TSTP Solution File: SEU188+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU188+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 : n015.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 12:07:53 EDT 2022
% Result : Theorem 1.10s 1.54s
% Output : CNFRefutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 210
% Syntax : Number of formulae : 2187 (1065 unt; 80 typ; 0 def)
% Number of atoms : 15352 (5488 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 34114 (5781 ~;5399 |; 364 &;22296 @)
% ( 96 <=>; 178 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 151 ( 151 >; 0 *; 0 +; 0 <<)
% Number of symbols : 83 ( 80 usr; 8 con; 0-5 aty)
% Number of variables : 6381 ( 0 ^6349 !; 32 ?;6381 :)
% 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_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_D,type,
sK10_D: $i > $i > $i > $i ).
thf(tp_sK11_SY304,type,
sK11_SY304: $i > $i > $i > $i ).
thf(tp_sK12_SY308,type,
sK12_SY308: $i > $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY309,type,
sK14_SY309: $i > $i > $i ).
thf(tp_sK15_D,type,
sK15_D: $i > $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_SY311,type,
sK18_SY311: $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_SY312,type,
sK22_SY312: $i > $i > $i > $i > $i ).
thf(tp_sK23_D,type,
sK23_D: $i > $i > $i > $i ).
thf(tp_sK24_SY315,type,
sK24_SY315: $i > $i > $i > $i ).
thf(tp_sK25_SY317,type,
sK25_SY317: $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_C,type,
sK29_C: $i > $i > $i ).
thf(tp_sK2_B,type,
sK2_B: $i > $i ).
thf(tp_sK30_C,type,
sK30_C: $i > $i > $i ).
thf(tp_sK31_C,type,
sK31_C: $i > $i > $i ).
thf(tp_sK32_B,type,
sK32_B: $i > $i ).
thf(tp_sK33_C,type,
sK33_C: $i > $i > $i ).
thf(tp_sK34_A,type,
sK34_A: $i ).
thf(tp_sK35_A,type,
sK35_A: $i ).
thf(tp_sK36_D,type,
sK36_D: $i > $i > $i > $i ).
thf(tp_sK37_C,type,
sK37_C: $i > $i > $i ).
thf(tp_sK38_SY323,type,
sK38_SY323: $i > $i > $i ).
thf(tp_sK39_D,type,
sK39_D: $i > $i > $i > $i ).
thf(tp_sK3_SY299,type,
sK3_SY299: $i > $i > $i ).
thf(tp_sK40_C,type,
sK40_C: $i > $i > $i ).
thf(tp_sK41_SY325,type,
sK41_SY325: $i > $i > $i ).
thf(tp_sK42_B,type,
sK42_B: $i > $i ).
thf(tp_sK43_D,type,
sK43_D: $i > $i > $i > $i ).
thf(tp_sK44_C,type,
sK44_C: $i > $i > $i ).
thf(tp_sK45_SY326,type,
sK45_SY326: $i > $i > $i ).
thf(tp_sK46_C,type,
sK46_C: $i > $i > $i ).
thf(tp_sK47_SY328,type,
sK47_SY328: $i > $i > $i ).
thf(tp_sK48_B,type,
sK48_B: $i > $i ).
thf(tp_sK49_B,type,
sK49_B: $i > $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_sK50_SY331,type,
sK50_SY331: $i > $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_B,type,
sK8_B: $i > $i ).
thf(tp_sK9_F,type,
sK9_F: $i > $i > $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/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(7,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(12,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(14,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(20,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(21,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(22,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(23,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(24,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(25,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(28,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(34,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(35,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(37,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(39,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(41,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(43,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(44,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(45,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(55,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(72,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(74,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(75,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(90,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(93,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(98,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(102,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(107,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(109,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(112,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(113,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(114,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(121,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(124,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(126,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(127,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(130,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(137,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(138,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(141,axiom,
! [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/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(142,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(145,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(146,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(148,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(151,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(152,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(167,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(169,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(170,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(171,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[170]) ).
thf(172,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[171]) ).
thf(173,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(174,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(175,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(176,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(177,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(178,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(184,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(185,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(186,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(187,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(191,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(192,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(194,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(195,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(196,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(197,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(198,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(199,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(201,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)],[79]) ).
