV283 @ SV301 )
= $false )
| ( ( in @ SV283 @ ( subset_complement @ SV246 @ SV301 ) )
= $false )
| ( ( element @ SV301 @ ( powerset @ SV246 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2001,plain,
! [SV256: $i,SV292: $i,SV303: $i] :
( ( ( empty @ SV303 )
= $false )
| ( ( element @ SV292 @ ( powerset @ SV303 ) )
= $false )
| ( ( in @ SV256 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2002,plain,
! [SV305: $i,SV379: $i] :
( ( ( in @ SV379 @ SV305 )
= $false )
| ( ( SV305 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2003,plain,
! [SV380: $i] :
( ( ( empty @ SV380 )
= $true )
| ( ( ! [SY2600: $i] :
( ~ ( element @ SY2600 @ SV380 )
| ( in @ SY2600 @ SV380 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2004,plain,
! [SV381: $i] :
( ( ( empty @ SV381 )
= $true )
| ( ( ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV381 )
| ( element @ SY2601 @ SV381 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2005,plain,
! [SV382: $i] :
( ( ( ~ ( empty @ SV382 ) )
= $true )
| ( ( ! [SY2602: $i] :
( ~ ( element @ SY2602 @ SV382 )
| ( empty @ SY2602 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2006,plain,
! [SV383: $i] :
( ( ( ~ ( empty @ SV383 ) )
= $true )
| ( ( ! [SY2603: $i] :
( ~ ( empty @ SY2603 )
| ( element @ SY2603 @ SV383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2007,plain,
! [SV306: $i,SV328: $i] :
( ( ( ~ ( ( ( sK30_C @ SV328 @ SV306 )
!= SV306 )
| ~ ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) ) )
= $false )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2008,plain,
! [SV306: $i,SV328: $i] :
( ( ( ~ ( ( ( sK30_C @ SV328 @ SV306 )
= SV306 )
| ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) ) )
= $false )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2009,plain,
! [SV329: $i,SV307: $i] :
( ( ( ~ ! [SY2536: $i] :
( ( SY2536 != SV307 )
| ( in @ SY2536 @ SV329 ) )
| ~ ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV329 )
| ( SY2537 = SV307 ) ) )
= $false )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2010,plain,
! [SV308: $i,SV330: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV308 ) )
= $false )
| ( ( disjoint @ SV308 @ SV330 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1938]) ).
thf(2011,plain,
! [SV308: $i,SV330: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV330 ) )
= $false )
| ( ( disjoint @ SV308 @ SV330 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1938]) ).
thf(2012,plain,
! [SV331: $i,SV309: $i,SV384: $i] :
( ( ( ~ ( in @ SV384 @ SV309 ) )
= $true )
| ( ( ~ ( in @ SV384 @ SV331 ) )
= $true )
| ( ( ~ ( disjoint @ SV309 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2013,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( ! [SY2539: $i] :
( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SY2539 )
| ~ ( in @ SY2539 @ SV310 ) )
| ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) ) )
= $false )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1940]) ).
thf(2014,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) )
| ~ ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 ) )
| ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) ) )
= $false )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1940]) ).
thf(2015,plain,
! [SV333: $i,SV311: $i] :
( ( ( ~ ! [SY2540: $i] :
( ! [SY2515: $i] :
( ~ ( in @ SY2540 @ SY2515 )
| ~ ( in @ SY2515 @ SV311 ) )
| ( in @ SY2540 @ SV333 ) )
| ~ ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV333 )
| ~ ( ~ ( in @ SY2542 @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) @ SV311 ) ) ) )
= $false )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2016,plain,
! [SV294: $i,SV258: $i,SV400: $i] :
( ( ( ~ ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
| ~ ( ~ ( element @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) ) )
= $true )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2017,plain,
! [SV294: $i,SV258: $i,SV401: $i] :
( ( ( ~ ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
| ( SV401
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2620: $i] :
( ~ ( element @ SY2620 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2620 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SY2620 ) @ SV294 ) )
| ~ ! [SY2621: $i] :
( ~ ( element @ SY2621 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2621 ) @ SV294 )
| ( in @ SY2621 @ SV401 ) ) ) )
= $true )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2018,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) ) )
= $false )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(2019,plain,
! [SV335: $i,SV260: $i,SV363: $i] :
( ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false )
| ( ( ~ ( ~ ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV260 )
| ~ ( in @ SY2578 @ SV335 )
| ( in @ SY2578 @ SV363 ) )
| ~ ~ ( ~ ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) )
| ~ ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2020,plain,
! [SV261: $i,SV385: $i] :
( ( ( ~ ( ~ ( ! [SY2604: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SY2604 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ ( sK18_SY2050 @ SV385 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) ) ) )
= $true )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2021,plain,
! [SV261: $i,SV386: $i] :
( ( ( ( SV386
!= ( relation_dom @ SV261 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2605: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2605 @ SY2397 ) @ SV261 )
| ( in @ SY2605 @ SV386 ) )
| ~ ! [SY2607: $i] :
( ~ ( in @ SY2607 @ SV386 )
| ( in @ ( ordered_pair @ SY2607 @ ( sK16_D @ SY2607 @ SV386 @ SV261 ) ) @ SV261 ) ) ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2022,plain,
! [SV336: $i,SV364: $i,SV262: $i] :
( ( ( ~ ( in @ SV262 @ SV364 ) )
= $true )
| ( ( ~ ( in @ SV336 @ SV364 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV262 @ SV336 ) @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2023,plain,
! [SV402: $i,SV262: $i] :
( ( ! [SY2622: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SV402 ) @ SY2622 )
| ( in @ SV262 @ SY2622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2024,plain,
! [SV403: $i,SV262: $i] :
( ( ! [SY2623: $i] :
( ~ ( subset @ ( unordered_pair @ SV262 @ SV403 ) @ SY2623 )
| ( in @ SV403 @ SY2623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2025,plain,
! [SV312: $i,SV337: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ~ ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) ) )
= $false )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1952]) ).
thf(2026,plain,
! [SV312: $i,SV337: $i] :
( ( ( ~ ( ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) ) )
= $false )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1952]) ).
thf(2027,plain,
! [SV313: $i,SV338: $i] :
( ( ( ~ ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV338 )
| ( subset @ SY2549 @ SV313 ) )
| ~ ! [SY2550: $i] :
( ~ ( subset @ SY2550 @ SV313 )
| ( in @ SY2550 @ SV338 ) ) )
= $false )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2028,plain,
! [SV387: $i] :
( ( ( SV387 = empty_set )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SY2608 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SY2608 @ SV387 ) @ ( sK33_SY2057 @ SY2608 @ SV387 ) ) )
| ~ ( in @ ( sK32_C @ SY2608 @ SV387 ) @ SY2608 ) )
| ~ ( ! [SY2609: $i] :
( ~ ( in @ SY2609 @ SV387 )
| ( in @ ( sK32_C @ SY2608 @ SV387 ) @ SY2609 ) )
| ( in @ ( sK32_C @ SY2608 @ SV387 ) @ SY2608 ) ) )
| ( SY2608
= ( set_meet @ SV387 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2029,plain,
! [SV388: $i] :
( ( ( SV388 = empty_set )
= $true )
| ( ( ! [SY2610: $i] :
( ( SY2610
!= ( set_meet @ SV388 ) )
| ~ ( ~ ! [SY2611: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2611 @ SY2610 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SY2611 @ ( sK31_D @ SY2611 @ SY2610 @ SV388 ) ) )
| ( in @ SY2611 @ SY2610 ) )
| ~ ! [SY2612: $i] :
( ~ ( in @ SY2612 @ SY2610 )
| ! [SY2613: $i] :
( ~ ( in @ SY2613 @ SV388 )
| ( in @ SY2612 @ SY2613 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2030,plain,
! [SV389: $i] :
( ( ( ( SV389 != empty_set ) )
= $true )
| ( ( ! [SY2614: $i] :
( ( SY2614
!= ( set_meet @ SV389 ) )
| ( SY2614 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2031,plain,
! [SV390: $i] :
( ( ( ( SV390 != empty_set ) )
= $true )
| ( ( ! [SY2615: $i] :
( ( SY2615 != empty_set )
| ( SY2615
= ( set_meet @ SV390 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2032,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) ) )
| ~ ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV263 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV339 ) ) )
= $false )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2033,plain,
! [SV340: $i,SV263: $i,SV366: $i] :
( ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false )
| ( ( ~ ( ~ ! [SY2581: $i] :
( ~ ( in @ SY2581 @ SV366 )
| ( SY2581 = SV263 )
| ( SY2581 = SV340 ) )
| ~ ~ ( ~ ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) )
| ~ ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2034,plain,
! [SV343: $i,SV264: $i,SV367: $i] :
( ( ( relation @ SV367 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV264 @ SV343 ) @ SV367 )
| ( in @ SV264 @ ( relation_dom @ SV367 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2035,plain,
! [SV344: $i,SV264: $i,SV368: $i] :
( ( ( relation @ SV368 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV264 @ SV344 ) @ SV368 )
| ( in @ SV344 @ ( relation_rng @ SV368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2036,plain,
! [SV265: $i,SV391: $i] :
( ( ( ~ ( ~ ( ! [SY2616: $i] :
~ ( in @ ( ordered_pair @ SY2616 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV391 @ SV265 ) @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) ) ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2037,plain,
! [SV265: $i,SV392: $i] :
( ( ( ( SV392
!= ( relation_rng @ SV265 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2617: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2617 ) @ SV265 )
| ( in @ SY2617 @ SV392 ) )
| ~ ! [SY2619: $i] :
( ~ ( in @ SY2619 @ SV392 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2619 @ SV392 @ SV265 ) @ SY2619 ) @ SV265 ) ) ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(2038,plain,
! [SV266: $i,SV296: $i] :
( ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
= $false )
| ( ( ~ ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 ) )
= $true )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2039,plain,
! [SV267: $i,SV347: $i] :
( ( ( subset @ SV347 @ ( sK4_B @ SV267 ) )
= $false )
| ( ( are_equipotent @ SV347 @ ( sK4_B @ SV267 ) )
= $true )
| ( ( in @ SV347 @ ( sK4_B @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2040,plain,
! [SV267: $i,SV404: $i] :
( ( ~ ( ~ ! [SY2624: $i] :
( ~ ( subset @ SY2624 @ SV404 )
| ( in @ SY2624 @ ( sK5_SY2040 @ SV404 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SV404 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2041,plain,
! [SV267: $i] :
( ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) )
| ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2042,plain,
! [SV393: $i,SV297: $i,SV369: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV369 )
| ~ ( in @ SV297 @ SV393 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV369 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2043,plain,
! [SV297: $i,SV268: $i] :
( ( ! [SY2488: $i] :
( ! [SY2489: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2488 @ SY2489 ) )
| ( in @ SV268 @ SY2488 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2044,plain,
! [SV297: $i,SV268: $i] :
( ( ! [SY2490: $i,SY2491: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SY2490 @ SY2491 ) )
| ( in @ SV297 @ SY2491 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2045,plain,
! [SV318: $i] :
( ( ( ! [SY2525: $i,SY2526: $i] :
( ( sK36_B @ SV318 )
!= ( ordered_pair @ SY2525 @ SY2526 ) ) )
= $true )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1976]) ).
thf(2046,plain,
! [SV318: $i] :
( ( ( in @ ( sK36_B @ SV318 ) @ SV318 )
= $true )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2047,plain,
! [SV319: $i,SV394: $i] :
( ( ( SV394
= ( ordered_pair @ ( sK34_C @ SV394 @ SV319 ) @ ( sK35_SY2059 @ SV394 @ SV319 ) ) )
= $true )
| ( ( ~ ( in @ SV394 @ SV319 ) )
= $true )
| ( ( relation @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2048,plain,
! [SV320: $i,SV348: $i] :
( ( ( in @ SV348 @ SV320 )
= $false )
| ( ( ( set_difference @ SV320 @ ( singleton @ SV348 ) )
= SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2049,plain,
! [SV405: $i,SV370: $i,SV298: $i,SV269: $i] :
( ( ( ( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SV370 @ SV405 ) ) )
= $true )
| ( ( SV269 = SV370 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2050,plain,
! [SV395: $i,SV371: $i,SV298: $i,SV269: $i] :
( ( ( ( ( ordered_pair @ SV269 @ SV298 )
!= ( ordered_pair @ SV371 @ SV395 ) ) )
= $true )
| ( ( SV298 = SV395 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2051,plain,
! [SV372: $i,SV350: $i,SV270: $i] :
( ( ( ~ ( ! [SY2587: $i,SY2588: $i] :
( ~ ( in @ SY2587 @ SV270 )
| ~ ( in @ SY2588 @ SV350 )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SY2587 @ SY2588 ) ) )
| ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) ) )
= $false )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2052,plain,
! [SV351: $i,SV270: $i,SV373: $i] :
( ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false )
| ( ( ~ ( ~ ! [SY2589: $i] :
( ! [SY2563: $i,SY2564: $i] :
( ~ ( in @ SY2563 @ SV270 )
| ~ ( in @ SY2564 @ SV351 )
| ( SY2589
!= ( ordered_pair @ SY2563 @ SY2564 ) ) )
| ( in @ SY2589 @ SV373 ) )
| ~ ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV373 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SY2592
!= ( ordered_pair @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2053,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) )
| ~ ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) )
= $false )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2054,plain,
! [SV353: $i,SV271: $i,SV375: $i] :
( ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false )
| ( ( ~ ( ~ ! [SY2593: $i] :
( ~ ( in @ SY2593 @ SV375 )
| ( in @ SY2593 @ SV271 )
| ( in @ SY2593 @ SV353 ) )
| ~ ~ ( ~ ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) )
| ~ ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2055,plain,
! [SV272: $i,SV354: $i] :
( ( ( subset @ SV354 @ ( sK39_B @ SV272 ) )
= $false )
| ( ( are_equipotent @ SV354 @ ( sK39_B @ SV272 ) )
= $true )
| ( ( in @ SV354 @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2056,plain,
! [SV272: $i,SV406: $i] :
( ( ~ ( in @ SV406 @ ( sK39_B @ SV272 ) )
| ( in @ ( powerset @ SV406 ) @ ( sK39_B @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2057,plain,
! [SV272: $i] :
( ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) )
| ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2058,plain,
! [SV273: $i,SV396: $i] :
( ( ( ~ ( relation @ SV396 ) )
= $true )
| ( ( ~ ( subset @ SV273 @ SV396 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SV396 ) ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2059,plain,
! [SV273: $i,SV397: $i] :
( ( ( ~ ( relation @ SV397 ) )
= $true )
| ( ( ~ ( subset @ SV273 @ SV397 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SV397 ) ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2060,plain,
! [SV398: $i,SV299: $i,SV376: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV376 )
| ~ ( in @ SV299 @ SV398 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV376 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2061,plain,
! [SV299: $i,SV274: $i] :
( ( ! [SY2498: $i] :
( ! [SY2499: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2498 @ SY2499 ) )
| ( in @ SV274 @ SY2498 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2062,plain,
! [SV299: $i,SV274: $i] :
( ( ! [SY2500: $i,SY2501: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SY2500 @ SY2501 ) )
| ( in @ SV299 @ SY2501 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2063,plain,
! [SV356: $i,SV323: $i,SV399: $i] :
( ( ( in @ SV399 @ ( set_intersection2 @ SV323 @ SV356 ) )
= $false )
| ( ( ~ ( disjoint @ SV323 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2064,plain,
! [SV324: $i,SV357: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV324 ) )
= $false )
| ( ( subset @ SV324 @ SV357 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2065,plain,
! [SV324: $i,SV357: $i] :
( ( ( ~ ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV357 ) )
= $false )
| ( ( subset @ SV324 @ SV357 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2066,plain,
! [SV358: $i,SV325: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ SV325 )
| ( in @ SV407 @ SV358 ) )
= $true )
| ( ( subset @ SV325 @ SV358 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2067,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) ) )
= $false )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2068,plain,
! [SV360: $i,SV275: $i,SV378: $i] :
( ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false )
| ( ( ~ ( ~ ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV275 )
| ( in @ SY2597 @ SV360 )
| ( in @ SY2597 @ SV378 ) )
| ~ ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) )
| ~ ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2069,plain,
! [SV245: $i,SV300: $i,SV361: $i] :
( ( ( in @ SV361 @ SV300 )
= $true )
| ( ( in @ SV361 @ ( subset_complement @ SV245 @ SV300 ) )
= $true )
| ( ( element @ SV361 @ SV245 )
= $false )
| ( ( element @ SV300 @ ( powerset @ SV245 ) )
= $false )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1999]) ).
thf(2070,plain,
! [SV380: $i,SV408: $i] :
( ( ( ~ ( element @ SV408 @ SV380 )
| ( in @ SV408 @ SV380 ) )
= $true )
| ( ( empty @ SV380 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2071,plain,
! [SV381: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ SV381 )
| ( element @ SV409 @ SV381 ) )
= $true )
| ( ( empty @ SV381 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2072,plain,
! [SV382: $i] :
( ( ( empty @ SV382 )
= $false )
| ( ( ! [SY2602: $i] :
( ~ ( element @ SY2602 @ SV382 )
| ( empty @ SY2602 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2073,plain,
! [SV383: $i] :
( ( ( empty @ SV383 )
= $false )
| ( ( ! [SY2603: $i] :
( ~ ( empty @ SY2603 )
| ( element @ SY2603 @ SV383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2074,plain,
! [SV306: $i,SV328: $i] :
( ( ( ( ( sK30_C @ SV328 @ SV306 )
!= SV306 )
| ~ ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2007]) ).
thf(2075,plain,
! [SV306: $i,SV328: $i] :
( ( ( ( ( sK30_C @ SV328 @ SV306 )
= SV306 )
| ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2076,plain,
! [SV329: $i,SV307: $i] :
( ( ( ~ ! [SY2536: $i] :
( ( SY2536 != SV307 )
| ( in @ SY2536 @ SV329 ) ) )
= $false )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2077,plain,
! [SV307: $i,SV329: $i] :
( ( ( ~ ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV329 )
| ( SY2537 = SV307 ) ) )
= $false )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2078,plain,
! [SV308: $i,SV330: $i] :
( ( ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV308 )
= $true )
| ( ( disjoint @ SV308 @ SV330 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2079,plain,
! [SV308: $i,SV330: $i] :
( ( ( in @ ( sK38_C @ SV330 @ SV308 ) @ SV330 )
= $true )
| ( ( disjoint @ SV308 @ SV330 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2080,plain,
! [SV331: $i,SV309: $i,SV384: $i] :
( ( ( in @ SV384 @ SV309 )
= $false )
| ( ( ~ ( in @ SV384 @ SV331 ) )
= $true )
| ( ( ~ ( disjoint @ SV309 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2081,plain,
! [SV310: $i,SV332: $i] :
( ( ( ! [SY2539: $i] :
( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SY2539 )
| ~ ( in @ SY2539 @ SV310 ) )
| ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2013]) ).
thf(2082,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) )
| ~ ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 ) )
| ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2083,plain,
! [SV333: $i,SV311: $i] :
( ( ( ~ ! [SY2540: $i] :
( ! [SY2515: $i] :
( ~ ( in @ SY2540 @ SY2515 )
| ~ ( in @ SY2515 @ SV311 ) )
| ( in @ SY2540 @ SV333 ) ) )
= $false )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2015]) ).
thf(2084,plain,
! [SV311: $i,SV333: $i] :
( ( ( ~ ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV333 )
| ~ ( ~ ( in @ SY2542 @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) @ SV311 ) ) ) )
= $false )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2015]) ).
thf(2085,plain,
! [SV294: $i,SV258: $i,SV400: $i] :
( ( ( ~ ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) ) )
= $true )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2086,plain,
! [SV294: $i,SV258: $i,SV401: $i] :
( ( ( ~ ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) ) )
= $true )
| ( ( ( SV401
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2620: $i] :
( ~ ( element @ SY2620 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2620 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SY2620 ) @ SV294 ) )
| ~ ! [SY2621: $i] :
( ~ ( element @ SY2621 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2621 ) @ SV294 )
| ( in @ SY2621 @ SV401 ) ) ) )
= $true )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2087,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) )
= $false )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2088,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) ) )
= $false )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2089,plain,
! [SV363: $i,SV335: $i,SV260: $i] :
( ( ( ~ ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV260 )
| ~ ( in @ SY2578 @ SV335 )
| ( in @ SY2578 @ SV363 ) )
| ~ ~ ( ~ ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) )
| ~ ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) ) )
= $false )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2090,plain,
! [SV261: $i,SV385: $i] :
( ( ( ~ ( ! [SY2604: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SY2604 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ ( sK18_SY2050 @ SV385 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) ) )
= $false )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2091,plain,
! [SV261: $i,SV386: $i] :
( ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( ~ ( ~ ! [SY2605: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2605 @ SY2397 ) @ SV261 )
| ( in @ SY2605 @ SV386 ) )
| ~ ! [SY2607: $i] :
( ~ ( in @ SY2607 @ SV386 )
| ( in @ ( ordered_pair @ SY2607 @ ( sK16_D @ SY2607 @ SV386 @ SV261 ) ) @ SV261 ) ) ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2092,plain,
! [SV336: $i,SV364: $i,SV262: $i] :
( ( ( in @ SV262 @ SV364 )
= $false )
| ( ( ~ ( in @ SV336 @ SV364 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV262 @ SV336 ) @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2093,plain,
! [SV410: $i,SV402: $i,SV262: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV262 @ SV402 ) @ SV410 )
| ( in @ SV262 @ SV410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2094,plain,
! [SV411: $i,SV403: $i,SV262: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV262 @ SV403 ) @ SV411 )
| ( in @ SV403 @ SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2095,plain,
! [SV312: $i,SV337: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ~ ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) )
= $true )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2025]) ).
thf(2096,plain,
! [SV312: $i,SV337: $i] :
( ( ( ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
| ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) )
= $true )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2097,plain,
! [SV313: $i,SV338: $i] :
( ( ( ~ ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV338 )
| ( subset @ SY2549 @ SV313 ) ) )
= $false )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2027]) ).
thf(2098,plain,
! [SV338: $i,SV313: $i] :
( ( ( ~ ! [SY2550: $i] :
( ~ ( subset @ SY2550 @ SV313 )
| ( in @ SY2550 @ SV338 ) ) )
= $false )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2027]) ).
thf(2099,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) )
| ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
| ~ ( ! [SY2625: $i] :
( ~ ( in @ SY2625 @ SV387 )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SY2625 ) )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) ) )
| ( SV412
= ( set_meet @ SV387 ) ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2100,plain,
! [SV388: $i,SV413: $i] :
( ( ( ( SV413
!= ( set_meet @ SV388 ) )
| ~ ( ~ ! [SY2626: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SY2626 @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) ) )
| ( in @ SY2626 @ SV413 ) )
| ~ ! [SY2627: $i] :
( ~ ( in @ SY2627 @ SV413 )
| ! [SY2613: $i] :
( ~ ( in @ SY2613 @ SV388 )
| ( in @ SY2627 @ SY2613 ) ) ) ) )
= $true )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2101,plain,
! [SV389: $i] :
( ( ( SV389 = empty_set )
= $false )
| ( ( ! [SY2614: $i] :
( ( SY2614
!= ( set_meet @ SV389 ) )
| ( SY2614 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2102,plain,
! [SV390: $i] :
( ( ( SV390 = empty_set )
= $false )
| ( ( ! [SY2615: $i] :
( ( SY2615 != empty_set )
| ( SY2615
= ( set_meet @ SV390 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2103,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) ) ) )
= $false )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2032]) ).
thf(2104,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV263 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV339 ) ) )
= $false )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2032]) ).
thf(2105,plain,
! [SV340: $i,SV263: $i,SV366: $i] :
( ( ( ~ ! [SY2581: $i] :
( ~ ( in @ SY2581 @ SV366 )
| ( SY2581 = SV263 )
| ( SY2581 = SV340 ) )
| ~ ~ ( ~ ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) )
| ~ ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) ) )
= $false )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2106,plain,
! [SV367: $i,SV343: $i,SV264: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV264 @ SV343 ) @ SV367 ) )
= $true )
| ( ( in @ SV264 @ ( relation_dom @ SV367 ) )
= $true )
| ( ( relation @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2107,plain,
! [SV368: $i,SV344: $i,SV264: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV264 @ SV344 ) @ SV368 ) )
= $true )
| ( ( in @ SV344 @ ( relation_rng @ SV368 ) )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2108,plain,
! [SV265: $i,SV391: $i] :
( ( ( ~ ( ! [SY2616: $i] :
~ ( in @ ( ordered_pair @ SY2616 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV391 @ SV265 ) @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) ) )
= $false )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2109,plain,
! [SV265: $i,SV392: $i] :
( ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( ~ ( ~ ! [SY2617: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2617 ) @ SV265 )
| ( in @ SY2617 @ SV392 ) )
| ~ ! [SY2619: $i] :
( ~ ( in @ SY2619 @ SV392 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2619 @ SV392 @ SV265 ) @ SY2619 ) @ SV265 ) ) ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2110,plain,
! [SV266: $i,SV296: $i] :
( ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV296 )
= $false )
| ( ( in @ ( sK6_C @ SV296 @ SV266 ) @ SV266 )
= $false )
| ( ( SV266 = SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2111,plain,
! [SV267: $i,SV404: $i] :
( ( ( ~ ( ~ ! [SY2624: $i] :
( ~ ( subset @ SY2624 @ SV404 )
| ( in @ SY2624 @ ( sK5_SY2040 @ SV404 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SV404 @ SV267 ) @ ( sK4_B @ SV267 ) ) ) )
= $true )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2112,plain,
! [SV267: $i] :
( ( ~ ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2041]) ).
thf(2113,plain,
! [SV267: $i] :
( ( ~ ( in @ SV267 @ ( sK4_B @ SV267 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2041]) ).
thf(2114,plain,
! [SV393: $i,SV297: $i,SV369: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV369 ) )
= $true )
| ( ( ~ ( in @ SV297 @ SV393 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV369 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2115,plain,
! [SV414: $i,SV297: $i,SV268: $i] :
( ( ! [SY2629: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV414 @ SY2629 ) )
| ( in @ SV268 @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2116,plain,
! [SV415: $i,SV297: $i,SV268: $i] :
( ( ! [SY2630: $i] :
( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV415 @ SY2630 ) )
| ( in @ SV297 @ SY2630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2117,plain,
! [SV416: $i,SV318: $i] :
( ( ( ! [SY2631: $i] :
( ( sK36_B @ SV318 )
!= ( ordered_pair @ SV416 @ SY2631 ) ) )
= $true )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2118,plain,
! [SV319: $i,SV394: $i] :
( ( ( in @ SV394 @ SV319 )
= $false )
| ( ( SV394
= ( ordered_pair @ ( sK34_C @ SV394 @ SV319 ) @ ( sK35_SY2059 @ SV394 @ SV319 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2119,plain,
! [SV405: $i,SV370: $i,SV298: $i,SV269: $i] :
( ( ( ( ordered_pair @ SV269 @ SV298 )
= ( ordered_pair @ SV370 @ SV405 ) )
= $false )
| ( ( SV269 = SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2120,plain,
! [SV395: $i,SV371: $i,SV298: $i,SV269: $i] :
( ( ( ( ordered_pair @ SV269 @ SV298 )
= ( ordered_pair @ SV371 @ SV395 ) )
= $false )
| ( ( SV298 = SV395 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2121,plain,
! [SV372: $i,SV350: $i,SV270: $i] :
( ( ( ~ ( ! [SY2587: $i,SY2588: $i] :
( ~ ( in @ SY2587 @ SV270 )
| ~ ( in @ SY2588 @ SV350 )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SY2587 @ SY2588 ) ) )
| ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) ) )
= $false )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2051]) ).
thf(2122,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) ) )
= $false )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2051]) ).
thf(2123,plain,
! [SV373: $i,SV351: $i,SV270: $i] :
( ( ( ~ ! [SY2589: $i] :
( ! [SY2563: $i,SY2564: $i] :
( ~ ( in @ SY2563 @ SV270 )
| ~ ( in @ SY2564 @ SV351 )
| ( SY2589
!= ( ordered_pair @ SY2563 @ SY2564 ) ) )
| ( in @ SY2589 @ SV373 ) )
| ~ ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV373 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SY2592
!= ( ordered_pair @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) ) ) ) ) )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2124,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) ) )
= $false )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2125,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) )
= $false )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2126,plain,
! [SV353: $i,SV271: $i,SV375: $i] :
( ( ( ~ ! [SY2593: $i] :
( ~ ( in @ SY2593 @ SV375 )
| ( in @ SY2593 @ SV271 )
| ( in @ SY2593 @ SV353 ) )
| ~ ~ ( ~ ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) )
| ~ ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) ) )
= $false )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2127,plain,
! [SV272: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ ( sK39_B @ SV272 ) ) )
= $true )
| ( ( in @ ( powerset @ SV406 ) @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2128,plain,
! [SV272: $i] :
( ( ~ ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2129,plain,
! [SV272: $i] :
( ( ~ ( in @ SV272 @ ( sK39_B @ SV272 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2130,plain,
! [SV273: $i,SV396: $i] :
( ( ( relation @ SV396 )
= $false )
| ( ( ~ ( subset @ SV273 @ SV396 )
| ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SV396 ) ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2131,plain,
! [SV273: $i,SV397: $i] :
( ( ( relation @ SV397 )
= $false )
| ( ( ~ ( subset @ SV273 @ SV397 )
| ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SV397 ) ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2132,plain,
! [SV398: $i,SV299: $i,SV376: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV376 ) )
= $true )
| ( ( ~ ( in @ SV299 @ SV398 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV376 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2060]) ).