thf(202,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)],[80]) ).
thf(203,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)],[83]) ).
thf(204,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(205,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)],[85]) ).
thf(206,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)],[86]) ).
thf(207,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)],[87]) ).
thf(208,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)],[88]) ).
thf(209,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(210,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(212,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(213,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(214,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(215,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(216,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(218,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(219,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(220,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(221,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(223,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(225,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(227,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)],[117]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(232,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)],[131]) ).
thf(233,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(234,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)],[134]) ).
thf(235,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(237,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)],[139]) ).
thf(238,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(239,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 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(240,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(241,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(242,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(243,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(245,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)],[152]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(247,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(248,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(249,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)],[157]) ).
thf(250,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(251,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)],[159]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(253,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)],[162]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(255,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(259,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(260,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(261,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(262,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(263,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(264,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(265,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(266,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(267,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(268,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(269,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(270,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(271,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(273,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(274,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(275,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(276,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(277,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(278,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)],[78]) ).
thf(279,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)],[82]) ).
thf(280,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(281,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)],[92]) ).
thf(282,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)],[93]) ).
thf(283,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(284,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(285,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(286,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(287,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(288,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(289,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(290,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(291,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(292,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(294,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(295,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)],[145]) ).
thf(296,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(297,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)],[147]) ).
thf(298,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(301,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(302,plain,
( ( ( relation @ sK1_A )
=> ( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
=> ( sK1_A = empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[172]) ).
thf(303,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[302]) ).
thf(304,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
= $true ),
inference(standard_cnf,[status(thm)],[302]) ).
thf(305,plain,
( ( sK1_A = empty_set )
= $false ),
inference(standard_cnf,[status(thm)],[302]) ).
thf(306,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[305]) ).
thf(307,plain,
( ( ! [A: $i] :
( ! [SY297: $i] :
( ~ ( subset @ SY297 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY297 @ ( sK2_B @ A ) )
| ( in @ SY297 @ ( sK2_B @ A ) ) )
& ! [SY298: $i] :
( ( ! [SY303: $i] :
( ~ ( subset @ SY303 @ SY298 )
| ( in @ SY303 @ ( sK3_SY299 @ SY298 @ A ) ) )
& ( in @ ( sK3_SY299 @ SY298 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY298 @ ( sK2_B @ A ) ) )
& ! [SY301: $i,SY302: $i] :
( ~ ( in @ SY301 @ ( sK2_B @ A ) )
| ~ ( subset @ SY302 @ SY301 )
| ( in @ SY302 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(310,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(311,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(312,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK4_C @ B @ A ) @ A )
| ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
& ( ( in @ ( sK4_C @ B @ A ) @ A )
| ( in @ ( sK4_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(314,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(317,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(318,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(319,plain,
( ( ! [A: $i] :
( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK6_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(320,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(321,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(322,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(323,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(325,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(326,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[193]) ).
thf(327,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[197]) ).
thf(328,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY307: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ SY307 ) @ A )
| ~ ( in @ ( ordered_pair @ SY307 @ ( sK11_SY304 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY304 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK12_SY308 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_SY308 @ C @ B @ A ) @ ( sK11_SY304 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY304 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_composition @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ! [F: $i] :
( ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B ) )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK9_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK9_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(329,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY309 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY309 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(330,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_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)],[201]) ).
thf(331,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY310: $i] :
( ~ ( in @ ( sK17_C @ B @ A ) @ SY310 )
| ~ ( in @ SY310 @ A ) )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK17_C @ B @ A ) @ ( sK18_SY311 @ B @ A ) )
& ( in @ ( sK18_SY311 @ B @ A ) @ A ) )
| ( in @ ( sK17_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 @ ( sK16_D @ C @ B @ A ) )
& ( in @ ( sK16_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[202]) ).
thf(332,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)],[203]) ).
thf(333,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)],[204]) ).
thf(334,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY313: $i,SY314: $i] :
( ~ ( in @ SY313 @ A )
| ~ ( in @ SY314 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY313 @ SY314 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY315 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY317 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY315 @ C @ B @ A ) @ ( sK25_SY317 @ 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_SY312 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY312 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(335,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)],[206]) ).
thf(336,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)],[207]) ).