thf(2133,plain,
! [SV417: $i,SV299: $i,SV274: $i] :
( ( ! [SY2632: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV417 @ SY2632 ) )
| ( in @ SV274 @ SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2134,plain,
! [SV418: $i,SV299: $i,SV274: $i] :
( ( ! [SY2633: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV418 @ SY2633 ) )
| ( in @ SV299 @ SY2633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2135,plain,
! [SV399: $i,SV356: $i,SV323: $i] :
( ( ( disjoint @ SV323 @ SV356 )
= $false )
| ( ( in @ SV399 @ ( set_intersection2 @ SV323 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2136,plain,
! [SV324: $i,SV357: $i] :
( ( ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV324 )
= $true )
| ( ( subset @ SV324 @ SV357 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2137,plain,
! [SV324: $i,SV357: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV357 ) )
= $true )
| ( ( subset @ SV324 @ SV357 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2138,plain,
! [SV358: $i,SV325: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ SV325 ) )
= $true )
| ( ( in @ SV407 @ SV358 )
= $true )
| ( ( subset @ SV325 @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2139,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) )
= $false )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2067]) ).
thf(2140,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) ) )
= $false )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2067]) ).
thf(2141,plain,
! [SV378: $i,SV360: $i,SV275: $i] :
( ( ( ~ ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV275 )
| ( in @ SY2597 @ SV360 )
| ( in @ SY2597 @ SV378 ) )
| ~ ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) )
| ~ ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) ) )
= $false )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2142,plain,
! [SV380: $i,SV408: $i] :
( ( ( ~ ( element @ SV408 @ SV380 ) )
= $true )
| ( ( in @ SV408 @ SV380 )
= $true )
| ( ( empty @ SV380 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2143,plain,
! [SV381: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ SV381 ) )
= $true )
| ( ( element @ SV409 @ SV381 )
= $true )
| ( ( empty @ SV381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2144,plain,
! [SV382: $i,SV419: $i] :
( ( ( ~ ( element @ SV419 @ SV382 )
| ( empty @ SV419 ) )
= $true )
| ( ( empty @ SV382 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2145,plain,
! [SV383: $i,SV420: $i] :
( ( ( ~ ( empty @ SV420 )
| ( element @ SV420 @ SV383 ) )
= $true )
| ( ( empty @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2146,plain,
! [SV306: $i,SV328: $i] :
( ( ( ( ( sK30_C @ SV328 @ SV306 )
!= SV306 ) )
= $true )
| ( ( ~ ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2074]) ).
thf(2147,plain,
! [SV306: $i,SV328: $i] :
( ( ( ( sK30_C @ SV328 @ SV306 )
= SV306 )
= $true )
| ( ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 )
= $true )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2148,plain,
! [SV329: $i,SV307: $i] :
( ( ( ! [SY2536: $i] :
( ( SY2536 != SV307 )
| ( in @ SY2536 @ SV329 ) ) )
= $true )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2149,plain,
! [SV307: $i,SV329: $i] :
( ( ( ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV329 )
| ( SY2537 = SV307 ) ) )
= $true )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2150,plain,
! [SV309: $i,SV331: $i,SV384: $i] :
( ( ( in @ SV384 @ SV331 )
= $false )
| ( ( in @ SV384 @ SV309 )
= $false )
| ( ( ~ ( disjoint @ SV309 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2151,plain,
! [SV310: $i,SV332: $i] :
( ( ( ! [SY2539: $i] :
( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SY2539 )
| ~ ( in @ SY2539 @ SV310 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2152,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) )
| ~ ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 ) ) )
= $true )
| ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2153,plain,
! [SV333: $i,SV311: $i] :
( ( ( ! [SY2540: $i] :
( ! [SY2515: $i] :
( ~ ( in @ SY2540 @ SY2515 )
| ~ ( in @ SY2515 @ SV311 ) )
| ( in @ SY2540 @ SV333 ) ) )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2154,plain,
! [SV311: $i,SV333: $i] :
( ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV333 )
| ~ ( ~ ( in @ SY2542 @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SY2542 @ SV333 @ SV311 ) @ SV311 ) ) ) )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2155,plain,
! [SV294: $i,SV258: $i,SV400: $i] :
( ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
| ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) ) )
= $true )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2156,plain,
! [SV294: $i,SV258: $i,SV401: $i] :
( ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( ( SV401
!= ( complements_of_subsets @ SV258 @ SV294 ) )
| ~ ( ~ ! [SY2620: $i] :
( ~ ( element @ SY2620 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2620 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SY2620 ) @ SV294 ) )
| ~ ! [SY2621: $i] :
( ~ ( element @ SY2621 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2621 ) @ SV294 )
| ( in @ SY2621 @ SV401 ) ) ) )
= $true )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2157,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2087]) ).
thf(2158,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2159,plain,
! [SV363: $i,SV335: $i,SV260: $i] :
( ( ( ~ ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV260 )
| ~ ( in @ SY2578 @ SV335 )
| ( in @ SY2578 @ SV363 ) ) )
= $false )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2089]) ).
thf(2160,plain,
! [SV335: $i,SV260: $i,SV363: $i] :
( ( ( ~ ~ ( ~ ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) )
| ~ ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) ) )
= $false )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2089]) ).
thf(2161,plain,
! [SV261: $i,SV385: $i] :
( ( ( ~ ( ! [SY2604: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SY2604 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) ) )
= $false )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2162,plain,
! [SV261: $i,SV385: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ ( sK18_SY2050 @ SV385 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) ) )
= $false )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2163,plain,
! [SV386: $i,SV261: $i] :
( ( ( ~ ! [SY2605: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2605 @ SY2397 ) @ SV261 )
| ( in @ SY2605 @ SV386 ) )
| ~ ! [SY2607: $i] :
( ~ ( in @ SY2607 @ SV386 )
| ( in @ ( ordered_pair @ SY2607 @ ( sK16_D @ SY2607 @ SV386 @ SV261 ) ) @ SV261 ) ) )
= $false )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2164,plain,
! [SV262: $i,SV364: $i,SV336: $i] :
( ( ( in @ SV336 @ SV364 )
= $false )
| ( ( in @ SV262 @ SV364 )
= $false )
| ( ( subset @ ( unordered_pair @ SV262 @ SV336 ) @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2165,plain,
! [SV410: $i,SV402: $i,SV262: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV262 @ SV402 ) @ SV410 ) )
= $true )
| ( ( in @ SV262 @ SV410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2166,plain,
! [SV411: $i,SV403: $i,SV262: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV262 @ SV403 ) @ SV411 ) )
= $true )
| ( ( in @ SV403 @ SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2167,plain,
! [SV312: $i,SV337: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 ) )
= $true )
| ( ( ~ ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) )
= $true )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2168,plain,
! [SV312: $i,SV337: $i] :
( ( ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
= $true )
| ( ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 )
= $true )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2169,plain,
! [SV313: $i,SV338: $i] :
( ( ( ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV338 )
| ( subset @ SY2549 @ SV313 ) ) )
= $true )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2170,plain,
! [SV338: $i,SV313: $i] :
( ( ( ! [SY2550: $i] :
( ~ ( subset @ SY2550 @ SV313 )
| ( in @ SY2550 @ SV338 ) ) )
= $true )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2171,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) )
| ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
| ~ ( ! [SY2625: $i] :
( ~ ( in @ SY2625 @ SV387 )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SY2625 ) )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) ) ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2172,plain,
! [SV388: $i,SV413: $i] :
( ( ( ( SV413
!= ( set_meet @ SV388 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2626: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SY2626 @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) ) )
| ( in @ SY2626 @ SV413 ) )
| ~ ! [SY2627: $i] :
( ~ ( in @ SY2627 @ SV413 )
| ! [SY2613: $i] :
( ~ ( in @ SY2613 @ SV388 )
| ( in @ SY2627 @ SY2613 ) ) ) ) )
= $true )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2173,plain,
! [SV389: $i,SV421: $i] :
( ( ( ( SV421
!= ( set_meet @ SV389 ) )
| ( SV421 = empty_set ) )
= $true )
| ( ( SV389 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2174,plain,
! [SV390: $i,SV422: $i] :
( ( ( ( SV422 != empty_set )
| ( SV422
= ( set_meet @ SV390 ) ) )
= $true )
| ( ( SV390 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2175,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) ) ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2103]) ).
thf(2176,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV263 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV339 ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2104]) ).
thf(2177,plain,
! [SV340: $i,SV263: $i,SV366: $i] :
( ( ( ~ ! [SY2581: $i] :
( ~ ( in @ SY2581 @ SV366 )
| ( SY2581 = SV263 )
| ( SY2581 = SV340 ) ) )
= $false )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2105]) ).
thf(2178,plain,
! [SV340: $i,SV366: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) )
| ~ ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) ) )
= $false )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2105]) ).
thf(2179,plain,
! [SV367: $i,SV343: $i,SV264: $i] :
( ( ( in @ ( ordered_pair @ SV264 @ SV343 ) @ SV367 )
= $false )
| ( ( in @ SV264 @ ( relation_dom @ SV367 ) )
= $true )
| ( ( relation @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2180,plain,
! [SV368: $i,SV344: $i,SV264: $i] :
( ( ( in @ ( ordered_pair @ SV264 @ SV344 ) @ SV368 )
= $false )
| ( ( in @ SV344 @ ( relation_rng @ SV368 ) )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2181,plain,
! [SV265: $i,SV391: $i] :
( ( ( ~ ( ! [SY2616: $i] :
~ ( in @ ( ordered_pair @ SY2616 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) ) )
= $false )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2108]) ).
thf(2182,plain,
! [SV265: $i,SV391: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV391 @ SV265 ) @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) ) )
= $false )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2108]) ).
thf(2183,plain,
! [SV392: $i,SV265: $i] :
( ( ( ~ ! [SY2617: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2617 ) @ SV265 )
| ( in @ SY2617 @ SV392 ) )
| ~ ! [SY2619: $i] :
( ~ ( in @ SY2619 @ SV392 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2619 @ SV392 @ SV265 ) @ SY2619 ) @ SV265 ) ) )
= $false )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2184,plain,
! [SV267: $i,SV404: $i] :
( ( ( ~ ! [SY2624: $i] :
( ~ ( subset @ SY2624 @ SV404 )
| ( in @ SY2624 @ ( sK5_SY2040 @ SV404 @ SV267 ) ) )
| ~ ( in @ ( sK5_SY2040 @ SV404 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
= $false )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2185,plain,
! [SV267: $i] :
( ( ! [SY2426: $i,SY2427: $i] :
( ~ ( in @ SY2426 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2427 @ SY2426 )
| ( in @ SY2427 @ ( sK4_B @ SV267 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2186,plain,
! [SV267: $i] :
( ( in @ SV267 @ ( sK4_B @ SV267 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2187,plain,
! [SV393: $i,SV297: $i,SV369: $i,SV268: $i] :
( ( ( in @ SV268 @ SV369 )
= $false )
| ( ( ~ ( in @ SV297 @ SV393 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV369 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2188,plain,
! [SV414: $i,SV297: $i,SV268: $i] :
( ( ( ! [SY2629: $i] :
~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV414 @ SY2629 ) ) )
= $true )
| ( ( in @ SV268 @ SV414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2189,plain,
! [SV423: $i,SV415: $i,SV297: $i,SV268: $i] :
( ( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV415 @ SV423 ) )
| ( in @ SV297 @ SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2190,plain,
! [SV424: $i,SV416: $i,SV318: $i] :
( ( ( ( ( sK36_B @ SV318 )
!= ( ordered_pair @ SV416 @ SV424 ) ) )
= $true )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2191,plain,
! [SV372: $i,SV350: $i,SV270: $i] :
( ( ( ! [SY2587: $i,SY2588: $i] :
( ~ ( in @ SY2587 @ SV270 )
| ~ ( in @ SY2588 @ SV350 )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SY2587 @ SY2588 ) ) )
| ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2192,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) ) )
| ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2193,plain,
! [SV373: $i,SV351: $i,SV270: $i] :
( ( ( ~ ! [SY2589: $i] :
( ! [SY2563: $i,SY2564: $i] :
( ~ ( in @ SY2563 @ SV270 )
| ~ ( in @ SY2564 @ SV351 )
| ( SY2589
!= ( ordered_pair @ SY2563 @ SY2564 ) ) )
| ( in @ SY2589 @ SV373 ) ) )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2194,plain,
! [SV270: $i,SV351: $i,SV373: $i] :
( ( ( ~ ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV373 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SY2592
!= ( ordered_pair @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) ) ) ) ) )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2195,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2196,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2125]) ).
thf(2197,plain,
! [SV353: $i,SV271: $i,SV375: $i] :
( ( ( ~ ! [SY2593: $i] :
( ~ ( in @ SY2593 @ SV375 )
| ( in @ SY2593 @ SV271 )
| ( in @ SY2593 @ SV353 ) ) )
= $false )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2198,plain,
! [SV353: $i,SV375: $i,SV271: $i] :
( ( ( ~ ~ ( ~ ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) )
| ~ ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) ) )
= $false )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2199,plain,
! [SV272: $i,SV406: $i] :
( ( ( in @ SV406 @ ( sK39_B @ SV272 ) )
= $false )
| ( ( in @ ( powerset @ SV406 ) @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2200,plain,
! [SV272: $i] :
( ( ! [SY2459: $i,SY2460: $i] :
( ~ ( in @ SY2459 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2460 @ SY2459 )
| ( in @ SY2460 @ ( sK39_B @ SV272 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2128]) ).
thf(2201,plain,
! [SV272: $i] :
( ( in @ SV272 @ ( sK39_B @ SV272 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2129]) ).