thf(337,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)],[208]) ).
thf(338,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)],[209]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK29_C @ B @ A )
!= A )
| ~ ( in @ ( sK29_C @ B @ A ) @ B ) )
& ( ( ( sK29_C @ B @ A )
= A )
| ( in @ ( sK29_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)],[210]) ).
thf(340,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[214]) ).
thf(342,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[215]) ).
thf(343,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[217]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[218]) ).
thf(345,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[219]) ).
thf(346,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[220]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[222]) ).
thf(348,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)],[224]) ).
thf(349,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[225]) ).
thf(350,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[226]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK30_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)],[227]) ).
thf(352,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[229]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[230]) ).
thf(354,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK31_C @ B @ A ) @ A )
& ( in @ ( sK31_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)],[232]) ).
thf(355,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)],[234]) ).
thf(356,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)],[235]) ).
thf(357,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)],[237]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[238]) ).
thf(359,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[239]) ).
thf(360,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(361,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[241]) ).
thf(362,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[242]) ).
thf(363,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[243]) ).
thf(364,plain,
( ( ! [A: $i] :
( ! [SY318: $i] :
( ~ ( subset @ SY318 @ ( sK32_B @ A ) )
| ( are_equipotent @ SY318 @ ( sK32_B @ A ) )
| ( in @ SY318 @ ( sK32_B @ A ) ) )
& ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK32_B @ A ) )
| ( in @ ( powerset @ SY319 ) @ ( sK32_B @ A ) ) )
& ! [SY320: $i,SY321: $i] :
( ~ ( in @ SY320 @ ( sK32_B @ A ) )
| ~ ( subset @ SY321 @ SY320 )
| ( in @ SY321 @ ( sK32_B @ A ) ) )
& ( in @ A @ ( sK32_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(366,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(367,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(368,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)],[249]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK33_C @ B @ A ) @ A )
& ~ ( in @ ( sK33_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(370,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)],[251]) ).
thf(371,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(372,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)],[253]) ).
thf(373,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[254]) ).
thf(374,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)],[255]) ).
thf(375,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[256]) ).
thf(376,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[257]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(378,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(379,plain,
( ( ~ ( empty @ sK34_A )
& ( relation @ sK34_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[264]) ).
thf(380,plain,
( ( ( empty @ sK35_A )
& ( relation @ sK35_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(381,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[266]) ).
thf(382,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(383,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(384,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[269]) ).
thf(385,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[270]) ).
thf(386,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[272]) ).
thf(387,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[274]) ).
thf(388,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[275]) ).
thf(389,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(390,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[277]) ).
thf(391,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY322: $i] :
~ ( in @ ( ordered_pair @ SY322 @ ( sK37_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK37_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK38_SY323 @ B @ A ) @ ( sK37_C @ B @ A ) ) @ A )
| ( in @ ( sK37_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 @ ( sK36_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(392,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY324: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ SY324 ) @ A )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY325 @ B @ A ) ) @ A )
| ( in @ ( sK40_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 @ ( sK39_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[279]) ).
thf(393,plain,
( ( ! [A: $i] :
( ( in @ ( sK42_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(394,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK45_SY326 @ B @ A ) @ A )
& ~ ( in @ ( sK44_C @ B @ A ) @ ( sK45_SY326 @ B @ A ) ) )
| ~ ( in @ ( sK44_C @ B @ A ) @ B ) )
& ( ! [SY327: $i] :
( ~ ( in @ SY327 @ A )
| ( in @ ( sK44_C @ B @ A ) @ SY327 ) )
| ( in @ ( sK44_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK43_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK43_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)],[281]) ).
thf(395,plain,
( ( ! [A: $i] :
( ( ! [SY329: $i,SY330: $i] :
( ( sK48_B @ A )
!= ( ordered_pair @ SY329 @ SY330 ) )
& ( in @ ( sK48_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK46_C @ B @ A ) @ ( sK47_SY328 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(396,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[283]) ).
thf(397,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK49_B @ A ) @ ( sK50_SY331 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(398,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(399,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(400,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[288]) ).
thf(401,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[289]) ).
thf(402,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[290]) ).
thf(403,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[291]) ).
thf(404,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[292]) ).