thf(2202,plain,
! [SV396: $i,SV273: $i] :
( ( ( ~ ( subset @ SV273 @ SV396 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SV396 ) )
= $true )
| ( ( relation @ SV396 )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2203,plain,
! [SV397: $i,SV273: $i] :
( ( ( ~ ( subset @ SV273 @ SV397 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SV397 ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2204,plain,
! [SV398: $i,SV299: $i,SV376: $i,SV274: $i] :
( ( ( in @ SV274 @ SV376 )
= $false )
| ( ( ~ ( in @ SV299 @ SV398 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV376 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2205,plain,
! [SV417: $i,SV299: $i,SV274: $i] :
( ( ( ! [SY2632: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV417 @ SY2632 ) ) )
= $true )
| ( ( in @ SV274 @ SV417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2206,plain,
! [SV425: $i,SV418: $i,SV299: $i,SV274: $i] :
( ( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV418 @ SV425 ) )
| ( in @ SV299 @ SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2207,plain,
! [SV324: $i,SV357: $i] :
( ( ( in @ ( sK20_C @ SV357 @ SV324 ) @ SV357 )
= $false )
| ( ( subset @ SV324 @ SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2208,plain,
! [SV358: $i,SV325: $i,SV407: $i] :
( ( ( in @ SV407 @ SV325 )
= $false )
| ( ( in @ SV407 @ SV358 )
= $true )
| ( ( subset @ SV325 @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2209,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2210,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) ) )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2211,plain,
! [SV378: $i,SV360: $i,SV275: $i] :
( ( ( ~ ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV275 )
| ( in @ SY2597 @ SV360 )
| ( in @ SY2597 @ SV378 ) ) )
= $false )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2141]) ).
thf(2212,plain,
! [SV360: $i,SV275: $i,SV378: $i] :
( ( ( ~ ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) )
| ~ ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) ) )
= $false )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2141]) ).
thf(2213,plain,
! [SV380: $i,SV408: $i] :
( ( ( element @ SV408 @ SV380 )
= $false )
| ( ( in @ SV408 @ SV380 )
= $true )
| ( ( empty @ SV380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2214,plain,
! [SV381: $i,SV409: $i] :
( ( ( in @ SV409 @ SV381 )
= $false )
| ( ( element @ SV409 @ SV381 )
= $true )
| ( ( empty @ SV381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2215,plain,
! [SV382: $i,SV419: $i] :
( ( ( ~ ( element @ SV419 @ SV382 ) )
= $true )
| ( ( empty @ SV419 )
= $true )
| ( ( empty @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2216,plain,
! [SV383: $i,SV420: $i] :
( ( ( ~ ( empty @ SV420 ) )
= $true )
| ( ( element @ SV420 @ SV383 )
= $true )
| ( ( empty @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2217,plain,
! [SV306: $i,SV328: $i] :
( ( ( ( sK30_C @ SV328 @ SV306 )
= SV306 )
= $false )
| ( ( ~ ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2218,plain,
! [SV329: $i,SV307: $i,SV426: $i] :
( ( ( ( SV426 != SV307 )
| ( in @ SV426 @ SV329 ) )
= $true )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2219,plain,
! [SV307: $i,SV329: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV329 )
| ( SV427 = SV307 ) )
= $true )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2220,plain,
! [SV384: $i,SV331: $i,SV309: $i] :
( ( ( disjoint @ SV309 @ SV331 )
= $false )
| ( ( in @ SV384 @ SV309 )
= $false )
| ( ( in @ SV384 @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2221,plain,
! [SV428: $i,SV310: $i,SV332: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV428 )
| ~ ( in @ SV428 @ SV310 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2222,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) )
| ~ ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 ) )
= $false )
| ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2223,plain,
! [SV333: $i,SV311: $i,SV429: $i] :
( ( ( ! [SY2634: $i] :
( ~ ( in @ SV429 @ SY2634 )
| ~ ( in @ SY2634 @ SV311 ) )
| ( in @ SV429 @ SV333 ) )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2224,plain,
! [SV311: $i,SV333: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV333 )
| ~ ( ~ ( in @ SV430 @ ( sK13_D @ SV430 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SV430 @ SV333 @ SV311 ) @ SV311 ) ) )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2225,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( ~ ( element @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) ) ) )
= $true )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2226,plain,
! [SV294: $i,SV258: $i,SV401: $i] :
( ( ( ( SV401
!= ( complements_of_subsets @ SV258 @ SV294 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2620: $i] :
( ~ ( element @ SY2620 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2620 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SY2620 ) @ SV294 ) )
| ~ ! [SY2621: $i] :
( ~ ( element @ SY2621 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2621 ) @ SV294 )
| ( in @ SY2621 @ SV401 ) ) ) )
= $true )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2227,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2228,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
| ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) )
= $false )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2229,plain,
! [SV363: $i,SV335: $i,SV260: $i] :
( ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV260 )
| ~ ( in @ SY2578 @ SV335 )
| ( in @ SY2578 @ SV363 ) ) )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2230,plain,
! [SV335: $i,SV260: $i,SV363: $i] :
( ( ( ~ ( ~ ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) )
| ~ ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) ) )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2231,plain,
! [SV261: $i,SV385: $i] :
( ( ( ! [SY2604: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SY2604 ) @ SV261 )
| ~ ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) )
= $true )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2232,plain,
! [SV261: $i,SV385: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ ( sK18_SY2050 @ SV385 @ SV261 ) ) @ SV261 )
| ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) )
= $true )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2162]) ).
thf(2233,plain,
! [SV386: $i,SV261: $i] :
( ( ( ~ ! [SY2605: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2605 @ SY2397 ) @ SV261 )
| ( in @ SY2605 @ SV386 ) ) )
= $false )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2163]) ).
thf(2234,plain,
! [SV261: $i,SV386: $i] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( in @ SY2607 @ SV386 )
| ( in @ ( ordered_pair @ SY2607 @ ( sK16_D @ SY2607 @ SV386 @ SV261 ) ) @ SV261 ) ) )
= $false )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2163]) ).
thf(2235,plain,
! [SV410: $i,SV402: $i,SV262: $i] :
( ( ( subset @ ( unordered_pair @ SV262 @ SV402 ) @ SV410 )
= $false )
| ( ( in @ SV262 @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2236,plain,
! [SV411: $i,SV403: $i,SV262: $i] :
( ( ( subset @ ( unordered_pair @ SV262 @ SV403 ) @ SV411 )
= $false )
| ( ( in @ SV403 @ SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2237,plain,
! [SV312: $i,SV337: $i] :
( ( ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
= $false )
| ( ( ~ ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 ) )
= $true )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2238,plain,
! [SV313: $i,SV338: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV338 )
| ( subset @ SV431 @ SV313 ) )
= $true )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2239,plain,
! [SV338: $i,SV313: $i,SV432: $i] :
( ( ( ~ ( subset @ SV432 @ SV313 )
| ( in @ SV432 @ SV338 ) )
= $true )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2240,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) )
| ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
| ~ ( ! [SY2625: $i] :
( ~ ( in @ SY2625 @ SV387 )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SY2625 ) )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) ) )
= $false )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2241,plain,
! [SV388: $i,SV413: $i] :
( ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( ~ ( ~ ! [SY2626: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SY2626 @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) ) )
| ( in @ SY2626 @ SV413 ) )
| ~ ! [SY2627: $i] :
( ~ ( in @ SY2627 @ SV413 )
| ! [SY2613: $i] :
( ~ ( in @ SY2613 @ SV388 )
| ( in @ SY2627 @ SY2613 ) ) ) ) )
= $true )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2242,plain,
! [SV389: $i,SV421: $i] :
( ( ( ( SV421
!= ( set_meet @ SV389 ) ) )
= $true )
| ( ( SV421 = empty_set )
= $true )
| ( ( SV389 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2243,plain,
! [SV390: $i,SV422: $i] :
( ( ( ( SV422 != empty_set ) )
= $true )
| ( ( SV422
= ( set_meet @ SV390 ) )
= $true )
| ( ( SV390 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2244,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) ) )
= $false )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2245,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
= $true )
| ( ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV263 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV339 ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2246,plain,
! [SV340: $i,SV263: $i,SV366: $i] :
( ( ( ! [SY2581: $i] :
( ~ ( in @ SY2581 @ SV366 )
| ( SY2581 = SV263 )
| ( SY2581 = SV340 ) ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2177]) ).
thf(2247,plain,
! [SV340: $i,SV366: $i,SV263: $i] :
( ( ( ~ ( ~ ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) )
| ~ ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2178]) ).
thf(2248,plain,
! [SV265: $i,SV391: $i] :
( ( ( ! [SY2616: $i] :
~ ( in @ ( ordered_pair @ SY2616 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ~ ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2181]) ).
thf(2249,plain,
! [SV265: $i,SV391: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV391 @ SV265 ) @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
| ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2182]) ).
thf(2250,plain,
! [SV392: $i,SV265: $i] :
( ( ( ~ ! [SY2617: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2617 ) @ SV265 )
| ( in @ SY2617 @ SV392 ) ) )
= $false )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2183]) ).
thf(2251,plain,
! [SV265: $i,SV392: $i] :
( ( ( ~ ! [SY2619: $i] :
( ~ ( in @ SY2619 @ SV392 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2619 @ SV392 @ SV265 ) @ SY2619 ) @ SV265 ) ) )
= $false )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2183]) ).
thf(2252,plain,
! [SV267: $i,SV404: $i] :
( ( ( ~ ! [SY2624: $i] :
( ~ ( subset @ SY2624 @ SV404 )
| ( in @ SY2624 @ ( sK5_SY2040 @ SV404 @ SV267 ) ) ) )
= $false )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2184]) ).
thf(2253,plain,
! [SV267: $i,SV404: $i] :
( ( ( ~ ( in @ ( sK5_SY2040 @ SV404 @ SV267 ) @ ( sK4_B @ SV267 ) ) )
= $false )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2184]) ).
thf(2254,plain,
! [SV267: $i,SV433: $i] :
( ( ! [SY2635: $i] :
( ~ ( in @ SV433 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SY2635 @ SV433 )
| ( in @ SY2635 @ ( sK4_B @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2255,plain,
! [SV369: $i,SV268: $i,SV393: $i,SV297: $i] :
( ( ( in @ SV297 @ SV393 )
= $false )
| ( ( in @ SV268 @ SV369 )
= $false )
| ( ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV369 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2256,plain,
! [SV434: $i,SV414: $i,SV297: $i,SV268: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV414 @ SV434 ) ) )
= $true )
| ( ( in @ SV268 @ SV414 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2257,plain,
! [SV423: $i,SV415: $i,SV297: $i,SV268: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV415 @ SV423 ) ) )
= $true )
| ( ( in @ SV297 @ SV423 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2258,plain,
! [SV424: $i,SV416: $i,SV318: $i] :
( ( ( ( sK36_B @ SV318 )
= ( ordered_pair @ SV416 @ SV424 ) )
= $false )
| ( ( relation @ SV318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2259,plain,
! [SV372: $i,SV350: $i,SV270: $i] :
( ( ( ! [SY2587: $i,SY2588: $i] :
( ~ ( in @ SY2587 @ SV270 )
| ~ ( in @ SY2588 @ SV350 )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SY2587 @ SY2588 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2260,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2192]) ).
thf(2261,plain,
! [SV373: $i,SV351: $i,SV270: $i] :
( ( ( ! [SY2589: $i] :
( ! [SY2563: $i,SY2564: $i] :
( ~ ( in @ SY2563 @ SV270 )
| ~ ( in @ SY2564 @ SV351 )
| ( SY2589
!= ( ordered_pair @ SY2563 @ SY2564 ) ) )
| ( in @ SY2589 @ SV373 ) ) )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2193]) ).
thf(2262,plain,
! [SV270: $i,SV351: $i,SV373: $i] :
( ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV373 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SY2592
!= ( ordered_pair @ ( sK21_E @ SY2592 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SY2592 @ SV373 @ SV351 @ SV270 ) ) ) ) ) )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2263,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) )
= $false )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2264,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
= $true )
| ( ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 )
| ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2265,plain,
! [SV353: $i,SV271: $i,SV375: $i] :
( ( ( ! [SY2593: $i] :
( ~ ( in @ SY2593 @ SV375 )
| ( in @ SY2593 @ SV271 )
| ( in @ SY2593 @ SV353 ) ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2266,plain,
! [SV353: $i,SV375: $i,SV271: $i] :
( ( ( ~ ( ~ ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) )
| ~ ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2198]) ).
thf(2267,plain,
! [SV272: $i,SV435: $i] :
( ( ! [SY2636: $i] :
( ~ ( in @ SV435 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SY2636 @ SV435 )
| ( in @ SY2636 @ ( sK39_B @ SV272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2268,plain,
! [SV396: $i,SV273: $i] :
( ( ( subset @ SV273 @ SV396 )
= $false )
| ( ( subset @ ( relation_dom @ SV273 ) @ ( relation_dom @ SV396 ) )
= $true )
| ( ( relation @ SV396 )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2269,plain,
! [SV397: $i,SV273: $i] :
( ( ( subset @ SV273 @ SV397 )
= $false )
| ( ( subset @ ( relation_rng @ SV273 ) @ ( relation_rng @ SV397 ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2270,plain,
! [SV376: $i,SV274: $i,SV398: $i,SV299: $i] :
( ( ( in @ SV299 @ SV398 )
= $false )
| ( ( in @ SV274 @ SV376 )
= $false )
| ( ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV376 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2271,plain,
! [SV436: $i,SV417: $i,SV299: $i,SV274: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV417 @ SV436 ) ) )
= $true )
| ( ( in @ SV274 @ SV417 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2272,plain,
! [SV425: $i,SV418: $i,SV299: $i,SV274: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV418 @ SV425 ) ) )
= $true )
| ( ( in @ SV299 @ SV425 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2273,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2274,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
| ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) )
= $false )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2275,plain,
! [SV378: $i,SV360: $i,SV275: $i] :
( ( ( ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV275 )
| ( in @ SY2597 @ SV360 )
| ( in @ SY2597 @ SV378 ) ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2276,plain,
! [SV360: $i,SV275: $i,SV378: $i] :
( ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) )
| ~ ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2277,plain,
! [SV382: $i,SV419: $i] :
( ( ( element @ SV419 @ SV382 )
= $false )
| ( ( empty @ SV419 )
= $true )
| ( ( empty @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2278,plain,
! [SV383: $i,SV420: $i] :
( ( ( empty @ SV420 )
= $false )
| ( ( element @ SV420 @ SV383 )
= $true )
| ( ( empty @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2279,plain,
! [SV306: $i,SV328: $i] :
( ( ( in @ ( sK30_C @ SV328 @ SV306 ) @ SV328 )
= $false )
| ( ( ( sK30_C @ SV328 @ SV306 )
= SV306 )
= $false )
| ( ( SV328
= ( singleton @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2280,plain,
! [SV329: $i,SV307: $i,SV426: $i] :
( ( ( ( SV426 != SV307 ) )
= $true )
| ( ( in @ SV426 @ SV329 )
= $true )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2281,plain,
! [SV307: $i,SV329: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV329 ) )
= $true )
| ( ( SV427 = SV307 )
= $true )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2282,plain,
! [SV428: $i,SV310: $i,SV332: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV428 ) )
= $true )
| ( ( ~ ( in @ SV428 @ SV310 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2283,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) ) )
= $false )
| ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2222]) ).
thf(2284,plain,
! [SV310: $i,SV332: $i] :
( ( ( ~ ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 ) )
= $false )
| ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2222]) ).
thf(2285,plain,
! [SV333: $i,SV311: $i,SV429: $i] :
( ( ( ! [SY2634: $i] :
( ~ ( in @ SV429 @ SY2634 )
| ~ ( in @ SY2634 @ SV311 ) ) )
= $true )
| ( ( in @ SV429 @ SV333 )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2286,plain,
! [SV311: $i,SV333: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV333 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV430 @ ( sK13_D @ SV430 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SV430 @ SV333 @ SV311 ) @ SV311 ) ) )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2287,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( element @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
= $false )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2288,plain,
! [SV294: $i,SV258: $i,SV401: $i] :
( ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( ~ ( ~ ! [SY2620: $i] :
( ~ ( element @ SY2620 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2620 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SY2620 ) @ SV294 ) )
| ~ ! [SY2621: $i] :
( ~ ( element @ SY2621 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2621 ) @ SV294 )
| ( in @ SY2621 @ SV401 ) ) ) )
= $true )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2289,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2290,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) )
= $false )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2228]) ).
thf(2291,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) ) )
= $false )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2228]) ).
thf(2292,plain,
! [SV363: $i,SV335: $i,SV260: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ SV260 )
| ~ ( in @ SV437 @ SV335 )
| ( in @ SV437 @ SV363 ) )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2293,plain,
! [SV335: $i,SV260: $i,SV363: $i] :
( ( ( ~ ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) )
| ~ ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) )
= $false )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2294,plain,
! [SV261: $i,SV385: $i] :
( ( ( ! [SY2604: $i] :
~ ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SY2604 ) @ SV261 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) )
= $true )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2295,plain,
! [SV261: $i,SV385: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ ( sK18_SY2050 @ SV385 @ SV261 ) ) @ SV261 )
= $true )
| ( ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 )
= $true )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2296,plain,
! [SV386: $i,SV261: $i] :
( ( ( ! [SY2605: $i] :
( ! [SY2397: $i] :
~ ( in @ ( ordered_pair @ SY2605 @ SY2397 ) @ SV261 )
| ( in @ SY2605 @ SV386 ) ) )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2233]) ).
thf(2297,plain,
! [SV261: $i,SV386: $i] :
( ( ( ! [SY2607: $i] :
( ~ ( in @ SY2607 @ SV386 )
| ( in @ ( ordered_pair @ SY2607 @ ( sK16_D @ SY2607 @ SV386 @ SV261 ) ) @ SV261 ) ) )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2298,plain,
! [SV312: $i,SV337: $i] :
( ( ( subset @ ( sK28_C @ SV337 @ SV312 ) @ SV312 )
= $false )
| ( ( in @ ( sK28_C @ SV337 @ SV312 ) @ SV337 )
= $false )
| ( ( SV337
= ( powerset @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2299,plain,
! [SV313: $i,SV338: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV338 ) )
= $true )
| ( ( subset @ SV431 @ SV313 )
= $true )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2300,plain,
! [SV338: $i,SV313: $i,SV432: $i] :
( ( ( ~ ( subset @ SV432 @ SV313 ) )
= $true )
| ( ( in @ SV432 @ SV338 )
= $true )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2301,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) )
| ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) ) )
= $false )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2240]) ).
thf(2302,plain,
! [SV412: $i,SV387: $i] :
( ( ( ~ ( ! [SY2625: $i] :
( ~ ( in @ SY2625 @ SV387 )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SY2625 ) )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) ) )
= $false )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2240]) ).
thf(2303,plain,
! [SV388: $i,SV413: $i] :
( ( ( ~ ! [SY2626: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SY2626 @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) ) )
| ( in @ SY2626 @ SV413 ) )
| ~ ! [SY2627: $i] :
( ~ ( in @ SY2627 @ SV413 )
| ! [SY2613: $i] :
( ~ ( in @ SY2613 @ SV388 )
| ( in @ SY2627 @ SY2613 ) ) ) )
= $false )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2304,plain,
! [SV389: $i,SV421: $i] :
( ( ( SV421
= ( set_meet @ SV389 ) )
= $false )
| ( ( SV421 = empty_set )
= $true )
| ( ( SV389 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2305,plain,
! [SV390: $i,SV422: $i] :
( ( ( SV422 = empty_set )
= $false )
| ( ( SV422
= ( set_meet @ SV390 ) )
= $true )
| ( ( SV390 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2306,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) ) )
= $false )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2244]) ).
thf(2307,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) ) )
= $false )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2244]) ).
thf(2308,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV263 )
= $true )
| ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV339 )
= $true )
| ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2309,plain,
! [SV340: $i,SV263: $i,SV366: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV366 )
| ( SV438 = SV263 )
| ( SV438 = SV340 ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2310,plain,
! [SV340: $i,SV366: $i,SV263: $i] :
( ( ( ~ ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) )
| ~ ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) )
= $false )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2311,plain,
! [SV265: $i,SV391: $i] :
( ( ( ! [SY2616: $i] :
~ ( in @ ( ordered_pair @ SY2616 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2312,plain,
! [SV265: $i,SV391: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY2046 @ SV391 @ SV265 ) @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
= $true )
| ( ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 )
= $true )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2313,plain,
! [SV392: $i,SV265: $i] :
( ( ( ! [SY2617: $i] :
( ! [SY2420: $i] :
~ ( in @ ( ordered_pair @ SY2420 @ SY2617 ) @ SV265 )
| ( in @ SY2617 @ SV392 ) ) )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2314,plain,
! [SV265: $i,SV392: $i] :
( ( ( ! [SY2619: $i] :
( ~ ( in @ SY2619 @ SV392 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY2619 @ SV392 @ SV265 ) @ SY2619 ) @ SV265 ) ) )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2315,plain,
! [SV267: $i,SV404: $i] :
( ( ( ! [SY2624: $i] :
( ~ ( subset @ SY2624 @ SV404 )
| ( in @ SY2624 @ ( sK5_SY2040 @ SV404 @ SV267 ) ) ) )
= $true )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2252]) ).
thf(2316,plain,
! [SV267: $i,SV404: $i] :
( ( ( in @ ( sK5_SY2040 @ SV404 @ SV267 ) @ ( sK4_B @ SV267 ) )
= $true )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2253]) ).
thf(2317,plain,
! [SV439: $i,SV267: $i,SV433: $i] :
( ( ~ ( in @ SV433 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SV439 @ SV433 )
| ( in @ SV439 @ ( sK4_B @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2318,plain,
! [SV434: $i,SV414: $i,SV297: $i,SV268: $i] :
( ( ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV414 @ SV434 ) )
= $false )
| ( ( in @ SV268 @ SV414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2319,plain,
! [SV423: $i,SV415: $i,SV297: $i,SV268: $i] :
( ( ( in @ ( ordered_pair @ SV268 @ SV297 ) @ ( cartesian_product2 @ SV415 @ SV423 ) )
= $false )
| ( ( in @ SV297 @ SV423 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2320,plain,
! [SV372: $i,SV350: $i,SV270: $i,SV440: $i] :
( ( ( ! [SY2637: $i] :
( ~ ( in @ SV440 @ SV270 )
| ~ ( in @ SY2637 @ SV350 )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SV440 @ SY2637 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2321,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2322,plain,
! [SV373: $i,SV441: $i,SV351: $i,SV270: $i] :
( ( ( ! [SY2638: $i,SY2639: $i] :
( ~ ( in @ SY2638 @ SV270 )
| ~ ( in @ SY2639 @ SV351 )
| ( SV441
!= ( ordered_pair @ SY2638 @ SY2639 ) ) )
| ( in @ SV441 @ SV373 ) )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2323,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ SV373 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SV442
!= ( ordered_pair @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) ) ) ) )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2324,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) ) )
= $false )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2263]) ).
thf(2325,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) ) )
= $false )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2263]) ).
thf(2326,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 )
= $true )
| ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 )
= $true )
| ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2327,plain,
! [SV353: $i,SV271: $i,SV375: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV375 )
| ( in @ SV443 @ SV271 )
| ( in @ SV443 @ SV353 ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2328,plain,
! [SV353: $i,SV375: $i,SV271: $i] :
( ( ( ~ ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) )
| ~ ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) )
= $false )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2329,plain,
! [SV444: $i,SV272: $i,SV435: $i] :
( ( ~ ( in @ SV435 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SV444 @ SV435 )
| ( in @ SV444 @ ( sK39_B @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2330,plain,
! [SV436: $i,SV417: $i,SV299: $i,SV274: $i] :
( ( ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV417 @ SV436 ) )
= $false )
| ( ( in @ SV274 @ SV417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2331,plain,
! [SV425: $i,SV418: $i,SV299: $i,SV274: $i] :
( ( ( in @ ( ordered_pair @ SV274 @ SV299 ) @ ( cartesian_product2 @ SV418 @ SV425 ) )
= $false )
| ( ( in @ SV299 @ SV425 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2332,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 ) )
= $true )
| ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2333,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) )
= $false )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2334,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) ) )
= $false )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2335,plain,
! [SV378: $i,SV360: $i,SV275: $i,SV445: $i] :
( ( ( ~ ( in @ SV445 @ SV275 )
| ( in @ SV445 @ SV360 )
| ( in @ SV445 @ SV378 ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2336,plain,
! [SV360: $i,SV275: $i,SV378: $i] :
( ( ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) )
| ~ ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) )
= $false )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2337,plain,
! [SV329: $i,SV307: $i,SV426: $i] :
( ( ( SV426 = SV307 )
= $false )
| ( ( in @ SV426 @ SV329 )
= $true )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2280]) ).
thf(2338,plain,
! [SV307: $i,SV329: $i,SV427: $i] :
( ( ( in @ SV427 @ SV329 )
= $false )
| ( ( SV427 = SV307 )
= $true )
| ( ( SV329
= ( singleton @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2339,plain,
! [SV428: $i,SV310: $i,SV332: $i] :
( ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV428 )
= $false )
| ( ( ~ ( in @ SV428 @ SV310 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2340,plain,
! [SV310: $i,SV332: $i] :
( ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ ( sK15_SY2048 @ SV332 @ SV310 ) )
= $true )
| ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2341,plain,
! [SV310: $i,SV332: $i] :
( ( ( in @ ( sK15_SY2048 @ SV332 @ SV310 ) @ SV310 )
= $true )
| ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2284]) ).
thf(2342,plain,
! [SV333: $i,SV311: $i,SV446: $i,SV429: $i] :
( ( ( ~ ( in @ SV429 @ SV446 )
| ~ ( in @ SV446 @ SV311 ) )
= $true )
| ( ( in @ SV429 @ SV333 )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2343,plain,
! [SV311: $i,SV333: $i,SV430: $i] :
( ( ( in @ SV430 @ SV333 )
= $false )
| ( ( ~ ( ~ ( in @ SV430 @ ( sK13_D @ SV430 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SV430 @ SV333 @ SV311 ) @ SV311 ) ) )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2344,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( element @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) ) )
= $false )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2287]) ).
thf(2345,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
= $false )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2287]) ).
thf(2346,plain,
! [SV294: $i,SV401: $i,SV258: $i] :
( ( ( ~ ! [SY2620: $i] :
( ~ ( element @ SY2620 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2620 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SY2620 ) @ SV294 ) )
| ~ ! [SY2621: $i] :
( ~ ( element @ SY2621 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2621 ) @ SV294 )
| ( in @ SY2621 @ SV401 ) ) )
= $false )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2347,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2348,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2290]) ).
thf(2349,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
| ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2350,plain,
! [SV363: $i,SV335: $i,SV260: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ SV260 )
| ~ ( in @ SV437 @ SV335 ) )
= $true )
| ( ( in @ SV437 @ SV363 )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2292]) ).
thf(2351,plain,
! [SV335: $i,SV260: $i,SV363: $i] :
( ( ( ~ ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) ) )
= $false )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2352,plain,
! [SV260: $i,SV335: $i,SV363: $i] :
( ( ( ~ ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) )
= $false )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2353,plain,
! [SV447: $i,SV261: $i,SV385: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SV447 ) @ SV261 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) )
= $true )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2354,plain,
! [SV386: $i,SV261: $i,SV448: $i] :
( ( ( ! [SY2640: $i] :
~ ( in @ ( ordered_pair @ SV448 @ SY2640 ) @ SV261 )
| ( in @ SV448 @ SV386 ) )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2355,plain,
! [SV261: $i,SV386: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ SV386 )
| ( in @ ( ordered_pair @ SV449 @ ( sK16_D @ SV449 @ SV386 @ SV261 ) ) @ SV261 ) )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2356,plain,
! [SV313: $i,SV338: $i,SV431: $i] :
( ( ( in @ SV431 @ SV338 )
= $false )
| ( ( subset @ SV431 @ SV313 )
= $true )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2357,plain,
! [SV338: $i,SV313: $i,SV432: $i] :
( ( ( subset @ SV432 @ SV313 )
= $false )
| ( ( in @ SV432 @ SV338 )
= $true )
| ( ( SV338
= ( powerset @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2358,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) )
| ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2301]) ).
thf(2359,plain,
! [SV412: $i,SV387: $i] :
( ( ( ! [SY2625: $i] :
( ~ ( in @ SY2625 @ SV387 )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SY2625 ) )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2302]) ).
thf(2360,plain,
! [SV388: $i,SV413: $i] :
( ( ( ~ ! [SY2626: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SY2626 @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) ) )
| ( in @ SY2626 @ SV413 ) ) )
= $false )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2361,plain,
! [SV388: $i,SV413: $i] :
( ( ( ~ ! [SY2627: $i] :
( ~ ( in @ SY2627 @ SV413 )
| ! [SY2613: $i] :
( ~ ( in @ SY2613 @ SV388 )
| ( in @ SY2627 @ SY2613 ) ) ) )
= $false )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2362,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2306]) ).
thf(2363,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
| ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2307]) ).
thf(2364,plain,
! [SV340: $i,SV263: $i,SV366: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV366 ) )
= $true )
| ( ( ( SV438 = SV263 )
| ( SV438 = SV340 ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2365,plain,
! [SV340: $i,SV366: $i,SV263: $i] :
( ( ( ~ ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) ) )
= $false )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2310]) ).