thf(405,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[293]) ).
thf(406,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)],[295]) ).
thf(407,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[296]) ).
thf(408,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)],[297]) ).
thf(409,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[299]) ).
thf(410,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(411,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[301]) ).
thf(412,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(413,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(414,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(415,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(416,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)],[408]) ).
thf(417,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(418,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)],[406]) ).
thf(419,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(420,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(421,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(422,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(423,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(424,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(425,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(426,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(427,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(428,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK49_B @ A ) @ ( sK50_SY331 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(429,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(430,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(431,plain,
( ( ! [A: $i] :
( ( ! [SY329: $i,SY330: $i] :
( ( sK48_B @ A )
!= ( ordered_pair @ SY329 @ SY330 ) )
& ( in @ ( sK48_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK46_C @ B @ A ) @ ( sK47_SY328 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(432,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK45_SY326 @ B @ A ) @ A )
& ~ ( in @ ( sK44_C @ B @ A ) @ ( sK45_SY326 @ B @ A ) ) )
| ~ ( in @ ( sK44_C @ B @ A ) @ B ) )
& ( ! [SY327: $i] :
( ~ ( in @ SY327 @ A )
| ( in @ ( sK44_C @ B @ A ) @ SY327 ) )
| ( in @ ( sK44_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK43_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK43_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)],[394]) ).
thf(433,plain,
( ( ! [A: $i] :
( ( in @ ( sK42_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(434,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY324: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ SY324 ) @ A )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY325 @ B @ A ) ) @ A )
| ( in @ ( sK40_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 @ ( sK39_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(435,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY322: $i] :
~ ( in @ ( ordered_pair @ SY322 @ ( sK37_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK37_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK38_SY323 @ B @ A ) @ ( sK37_C @ B @ A ) ) @ A )
| ( in @ ( sK37_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 @ ( sK36_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(436,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(437,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(438,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(439,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(440,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(442,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(443,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(444,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(445,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(446,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(447,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(448,plain,
( ( ( empty @ sK35_A )
& ( relation @ sK35_A ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(449,plain,
( ( ~ ( empty @ sK34_A )
& ( relation @ sK34_A ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(450,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(451,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(452,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(453,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(454,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(456,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(458,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)],[374]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(460,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)],[372]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(462,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)],[370]) ).
thf(463,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK33_C @ B @ A ) @ A )
& ~ ( in @ ( sK33_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(464,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)],[368]) ).
thf(465,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(466,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(467,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(468,plain,
( ( ! [A: $i] :
( ! [SY318: $i] :
( ~ ( subset @ SY318 @ ( sK32_B @ A ) )
| ( are_equipotent @ SY318 @ ( sK32_B @ A ) )
| ( in @ SY318 @ ( sK32_B @ A ) ) )
& ! [SY319: $i] :
( ~ ( in @ SY319 @ ( sK32_B @ A ) )
| ( in @ ( powerset @ SY319 ) @ ( sK32_B @ A ) ) )
& ! [SY320: $i,SY321: $i] :
( ~ ( in @ SY320 @ ( sK32_B @ A ) )
| ~ ( subset @ SY321 @ SY320 )
| ( in @ SY321 @ ( sK32_B @ A ) ) )
& ( in @ A @ ( sK32_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(469,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(470,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(471,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(472,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(473,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(474,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(475,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(476,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)],[357]) ).
thf(477,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(478,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)],[356]) ).
thf(479,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)],[355]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(481,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK31_C @ B @ A ) @ A )
& ( in @ ( sK31_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(482,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(484,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(485,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK30_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)],[351]) ).
thf(487,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(488,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(489,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)],[348]) ).
thf(490,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(491,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(494,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(497,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(498,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(500,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(503,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK29_C @ B @ A )
!= A )
| ~ ( in @ ( sK29_C @ B @ A ) @ B ) )
& ( ( ( sK29_C @ B @ A )
= A )
| ( in @ ( sK29_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)],[339]) ).
thf(504,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)],[338]) ).
thf(505,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)],[337]) ).
thf(506,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)],[336]) ).
thf(507,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)],[335]) ).