thf(2366,plain,
! [SV263: $i,SV366: $i,SV340: $i] :
( ( ( ~ ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) )
= $false )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2310]) ).
thf(2367,plain,
! [SV265: $i,SV391: $i,SV450: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV450 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2368,plain,
! [SV392: $i,SV265: $i,SV451: $i] :
( ( ( ! [SY2641: $i] :
~ ( in @ ( ordered_pair @ SY2641 @ SV451 ) @ SV265 )
| ( in @ SV451 @ SV392 ) )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2369,plain,
! [SV265: $i,SV392: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ SV392 )
| ( in @ ( ordered_pair @ ( sK9_D @ SV452 @ SV392 @ SV265 ) @ SV452 ) @ SV265 ) )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2370,plain,
! [SV267: $i,SV404: $i,SV453: $i] :
( ( ( ~ ( subset @ SV453 @ SV404 )
| ( in @ SV453 @ ( sK5_SY2040 @ SV404 @ SV267 ) ) )
= $true )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2371,plain,
! [SV267: $i,SV404: $i] :
( ( ( in @ SV404 @ ( sK4_B @ SV267 ) )
= $false )
| ( ( in @ ( sK5_SY2040 @ SV404 @ SV267 ) @ ( sK4_B @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2372,plain,
! [SV439: $i,SV267: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK4_B @ SV267 ) )
| ~ ( subset @ SV439 @ SV433 ) )
= $true )
| ( ( in @ SV439 @ ( sK4_B @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2373,plain,
! [SV372: $i,SV350: $i,SV454: $i,SV270: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV270 )
| ~ ( in @ SV454 @ SV350 )
| ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SV440 @ SV454 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2374,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2375,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2376,plain,
! [SV373: $i,SV441: $i,SV351: $i,SV270: $i] :
( ( ( ! [SY2638: $i,SY2639: $i] :
( ~ ( in @ SY2638 @ SV270 )
| ~ ( in @ SY2639 @ SV351 )
| ( SV441
!= ( ordered_pair @ SY2638 @ SY2639 ) ) ) )
= $true )
| ( ( in @ SV441 @ SV373 )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2377,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ SV373 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SV442
!= ( ordered_pair @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) ) ) ) )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2378,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2379,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
| ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2325]) ).
thf(2380,plain,
! [SV353: $i,SV271: $i,SV375: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV375 ) )
= $true )
| ( ( ( in @ SV443 @ SV271 )
| ( in @ SV443 @ SV353 ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2381,plain,
! [SV353: $i,SV375: $i,SV271: $i] :
( ( ( ~ ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) ) )
= $false )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2328]) ).
thf(2382,plain,
! [SV271: $i,SV375: $i,SV353: $i] :
( ( ( ~ ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) )
= $false )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2328]) ).
thf(2383,plain,
! [SV444: $i,SV272: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ ( sK39_B @ SV272 ) )
| ~ ( subset @ SV444 @ SV435 ) )
= $true )
| ( ( in @ SV444 @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2384,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
= $false )
| ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2385,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2386,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
| ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 ) )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2387,plain,
! [SV378: $i,SV360: $i,SV275: $i,SV445: $i] :
( ( ( ~ ( in @ SV445 @ SV275 )
| ( in @ SV445 @ SV360 ) )
= $true )
| ( ( in @ SV445 @ SV378 )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2388,plain,
! [SV360: $i,SV275: $i,SV378: $i] :
( ( ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) ) )
= $false )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2389,plain,
! [SV275: $i,SV360: $i,SV378: $i] :
( ( ( ~ ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) )
= $false )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2390,plain,
! [SV332: $i,SV310: $i,SV428: $i] :
( ( ( in @ SV428 @ SV310 )
= $false )
| ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV428 )
= $false )
| ( ( ~ ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 ) )
= $true )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2391,plain,
! [SV333: $i,SV311: $i,SV446: $i,SV429: $i] :
( ( ( ~ ( in @ SV429 @ SV446 ) )
= $true )
| ( ( ~ ( in @ SV446 @ SV311 ) )
= $true )
| ( ( in @ SV429 @ SV333 )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2392,plain,
! [SV311: $i,SV333: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ ( sK13_D @ SV430 @ SV333 @ SV311 ) )
| ~ ( in @ ( sK13_D @ SV430 @ SV333 @ SV311 ) @ SV311 ) )
= $false )
| ( ( in @ SV430 @ SV333 )
= $false )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2393,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( element @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ ( powerset @ SV258 ) )
= $true )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2344]) ).
thf(2394,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) ) )
= $true )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2395,plain,
! [SV294: $i,SV401: $i,SV258: $i] :
( ( ( ~ ! [SY2620: $i] :
( ~ ( element @ SY2620 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2620 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SY2620 ) @ SV294 ) ) )
= $false )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2346]) ).
thf(2396,plain,
! [SV401: $i,SV294: $i,SV258: $i] :
( ( ( ~ ! [SY2621: $i] :
( ~ ( element @ SY2621 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2621 ) @ SV294 )
| ( in @ SY2621 @ SV401 ) ) )
= $false )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2346]) ).
thf(2397,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
= $false )
| ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2398,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
= $true )
| ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2399,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
= $true )
| ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 )
= $true )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2400,plain,
! [SV363: $i,SV335: $i,SV260: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ SV260 ) )
= $true )
| ( ( ~ ( in @ SV437 @ SV335 ) )
= $true )
| ( ( in @ SV437 @ SV363 )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2401,plain,
! [SV335: $i,SV260: $i,SV363: $i] :
( ( ( ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV363 )
| ( in @ SY2579 @ SV260 ) ) )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2402,plain,
! [SV260: $i,SV335: $i,SV363: $i] :
( ( ( ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SV363 )
| ( in @ SY2580 @ SV335 ) ) )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2403,plain,
! [SV447: $i,SV261: $i,SV385: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SV447 ) @ SV261 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 ) )
= $true )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2404,plain,
! [SV386: $i,SV261: $i,SV448: $i] :
( ( ( ! [SY2640: $i] :
~ ( in @ ( ordered_pair @ SV448 @ SY2640 ) @ SV261 ) )
= $true )
| ( ( in @ SV448 @ SV386 )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2405,plain,
! [SV261: $i,SV386: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ SV386 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV449 @ ( sK16_D @ SV449 @ SV386 @ SV261 ) ) @ SV261 )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2406,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2407,plain,
! [SV412: $i,SV387: $i] :
( ( ( ! [SY2625: $i] :
( ~ ( in @ SY2625 @ SV387 )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SY2625 ) ) )
= $true )
| ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2408,plain,
! [SV388: $i,SV413: $i] :
( ( ( ! [SY2626: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SY2626 @ ( sK31_D @ SY2626 @ SV413 @ SV388 ) ) )
| ( in @ SY2626 @ SV413 ) ) )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2409,plain,
! [SV388: $i,SV413: $i] :
( ( ( ! [SY2627: $i] :
( ~ ( in @ SY2627 @ SV413 )
| ! [SY2613: $i] :
( ~ ( in @ SY2613 @ SV388 )
| ( in @ SY2627 @ SY2613 ) ) ) )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2361]) ).
thf(2410,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 ) )
= $true )
| ( ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2411,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 ) )
= $true )
| ( ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2412,plain,
! [SV340: $i,SV263: $i,SV366: $i,SV438: $i] :
( ( ( in @ SV438 @ SV366 )
= $false )
| ( ( ( SV438 = SV263 )
| ( SV438 = SV340 ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2413,plain,
! [SV340: $i,SV366: $i,SV263: $i] :
( ( ( ! [SY2582: $i] :
( ( SY2582 != SV263 )
| ( in @ SY2582 @ SV366 ) ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2365]) ).
thf(2414,plain,
! [SV263: $i,SV366: $i,SV340: $i] :
( ( ( ! [SY2583: $i] :
( ( SY2583 != SV340 )
| ( in @ SY2583 @ SV366 ) ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2415,plain,
! [SV265: $i,SV391: $i,SV450: $i] :
( ( ( in @ ( ordered_pair @ SV450 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
= $false )
| ( ( ~ ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2416,plain,
! [SV392: $i,SV265: $i,SV451: $i] :
( ( ( ! [SY2641: $i] :
~ ( in @ ( ordered_pair @ SY2641 @ SV451 ) @ SV265 ) )
= $true )
| ( ( in @ SV451 @ SV392 )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2417,plain,
! [SV265: $i,SV392: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ SV392 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV452 @ SV392 @ SV265 ) @ SV452 ) @ SV265 )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2418,plain,
! [SV267: $i,SV404: $i,SV453: $i] :
( ( ( ~ ( subset @ SV453 @ SV404 ) )
= $true )
| ( ( in @ SV453 @ ( sK5_SY2040 @ SV404 @ SV267 ) )
= $true )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2419,plain,
! [SV439: $i,SV267: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK4_B @ SV267 ) ) )
= $true )
| ( ( ~ ( subset @ SV439 @ SV433 ) )
= $true )
| ( ( in @ SV439 @ ( sK4_B @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2420,plain,
! [SV372: $i,SV350: $i,SV454: $i,SV270: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV270 )
| ~ ( in @ SV454 @ SV350 ) )
= $true )
| ( ( ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SV440 @ SV454 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2421,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2374]) ).
thf(2422,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ( sK23_D @ SV372 @ SV350 @ SV270 )
= ( ordered_pair @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2375]) ).
thf(2423,plain,
! [SV373: $i,SV441: $i,SV351: $i,SV270: $i,SV455: $i] :
( ( ( ! [SY2642: $i] :
( ~ ( in @ SV455 @ SV270 )
| ~ ( in @ SY2642 @ SV351 )
| ( SV441
!= ( ordered_pair @ SV455 @ SY2642 ) ) ) )
= $true )
| ( ( in @ SV441 @ SV373 )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2424,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( in @ SV442 @ SV373 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SV442
!= ( ordered_pair @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) ) ) ) )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2425,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2426,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2427,plain,
! [SV353: $i,SV271: $i,SV375: $i,SV443: $i] :
( ( ( in @ SV443 @ SV375 )
= $false )
| ( ( ( in @ SV443 @ SV271 )
| ( in @ SV443 @ SV353 ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2428,plain,
! [SV353: $i,SV375: $i,SV271: $i] :
( ( ( ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SV271 )
| ( in @ SY2594 @ SV375 ) ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2429,plain,
! [SV271: $i,SV375: $i,SV353: $i] :
( ( ( ! [SY2595: $i] :
( ~ ( in @ SY2595 @ SV353 )
| ( in @ SY2595 @ SV375 ) ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2382]) ).
thf(2430,plain,
! [SV444: $i,SV272: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ ( sK39_B @ SV272 ) ) )
= $true )
| ( ( ~ ( subset @ SV444 @ SV435 ) )
= $true )
| ( ( in @ SV444 @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2431,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 )
= $false )
| ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
= $true )
| ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
= $false )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2432,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV275 )
= $true )
| ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2433,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 ) )
= $true )
| ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2434,plain,
! [SV378: $i,SV360: $i,SV275: $i,SV445: $i] :
( ( ( ~ ( in @ SV445 @ SV275 ) )
= $true )
| ( ( in @ SV445 @ SV360 )
= $true )
| ( ( in @ SV445 @ SV378 )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2435,plain,
! [SV360: $i,SV275: $i,SV378: $i] :
( ( ( ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV378 )
| ( in @ SY2598 @ SV275 ) ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2388]) ).
thf(2436,plain,
! [SV275: $i,SV360: $i,SV378: $i] :
( ( ( ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV378 )
| ~ ( in @ SY2599 @ SV360 ) ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2389]) ).
thf(2437,plain,
! [SV428: $i,SV310: $i,SV332: $i] :
( ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV332 )
= $false )
| ( ( in @ ( sK14_C @ SV332 @ SV310 ) @ SV428 )
= $false )
| ( ( in @ SV428 @ SV310 )
= $false )
| ( ( SV332
= ( union @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2438,plain,
! [SV333: $i,SV311: $i,SV446: $i,SV429: $i] :
( ( ( in @ SV429 @ SV446 )
= $false )
| ( ( ~ ( in @ SV446 @ SV311 ) )
= $true )
| ( ( in @ SV429 @ SV333 )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2439,plain,
! [SV311: $i,SV333: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ ( sK13_D @ SV430 @ SV333 @ SV311 ) ) )
= $false )
| ( ( in @ SV430 @ SV333 )
= $false )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2440,plain,
! [SV311: $i,SV333: $i,SV430: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV430 @ SV333 @ SV311 ) @ SV311 ) )
= $false )
| ( ( in @ SV430 @ SV333 )
= $false )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2441,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
| ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) )
= $false )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2442,plain,
! [SV294: $i,SV401: $i,SV258: $i] :
( ( ( ! [SY2620: $i] :
( ~ ( element @ SY2620 @ ( powerset @ SV258 ) )
| ~ ( in @ SY2620 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SY2620 ) @ SV294 ) ) )
= $true )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2395]) ).
thf(2443,plain,
! [SV401: $i,SV294: $i,SV258: $i] :
( ( ( ! [SY2621: $i] :
( ~ ( element @ SY2621 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SY2621 ) @ SV294 )
| ( in @ SY2621 @ SV401 ) ) )
= $true )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2444,plain,
! [SV260: $i,SV334: $i,SV362: $i] :
( ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV362 )
= $false )
| ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV260 )
= $false )
| ( ( in @ ( sK19_D @ SV362 @ SV334 @ SV260 ) @ SV334 )
= $false )
| ( ( SV362
= ( set_intersection2 @ SV260 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2445,plain,
! [SV363: $i,SV335: $i,SV260: $i,SV437: $i] :
( ( ( in @ SV437 @ SV260 )
= $false )
| ( ( ~ ( in @ SV437 @ SV335 ) )
= $true )
| ( ( in @ SV437 @ SV363 )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2446,plain,
! [SV335: $i,SV260: $i,SV363: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV363 )
| ( in @ SV456 @ SV260 ) )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2447,plain,
! [SV260: $i,SV335: $i,SV363: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ SV363 )
| ( in @ SV457 @ SV335 ) )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2448,plain,
! [SV447: $i,SV261: $i,SV385: $i] :
( ( ( in @ ( sK17_C @ SV385 @ SV261 ) @ SV385 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_C @ SV385 @ SV261 ) @ SV447 ) @ SV261 )
= $false )
| ( ( SV385
= ( relation_dom @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2449,plain,
! [SV386: $i,SV261: $i,SV458: $i,SV448: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV448 @ SV458 ) @ SV261 ) )
= $true )
| ( ( in @ SV448 @ SV386 )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2450,plain,
! [SV261: $i,SV386: $i,SV449: $i] :
( ( ( in @ SV449 @ SV386 )
= $false )
| ( ( in @ ( ordered_pair @ SV449 @ ( sK16_D @ SV449 @ SV386 @ SV261 ) ) @ SV261 )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2451,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
| ~ ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2452,plain,
! [SV412: $i,SV387: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV387 )
| ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV459 ) )
= $true )
| ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2453,plain,
! [SV388: $i,SV413: $i,SV460: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_D @ SV460 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SV460 @ ( sK31_D @ SV460 @ SV413 @ SV388 ) ) )
| ( in @ SV460 @ SV413 ) )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2454,plain,
! [SV388: $i,SV413: $i,SV461: $i] :
( ( ( ~ ( in @ SV461 @ SV413 )
| ! [SY2643: $i] :
( ~ ( in @ SY2643 @ SV388 )
| ( in @ SV461 @ SY2643 ) ) )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2455,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
= $false )
| ( ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV263 ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2456,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
= $false )
| ( ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
!= SV339 ) )
= $true )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2457,plain,
! [SV366: $i,SV340: $i,SV263: $i,SV438: $i] :
( ( ( SV438 = SV263 )
= $true )
| ( ( SV438 = SV340 )
= $true )
| ( ( in @ SV438 @ SV366 )
= $false )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2458,plain,
! [SV340: $i,SV366: $i,SV263: $i,SV462: $i] :
( ( ( ( SV462 != SV263 )
| ( in @ SV462 @ SV366 ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2459,plain,
! [SV263: $i,SV366: $i,SV340: $i,SV463: $i] :
( ( ( ( SV463 != SV340 )
| ( in @ SV463 @ SV366 ) )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(2460,plain,
! [SV450: $i,SV265: $i,SV391: $i] :
( ( ( in @ ( sK10_C @ SV391 @ SV265 ) @ SV391 )
= $false )
| ( ( in @ ( ordered_pair @ SV450 @ ( sK10_C @ SV391 @ SV265 ) ) @ SV265 )
= $false )
| ( ( SV391
= ( relation_rng @ SV265 ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2461,plain,
! [SV392: $i,SV265: $i,SV451: $i,SV464: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV464 @ SV451 ) @ SV265 ) )
= $true )
| ( ( in @ SV451 @ SV392 )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2462,plain,
! [SV265: $i,SV392: $i,SV452: $i] :
( ( ( in @ SV452 @ SV392 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV452 @ SV392 @ SV265 ) @ SV452 ) @ SV265 )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2463,plain,
! [SV267: $i,SV404: $i,SV453: $i] :
( ( ( subset @ SV453 @ SV404 )
= $false )
| ( ( in @ SV453 @ ( sK5_SY2040 @ SV404 @ SV267 ) )
= $true )
| ( ( ~ ( in @ SV404 @ ( sK4_B @ SV267 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2464,plain,
! [SV439: $i,SV267: $i,SV433: $i] :
( ( ( in @ SV433 @ ( sK4_B @ SV267 ) )
= $false )
| ( ( ~ ( subset @ SV439 @ SV433 ) )
= $true )
| ( ( in @ SV439 @ ( sK4_B @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2465,plain,
! [SV372: $i,SV350: $i,SV454: $i,SV270: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV270 ) )
= $true )
| ( ( ~ ( in @ SV454 @ SV350 ) )
= $true )
| ( ( ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SV440 @ SV454 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2466,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
= $false )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2467,plain,
! [SV373: $i,SV441: $i,SV351: $i,SV465: $i,SV270: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV270 )
| ~ ( in @ SV465 @ SV351 )
| ( SV441
!= ( ordered_pair @ SV455 @ SV465 ) ) )
= $true )
| ( ( in @ SV441 @ SV373 )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(2468,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
| ( SV442
!= ( ordered_pair @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) ) ) )
= $false )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2469,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2470,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 ) )
= $true )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2471,plain,
! [SV375: $i,SV353: $i,SV271: $i,SV443: $i] :
( ( ( in @ SV443 @ SV271 )
= $true )
| ( ( in @ SV443 @ SV353 )
= $true )
| ( ( in @ SV443 @ SV375 )
= $false )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2472,plain,
! [SV353: $i,SV375: $i,SV271: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ SV271 )
| ( in @ SV466 @ SV375 ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2473,plain,
! [SV271: $i,SV375: $i,SV353: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ SV353 )
| ( in @ SV467 @ SV375 ) )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(2474,plain,
! [SV444: $i,SV272: $i,SV435: $i] :
( ( ( in @ SV435 @ ( sK39_B @ SV272 ) )
= $false )
| ( ( ~ ( subset @ SV444 @ SV435 ) )
= $true )
| ( ( in @ SV444 @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2475,plain,
! [SV275: $i,SV359: $i,SV377: $i] :
( ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV359 )
= $false )
| ( ( in @ ( sK12_D @ SV377 @ SV359 @ SV275 ) @ SV377 )
= $true )
| ( ( SV377
= ( set_difference @ SV275 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2476,plain,
! [SV378: $i,SV360: $i,SV275: $i,SV445: $i] :
( ( ( in @ SV445 @ SV275 )
= $false )
| ( ( in @ SV445 @ SV360 )
= $true )
| ( ( in @ SV445 @ SV378 )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2477,plain,
! [SV360: $i,SV275: $i,SV378: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV378 )
| ( in @ SV468 @ SV275 ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(2478,plain,
! [SV275: $i,SV360: $i,SV378: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ SV378 )
| ~ ( in @ SV469 @ SV360 ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2479,plain,
! [SV333: $i,SV429: $i,SV311: $i,SV446: $i] :
( ( ( in @ SV446 @ SV311 )
= $false )
| ( ( in @ SV429 @ SV446 )
= $false )
| ( ( in @ SV429 @ SV333 )
= $true )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2480,plain,
! [SV311: $i,SV333: $i,SV430: $i] :
( ( ( in @ SV430 @ ( sK13_D @ SV430 @ SV333 @ SV311 ) )
= $true )
| ( ( in @ SV430 @ SV333 )
= $false )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2439]) ).
thf(2481,plain,
! [SV311: $i,SV333: $i,SV430: $i] :
( ( ( in @ ( sK13_D @ SV430 @ SV333 @ SV311 ) @ SV311 )
= $true )
| ( ( in @ SV430 @ SV333 )
= $false )
| ( ( SV333
= ( union @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2482,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) )
= $false )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2483,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) ) )
= $false )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2484,plain,
! [SV294: $i,SV401: $i,SV258: $i,SV470: $i] :
( ( ( ~ ( element @ SV470 @ ( powerset @ SV258 ) )
| ~ ( in @ SV470 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SV470 ) @ SV294 ) )
= $true )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2485,plain,
! [SV401: $i,SV294: $i,SV258: $i,SV471: $i] :
( ( ( ~ ( element @ SV471 @ ( powerset @ SV258 ) )
| ~ ( in @ ( subset_complement @ SV258 @ SV471 ) @ SV294 )
| ( in @ SV471 @ SV401 ) )
= $true )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2486,plain,
! [SV363: $i,SV260: $i,SV335: $i,SV437: $i] :
( ( ( in @ SV437 @ SV335 )
= $false )
| ( ( in @ SV437 @ SV260 )
= $false )
| ( ( in @ SV437 @ SV363 )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2487,plain,
! [SV335: $i,SV260: $i,SV363: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV363 ) )
= $true )
| ( ( in @ SV456 @ SV260 )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2488,plain,
! [SV260: $i,SV335: $i,SV363: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ SV363 ) )
= $true )
| ( ( in @ SV457 @ SV335 )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2489,plain,
! [SV386: $i,SV261: $i,SV458: $i,SV448: $i] :
( ( ( in @ ( ordered_pair @ SV448 @ SV458 ) @ SV261 )
= $false )
| ( ( in @ SV448 @ SV386 )
= $true )
| ( ( SV386
= ( relation_dom @ SV261 ) )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2490,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2451]) ).
thf(2491,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2451]) ).
thf(2492,plain,
! [SV412: $i,SV387: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV387 ) )
= $true )
| ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV459 )
= $true )
| ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2493,plain,
! [SV388: $i,SV413: $i,SV460: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_D @ SV460 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SV460 @ ( sK31_D @ SV460 @ SV413 @ SV388 ) ) ) )
= $true )
| ( ( in @ SV460 @ SV413 )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2494,plain,
! [SV388: $i,SV413: $i,SV461: $i] :
( ( ( ~ ( in @ SV461 @ SV413 ) )
= $true )
| ( ( ! [SY2643: $i] :
( ~ ( in @ SY2643 @ SV388 )
| ( in @ SV461 @ SY2643 ) ) )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2495,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV263 )
= $false )
| ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
= $false )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2496,plain,
! [SV263: $i,SV339: $i,SV365: $i] :
( ( ( ( sK27_D @ SV365 @ SV339 @ SV263 )
= SV339 )
= $false )
| ( ( in @ ( sK27_D @ SV365 @ SV339 @ SV263 ) @ SV365 )
= $false )
| ( ( SV365
= ( unordered_pair @ SV263 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2497,plain,
! [SV340: $i,SV366: $i,SV263: $i,SV462: $i] :
( ( ( ( SV462 != SV263 ) )
= $true )
| ( ( in @ SV462 @ SV366 )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2498,plain,
! [SV263: $i,SV366: $i,SV340: $i,SV463: $i] :
( ( ( ( SV463 != SV340 ) )
= $true )
| ( ( in @ SV463 @ SV366 )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2499,plain,
! [SV392: $i,SV265: $i,SV451: $i,SV464: $i] :
( ( ( in @ ( ordered_pair @ SV464 @ SV451 ) @ SV265 )
= $false )
| ( ( in @ SV451 @ SV392 )
= $true )
| ( ( SV392
= ( relation_rng @ SV265 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2500,plain,
! [SV453: $i,SV267: $i,SV404: $i] :
( ( ( in @ SV404 @ ( sK4_B @ SV267 ) )
= $false )
| ( ( in @ SV453 @ ( sK5_SY2040 @ SV404 @ SV267 ) )
= $true )
| ( ( subset @ SV453 @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2501,plain,
! [SV267: $i,SV433: $i,SV439: $i] :
( ( ( subset @ SV439 @ SV433 )
= $false )
| ( ( in @ SV433 @ ( sK4_B @ SV267 ) )
= $false )
| ( ( in @ SV439 @ ( sK4_B @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2502,plain,
! [SV372: $i,SV350: $i,SV454: $i,SV270: $i,SV440: $i] :
( ( ( in @ SV440 @ SV270 )
= $false )
| ( ( ~ ( in @ SV454 @ SV350 ) )
= $true )
| ( ( ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SV440 @ SV454 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2503,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 ) )
= $false )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2504,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( ~ ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 ) )
= $false )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2505,plain,
! [SV373: $i,SV441: $i,SV351: $i,SV465: $i,SV270: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV270 )
| ~ ( in @ SV465 @ SV351 ) )
= $true )
| ( ( ( SV441
!= ( ordered_pair @ SV455 @ SV465 ) ) )
= $true )
| ( ( in @ SV441 @ SV373 )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2506,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 ) ) )
= $false )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2468]) ).
thf(2507,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ( SV442
!= ( ordered_pair @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) ) ) )
= $false )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2468]) ).
thf(2508,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV271 )
= $false )
| ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
= $false )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2509,plain,
! [SV271: $i,SV352: $i,SV374: $i] :
( ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV352 )
= $false )
| ( ( in @ ( sK26_D @ SV374 @ SV352 @ SV271 ) @ SV374 )
= $false )
| ( ( SV374
= ( set_union2 @ SV271 @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2510,plain,
! [SV353: $i,SV375: $i,SV271: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ SV271 ) )
= $true )
| ( ( in @ SV466 @ SV375 )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2511,plain,
! [SV271: $i,SV375: $i,SV353: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ SV353 ) )
= $true )
| ( ( in @ SV467 @ SV375 )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2512,plain,
! [SV272: $i,SV435: $i,SV444: $i] :
( ( ( subset @ SV444 @ SV435 )
= $false )
| ( ( in @ SV435 @ ( sK39_B @ SV272 ) )
= $false )
| ( ( in @ SV444 @ ( sK39_B @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2513,plain,
! [SV360: $i,SV275: $i,SV378: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV378 ) )
= $true )
| ( ( in @ SV468 @ SV275 )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2514,plain,
! [SV275: $i,SV360: $i,SV378: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ SV378 ) )
= $true )
| ( ( ~ ( in @ SV469 @ SV360 ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2515,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
= $true )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2482]) ).
thf(2516,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
| ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
= $true )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2517,plain,
! [SV294: $i,SV401: $i,SV258: $i,SV470: $i] :
( ( ( ~ ( element @ SV470 @ ( powerset @ SV258 ) ) )
= $true )
| ( ( ~ ( in @ SV470 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SV470 ) @ SV294 ) )
= $true )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2518,plain,
! [SV401: $i,SV294: $i,SV258: $i,SV471: $i] :
( ( ( ~ ( element @ SV471 @ ( powerset @ SV258 ) ) )
= $true )
| ( ( ~ ( in @ ( subset_complement @ SV258 @ SV471 ) @ SV294 )
| ( in @ SV471 @ SV401 ) )
= $true )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2485]) ).
thf(2519,plain,
! [SV335: $i,SV260: $i,SV363: $i,SV456: $i] :
( ( ( in @ SV456 @ SV363 )
= $false )
| ( ( in @ SV456 @ SV260 )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2520,plain,
! [SV260: $i,SV335: $i,SV363: $i,SV457: $i] :
( ( ( in @ SV457 @ SV363 )
= $false )
| ( ( in @ SV457 @ SV335 )
= $true )
| ( ( SV363
= ( set_intersection2 @ SV260 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2521,plain,
! [SV387: $i,SV412: $i] :
( ( ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2490]) ).
thf(2522,plain,
! [SV387: $i,SV412: $i] :
( ( ( ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2491]) ).