thf(508,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY313: $i,SY314: $i] :
( ~ ( in @ SY313 @ A )
| ~ ( in @ SY314 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY313 @ SY314 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY315 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY317 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY315 @ C @ B @ A ) @ ( sK25_SY317 @ 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_SY312 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY312 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(509,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)],[333]) ).
thf(510,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)],[332]) ).
thf(511,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY310: $i] :
( ~ ( in @ ( sK17_C @ B @ A ) @ SY310 )
| ~ ( in @ SY310 @ A ) )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK17_C @ B @ A ) @ ( sK18_SY311 @ B @ A ) )
& ( in @ ( sK18_SY311 @ B @ A ) @ A ) )
| ( in @ ( sK17_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 @ ( sK16_D @ C @ B @ A ) )
& ( in @ ( sK16_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(512,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_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)],[330]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(514,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY309 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY309 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(515,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY307: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ SY307 ) @ A )
| ~ ( in @ ( ordered_pair @ SY307 @ ( sK11_SY304 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY304 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK12_SY308 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_SY308 @ C @ B @ A ) @ ( sK11_SY304 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY304 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_composition @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ! [F: $i] :
( ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B ) )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK9_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK9_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(517,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(518,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(519,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(520,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(521,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(522,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(523,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(524,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(525,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(526,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(527,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(528,plain,
( ( ! [A: $i] :
( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK6_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(529,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(530,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(534,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK4_C @ B @ A ) @ A )
| ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
& ( ( in @ ( sK4_C @ B @ A ) @ A )
| ( in @ ( sK4_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(535,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(536,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(537,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(540,plain,
( ( ! [A: $i] :
( ! [SY297: $i] :
( ~ ( subset @ SY297 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY297 @ ( sK2_B @ A ) )
| ( in @ SY297 @ ( sK2_B @ A ) ) )
& ! [SY298: $i] :
( ( ! [SY303: $i] :
( ~ ( subset @ SY303 @ SY298 )
| ( in @ SY303 @ ( sK3_SY299 @ SY298 @ A ) ) )
& ( in @ ( sK3_SY299 @ SY298 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY298 @ ( sK2_B @ A ) ) )
& ! [SY301: $i,SY302: $i] :
( ~ ( in @ SY301 @ ( sK2_B @ A ) )
| ~ ( subset @ SY302 @ SY301 )
| ( in @ SY302 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(541,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(542,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(543,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(544,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK30_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)],[486]) ).
thf(545,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)],[510]) ).
thf(546,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)],[462]) ).
thf(547,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(548,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)],[418]) ).
thf(549,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK11_SY304 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY304 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY308 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY304 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY304 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) )
| ( SX2
= ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_composition @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ! [SX5: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ ( sK9_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(550,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK37_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK37_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SX1 @ SX0 ) @ ( sK37_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK37_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 @ ( sK36_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(551,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)],[506]) ).
thf(552,plain,
( ( ~ ( ~ ( empty @ sK35_A )
| ~ ( relation @ sK35_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(553,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)],[504]) ).
thf(554,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK48_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK48_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK46_C @ SX1 @ SX0 ) @ ( sK47_SY328 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(555,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)],[489]) ).
thf(556,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(557,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK6_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK6_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(558,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)],[478]) ).
thf(559,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_SY315 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_SY317 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK24_SY315 @ SX2 @ SX1 @ SX0 ) @ ( sK25_SY317 @ 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_SY312 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY312 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(560,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)],[464]) ).
thf(561,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)],[505]) ).
thf(562,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(563,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)],[507]) ).
thf(564,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)],[509]) ).
thf(565,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)],[476]) ).
thf(566,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(567,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK2_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK2_B @ SX0 ) )
| ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK3_SY299 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK3_SY299 @ SX1 @ SX0 ) @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK2_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK2_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(568,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)],[458]) ).
thf(569,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY311 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY311 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_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 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(570,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY325 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK40_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 @ ( sK39_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(571,plain,
( ( ~ ( ~ ~ ( empty @ sK34_A )
| ~ ( relation @ sK34_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(572,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(573,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(574,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(575,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(576,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK32_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK32_B @ SX0 ) )
| ( in @ SX1 @ ( sK32_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK32_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK32_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK32_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK32_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK32_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(577,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(578,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(579,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(580,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(581,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)],[479]) ).