thf(2523,plain,
! [SV412: $i,SV387: $i,SV459: $i] :
( ( ( in @ SV459 @ SV387 )
= $false )
| ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV459 )
= $true )
| ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2524,plain,
! [SV388: $i,SV413: $i,SV460: $i] :
( ( ( ~ ( in @ ( sK31_D @ SV460 @ SV413 @ SV388 ) @ SV388 )
| ~ ~ ( in @ SV460 @ ( sK31_D @ SV460 @ SV413 @ SV388 ) ) )
= $false )
| ( ( in @ SV460 @ SV413 )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2525,plain,
! [SV388: $i,SV413: $i,SV461: $i] :
( ( ( in @ SV461 @ SV413 )
= $false )
| ( ( ! [SY2643: $i] :
( ~ ( in @ SY2643 @ SV388 )
| ( in @ SV461 @ SY2643 ) ) )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2526,plain,
! [SV340: $i,SV366: $i,SV263: $i,SV462: $i] :
( ( ( SV462 = SV263 )
= $false )
| ( ( in @ SV462 @ SV366 )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2527,plain,
! [SV263: $i,SV366: $i,SV340: $i,SV463: $i] :
( ( ( SV463 = SV340 )
= $false )
| ( ( in @ SV463 @ SV366 )
= $true )
| ( ( SV366
= ( unordered_pair @ SV263 @ SV340 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2528,plain,
! [SV372: $i,SV270: $i,SV440: $i,SV350: $i,SV454: $i] :
( ( ( in @ SV454 @ SV350 )
= $false )
| ( ( in @ SV440 @ SV270 )
= $false )
| ( ( ( ( sK23_D @ SV372 @ SV350 @ SV270 )
!= ( ordered_pair @ SV440 @ SV454 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2529,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( in @ ( sK24_SY2054 @ SV372 @ SV350 @ SV270 ) @ SV270 )
= $true )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2530,plain,
! [SV270: $i,SV350: $i,SV372: $i] :
( ( ( in @ ( sK25_SY2056 @ SV372 @ SV350 @ SV270 ) @ SV350 )
= $true )
| ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2504]) ).
thf(2531,plain,
! [SV373: $i,SV441: $i,SV351: $i,SV465: $i,SV270: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV270 ) )
= $true )
| ( ( ~ ( in @ SV465 @ SV351 ) )
= $true )
| ( ( ( SV441
!= ( ordered_pair @ SV455 @ SV465 ) ) )
= $true )
| ( ( in @ SV441 @ SV373 )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2532,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 ) ) )
= $true )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2533,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( SV442
= ( ordered_pair @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) ) )
= $true )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2534,plain,
! [SV353: $i,SV375: $i,SV271: $i,SV466: $i] :
( ( ( in @ SV466 @ SV271 )
= $false )
| ( ( in @ SV466 @ SV375 )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2535,plain,
! [SV271: $i,SV375: $i,SV353: $i,SV467: $i] :
( ( ( in @ SV467 @ SV353 )
= $false )
| ( ( in @ SV467 @ SV375 )
= $true )
| ( ( SV375
= ( set_union2 @ SV271 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2536,plain,
! [SV360: $i,SV275: $i,SV378: $i,SV468: $i] :
( ( ( in @ SV468 @ SV378 )
= $false )
| ( ( in @ SV468 @ SV275 )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2537,plain,
! [SV275: $i,SV360: $i,SV378: $i,SV469: $i] :
( ( ( in @ SV469 @ SV378 )
= $false )
| ( ( ~ ( in @ SV469 @ SV360 ) )
= $true )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2538,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 ) )
= $true )
| ( ( ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
= $true )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2539,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
= $true )
| ( ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 )
= $true )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2540,plain,
! [SV294: $i,SV401: $i,SV258: $i,SV470: $i] :
( ( ( element @ SV470 @ ( powerset @ SV258 ) )
= $false )
| ( ( ~ ( in @ SV470 @ SV401 )
| ( in @ ( subset_complement @ SV258 @ SV470 ) @ SV294 ) )
= $true )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2541,plain,
! [SV401: $i,SV294: $i,SV258: $i,SV471: $i] :
( ( ( element @ SV471 @ ( powerset @ SV258 ) )
= $false )
| ( ( ~ ( in @ ( subset_complement @ SV258 @ SV471 ) @ SV294 )
| ( in @ SV471 @ SV401 ) )
= $true )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2542,plain,
! [SV387: $i,SV412: $i] :
( ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 )
= $false )
| ( ( in @ ( sK33_SY2057 @ SV412 @ SV387 ) @ SV387 )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2543,plain,
! [SV387: $i,SV412: $i] :
( ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 ) )
= $true )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2544,plain,
! [SV388: $i,SV413: $i,SV460: $i] :
( ( ( ~ ( in @ ( sK31_D @ SV460 @ SV413 @ SV388 ) @ SV388 ) )
= $false )
| ( ( in @ SV460 @ SV413 )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2545,plain,
! [SV388: $i,SV413: $i,SV460: $i] :
( ( ( ~ ~ ( in @ SV460 @ ( sK31_D @ SV460 @ SV413 @ SV388 ) ) )
= $false )
| ( ( in @ SV460 @ SV413 )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2546,plain,
! [SV413: $i,SV461: $i,SV388: $i,SV472: $i] :
( ( ( ~ ( in @ SV472 @ SV388 )
| ( in @ SV461 @ SV472 ) )
= $true )
| ( ( in @ SV461 @ SV413 )
= $false )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2547,plain,
! [SV454: $i,SV440: $i,SV270: $i,SV350: $i,SV372: $i] :
( ( ( ( sK23_D @ SV372 @ SV350 @ SV270 )
= ( ordered_pair @ SV440 @ SV454 ) )
= $false )
| ( ( in @ SV440 @ SV270 )
= $false )
| ( ( in @ SV454 @ SV350 )
= $false )
| ( ( ~ ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2548,plain,
! [SV373: $i,SV441: $i,SV351: $i,SV465: $i,SV270: $i,SV455: $i] :
( ( ( in @ SV455 @ SV270 )
= $false )
| ( ( ~ ( in @ SV465 @ SV351 ) )
= $true )
| ( ( ( SV441
!= ( ordered_pair @ SV455 @ SV465 ) ) )
= $true )
| ( ( in @ SV441 @ SV373 )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2549,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 )
| ~ ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
= $false )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2550,plain,
! [SV275: $i,SV378: $i,SV360: $i,SV469: $i] :
( ( ( in @ SV469 @ SV360 )
= $false )
| ( ( in @ SV469 @ SV378 )
= $false )
| ( ( SV378
= ( set_difference @ SV275 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2551,plain,
! [SV258: $i,SV294: $i,SV400: $i] :
( ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
= $false )
| ( ( ~ ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 ) )
= $true )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2552,plain,
! [SV294: $i,SV258: $i,SV401: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV401 ) )
= $true )
| ( ( in @ ( subset_complement @ SV258 @ SV470 ) @ SV294 )
= $true )
| ( ( element @ SV470 @ ( powerset @ SV258 ) )
= $false )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2553,plain,
! [SV401: $i,SV294: $i,SV471: $i,SV258: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV258 @ SV471 ) @ SV294 ) )
= $true )
| ( ( in @ SV471 @ SV401 )
= $true )
| ( ( element @ SV471 @ ( powerset @ SV258 ) )
= $false )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2554,plain,
! [SV387: $i,SV412: $i] :
( ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ SV412 )
= $false )
| ( ( in @ ( sK32_C @ SV412 @ SV387 ) @ ( sK33_SY2057 @ SV412 @ SV387 ) )
= $false )
| ( ( SV412
= ( set_meet @ SV387 ) )
= $true )
| ( ( SV387 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2555,plain,
! [SV388: $i,SV413: $i,SV460: $i] :
( ( ( in @ ( sK31_D @ SV460 @ SV413 @ SV388 ) @ SV388 )
= $true )
| ( ( in @ SV460 @ SV413 )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2544]) ).
thf(2556,plain,
! [SV388: $i,SV413: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ ( sK31_D @ SV460 @ SV413 @ SV388 ) ) )
= $true )
| ( ( in @ SV460 @ SV413 )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2545]) ).
thf(2557,plain,
! [SV413: $i,SV461: $i,SV388: $i,SV472: $i] :
( ( ( ~ ( in @ SV472 @ SV388 ) )
= $true )
| ( ( in @ SV461 @ SV472 )
= $true )
| ( ( in @ SV461 @ SV413 )
= $false )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2558,plain,
! [SV440: $i,SV454: $i,SV270: $i,SV350: $i,SV372: $i] :
( ( ( in @ ( sK23_D @ SV372 @ SV350 @ SV270 ) @ SV372 )
= $false )
| ( ( in @ SV454 @ SV350 )
= $false )
| ( ( in @ SV440 @ SV270 )
= $false )
| ( ( ( sK23_D @ SV372 @ SV350 @ SV270 )
= ( ordered_pair @ SV440 @ SV454 ) )
= $false )
| ( ( SV372
= ( cartesian_product2 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2559,plain,
! [SV373: $i,SV441: $i,SV270: $i,SV455: $i,SV351: $i,SV465: $i] :
( ( ( in @ SV465 @ SV351 )
= $false )
| ( ( in @ SV455 @ SV270 )
= $false )
| ( ( ( SV441
!= ( ordered_pair @ SV455 @ SV465 ) ) )
= $true )
| ( ( in @ SV441 @ SV373 )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2560,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 ) )
= $false )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2549]) ).
thf(2561,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( ~ ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 ) )
= $false )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2549]) ).
thf(2562,plain,
! [SV294: $i,SV400: $i,SV258: $i] :
( ( ( in @ ( subset_complement @ SV258 @ ( sK8_D @ SV400 @ SV294 @ SV258 ) ) @ SV294 )
= $false )
| ( ( in @ ( sK8_D @ SV400 @ SV294 @ SV258 ) @ SV400 )
= $false )
| ( ( SV400
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $true )
| ( ( element @ SV400 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2563,plain,
! [SV294: $i,SV258: $i,SV401: $i,SV470: $i] :
( ( ( in @ SV470 @ SV401 )
= $false )
| ( ( in @ ( subset_complement @ SV258 @ SV470 ) @ SV294 )
= $true )
| ( ( element @ SV470 @ ( powerset @ SV258 ) )
= $false )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2564,plain,
! [SV401: $i,SV294: $i,SV471: $i,SV258: $i] :
( ( ( in @ ( subset_complement @ SV258 @ SV471 ) @ SV294 )
= $false )
| ( ( in @ SV471 @ SV401 )
= $true )
| ( ( element @ SV471 @ ( powerset @ SV258 ) )
= $false )
| ( ( SV401
= ( complements_of_subsets @ SV258 @ SV294 ) )
= $false )
| ( ( element @ SV401 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false )
| ( ( element @ SV294 @ ( powerset @ ( powerset @ SV258 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2565,plain,
! [SV388: $i,SV413: $i,SV460: $i] :
( ( ( in @ SV460 @ ( sK31_D @ SV460 @ SV413 @ SV388 ) )
= $false )
| ( ( in @ SV460 @ SV413 )
= $true )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2566,plain,
! [SV413: $i,SV461: $i,SV388: $i,SV472: $i] :
( ( ( in @ SV472 @ SV388 )
= $false )
| ( ( in @ SV461 @ SV472 )
= $true )
| ( ( in @ SV461 @ SV413 )
= $false )
| ( ( SV413
= ( set_meet @ SV388 ) )
= $false )
| ( ( SV388 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2567,plain,
! [SV373: $i,SV351: $i,SV270: $i,SV465: $i,SV455: $i,SV441: $i] :
( ( ( SV441
= ( ordered_pair @ SV455 @ SV465 ) )
= $false )
| ( ( in @ SV455 @ SV270 )
= $false )
| ( ( in @ SV465 @ SV351 )
= $false )
| ( ( in @ SV441 @ SV373 )
= $true )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2568,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( in @ ( sK21_E @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV270 )
= $true )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2569,plain,
! [SV270: $i,SV351: $i,SV373: $i,SV442: $i] :
( ( ( in @ ( sK22_SY2051 @ SV442 @ SV373 @ SV351 @ SV270 ) @ SV351 )
= $true )
| ( ( in @ SV442 @ SV373 )
= $false )
| ( ( SV373
= ( cartesian_product2 @ SV270 @ SV351 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2561]) ).
thf(2570,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1472,2569,2568,2567,2566,2565,2564,2563,2562,2558,2555,2554,2550,2542,2539,2536,2535,2534,2533,2530,2529,2527,2526,2523,2520,2519,2512,2509,2508,2501,2500,2499,2496,2495,2489,2486,2481,2480,2479,2476,2475,2471,2462,2460,2457,2450,2448,2444,2437,2432,2431,2422,2399,2398,2393,2371,2357,2356,2341,2340,2338,2337,2331,2330,2326,2319,2318,2312,2308,2305,2304,2298,2295,2279,2278,2277,2270,2269,2268,2258,2255,2236,2235,2220,2214,2213,2208,2207,2201,2199,2186,2180,2179,2168,2164,2147,2136,2135,2120,2119,2118,2110,2079,2078,2069,2055,2048,2046,2039,2002,2001,2000,1969,1965,1964,1961,1960,1944,1929,1926,1920,1906,1871,1855,1852,1786,1785,1782,1780,1775,1714,1711,1708,1707,1703,1688,1687,1641,1640,1634,1630,1573,1528,1473]) ).
thf(2571,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2570,1418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 14:08:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41 ...
% 0.19/0.46
% 0.19/0.46 No.of.Axioms: 149
% 0.19/0.46
% 0.19/0.46 Length.of.Defs: 0
% 0.19/0.46
% 0.19/0.46 Contains.Choice.Funs: false
% 0.19/0.50 ..........
% 0.19/0.55 (rf:2,axioms:128,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:151,loop_count:0,foatp_calls:0,translation:fof_full).................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 75.41/75.72 ......ignored arguments false
% 75.44/75.79 ....
% 75.52/75.84 (rf:0,axioms:149,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:151,loop_count:0,foatp_calls:0,translation:fof_full)...................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 150.18/150.58 ...............
% 150.40/150.71 (rf:2,axioms:128,ps:0,u:1,ude:true,rLeibEQ:false,rAndEQ:false,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:151,loop_count:0,foatp_calls:0,translation:fof_full).................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 225.07/225.41 ..................
% 225.29/225.61 (rf:-1,axioms:53,ps:0,u:1,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:151,loop_count:0,foatp_calls:0,translation:fof_full).........................................................................................................................................................................................
% 231.00/231.33
% 231.00/231.33 ********************************
% 231.00/231.33 * All subproblems solved! *
% 231.00/231.33 ********************************
% 231.00/231.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:55,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:71,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2570,loop_count:0,foatp_calls:1,translation:fof_full)
% 232.87/233.20
% 232.87/233.20 %**** Beginning of derivation protocol ****
% 232.87/233.20 % SZS output start CNFRefutation
% See solution above
% 232.87/233.22
% 232.87/233.22 %**** End of derivation protocol ****
% 232.87/233.22 %**** no. of clauses in derivation: 2475 ****
% 232.87/233.22 %**** clause counter: 2570 ****
% 232.87/233.22
% 232.87/233.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:55,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:71,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2570,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------