thf(582,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY309 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY309 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( relation_inverse @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(583,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK29_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK29_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK29_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)],[503]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK33_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK33_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(585,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_field @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(586,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(587,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK31_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK31_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)],[481]) ).
thf(588,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK15_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)],[512]) ).
thf(589,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(590,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(591,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(592,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY326 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK43_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)],[432]) ).
thf(593,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)],[416]) ).
thf(594,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(595,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(596,plain,
! [SV1: $i] :
( ( ( ( singleton @ SV1 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(597,plain,
! [SV2: $i] :
( ( ~ ( relation @ SV2 )
| ( subset @ SV2 @ ( cartesian_product2 @ ( relation_dom @ SV2 ) @ ( relation_rng @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(598,plain,
! [SV3: $i] :
( ( subset @ empty_set @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(599,plain,
! [SV4: $i] :
( ( ~ ( subset @ SV4 @ empty_set )
| ( SV4 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(600,plain,
! [SV5: $i] :
( ( ~ ( relation @ SV5 )
| ! [SY332: $i] :
( ~ ( relation @ SY332 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SY332 ) ) @ ( relation_dom @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(601,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ! [SY333: $i] :
( ~ ( relation @ SY333 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SY333 ) ) @ ( relation_rng @ SY333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(602,plain,
! [SV7: $i] :
( ( ~ ( relation @ SV7 )
| ! [SY334: $i] :
( ~ ( relation @ SY334 )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SY334 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SY334 ) )
= ( relation_dom @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(603,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ! [SY335: $i] :
( ~ ( relation @ SY335 )
| ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SY335 ) )
| ( ( relation_rng @ ( relation_composition @ SY335 @ SV8 ) )
= ( relation_rng @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(604,plain,
! [SV9: $i] :
( ( ~ ( relation @ SV9 )
| ( in @ ( ordered_pair @ ( sK49_B @ SV9 ) @ ( sK50_SY331 @ SV9 ) ) @ SV9 )
| ( SV9 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(605,plain,
! [SV10: $i] :
( ( ~ ( empty @ SV10 )
| ( relation @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(606,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(607,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ( relation @ ( relation_inverse @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(608,plain,
! [SV13: $i] :
( ( ! [SY336: $i] :
( ~ ( relation @ SV13 )
| ~ ( relation @ SY336 )
| ( relation @ ( relation_composition @ SV13 @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(609,plain,
! [SV14: $i] :
( ( ! [SY337: $i] :
( ~ ( relation @ SV14 )
| ~ ( relation @ SY337 )
| ( relation @ ( set_union2 @ SV14 @ SY337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(610,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
| ~ ( relation @ SV15 )
| ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(611,plain,
! [SV16: $i] :
( ( ( empty @ SV16 )
| ~ ( relation @ SV16 )
| ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(612,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(613,plain,
! [SV18: $i] :
( ( ( set_union2 @ SV18 @ empty_set )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(614,plain,
! [SV19: $i] :
( ( ( set_intersection2 @ SV19 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(615,plain,
! [SV20: $i] :
( ( ( set_difference @ SV20 @ empty_set )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(616,plain,
! [SV21: $i] :
( ( ( set_difference @ empty_set @ SV21 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(617,plain,
! [SV22: $i] :
( ( ~ ( empty @ SV22 )
| ( SV22 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(618,plain,
! [SV23: $i] :
( ( ! [SY338: $i] :
( ~ ( in @ SV23 @ SY338 )
| ( ( set_union2 @ ( singleton @ SV23 ) @ SY338 )
= SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(619,plain,
! [SV24: $i] :
( ( ! [SY339: $i] :
( ~ ( disjoint @ ( singleton @ SV24 ) @ SY339 )
| ~ ( in @ SV24 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(620,plain,
! [SV25: $i] :
( ( ! [SY340: $i] :
( ( in @ SV25 @ SY340 )
| ( disjoint @ ( singleton @ SV25 ) @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(621,plain,
! [SV26: $i] :
( ( ! [SY341: $i] :
( ~ ( element @ SY341 @ ( powerset @ SV26 ) )
| ! [SY342: $i] :
( ~ ( in @ SY342 @ SY341 )
| ( in @ SY342 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(622,plain,
! [SV27: $i] :
( ( ! [SY343: $i] :
( ~ ( subset @ SV27 @ SY343 )
| ! [SY344: $i] :
( ( in @ SY344 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SY343 @ ( singleton @ SY344 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(623,plain,
! [SV28: $i] :
( ( ! [SY345: $i] :
( ~ ( in @ SV28 @ SY345 )
| ( subset @ SV28 @ ( union @ SY345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(624,plain,
! [SV29: $i] :
( ( ! [SY346: $i,SY347: $i,SY348: $i] :
( ~ ( subset @ SV29 @ SY346 )
| ~ ( subset @ SY347 @ SY348 )
| ( subset @ ( cartesian_product2 @ SV29 @ SY347 ) @ ( cartesian_product2 @ SY346 @ SY348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(625,plain,
! [SV30: $i] :
( ( ! [SY349: $i] :
( ~ ( subset @ SV30 @ SY349 )
| ( ( set_union2 @ SV30 @ SY349 )
= SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(626,plain,
! [SV31: $i] :
( ( ! [SY350: $i] : ( subset @ ( set_intersection2 @ SV31 @ SY350 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(627,plain,
! [SV32: $i] :
( ( ! [SY351: $i,SY352: $i] :
( ~ ( subset @ SV32 @ SY351 )
| ~ ( subset @ SV32 @ SY352 )
| ( subset @ SV32 @ ( set_intersection2 @ SY351 @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(628,plain,
! [SV33: $i] :
( ( ! [SY353: $i,SY354: $i] :
( ~ ( subset @ SV33 @ SY353 )
| ~ ( subset @ SY353 @ SY354 )
| ( subset @ SV33 @ SY354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(629,plain,
! [SV34: $i] :
( ( ! [SY355: $i] :
( ~ ( subset @ SV34 @ SY355 )
| ! [SY356: $i] : ( subset @ ( set_intersection2 @ SV34 @ SY356 ) @ ( set_intersection2 @ SY355 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(630,plain,
! [SV35: $i] :
( ( ! [SY357: $i] :
( ~ ( subset @ SV35 @ SY357 )
| ( ( set_intersection2 @ SV35 @ SY357 )
= SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(631,plain,
! [SV36: $i] :
( ( ! [SY358: $i] :
( ~ ( subset @ SV36 @ SY358 )
| ! [SY359: $i] : ( subset @ ( set_difference @ SV36 @ SY359 ) @ ( set_difference @ SY358 @ SY359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(632,plain,
! [SV37: $i] :
( ( ! [SY360: $i] : ( subset @ ( set_difference @ SV37 @ SY360 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(633,plain,
! [SV38: $i] :
( ( ! [SY361: $i] :
( ( set_union2 @ SV38 @ ( set_difference @ SY361 @ SV38 ) )
= ( set_union2 @ SV38 @ SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(634,plain,
! [SV39: $i] :
( ( ! [SY362: $i] :
( ( set_difference @ ( set_union2 @ SV39 @ SY362 ) @ SY362 )
= ( set_difference @ SV39 @ SY362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(635,plain,
! [SV40: $i] :
( ( ! [SY363: $i] :
( ~ ( subset @ SV40 @ SY363 )
| ( SY363
= ( set_union2 @ SV40 @ ( set_difference @ SY363 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(636,plain,
! [SV41: $i] :
( ( ! [SY364: $i] :
( ~ ( in @ SV41 @ SY364 )
| ( ( set_union2 @ ( singleton @ SV41 ) @ SY364 )
= SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(637,plain,
! [SV42: $i] :
( ( ! [SY365: $i] :
( ( set_difference @ SV42 @ ( set_difference @ SV42 @ SY365 ) )
= ( set_intersection2 @ SV42 @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(638,plain,
! [SV43: $i] :
( ( ! [SY366: $i] :
( ~ ( proper_subset @ SY366 @ SV43 )
| ~ ( subset @ SV43 @ SY366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(639,plain,
! [SV44: $i] :
( ( ! [SY367: $i,SY368: $i] :
( ~ ( disjoint @ SY367 @ SY368 )
| ~ ( subset @ SV44 @ SY367 )
| ( disjoint @ SV44 @ SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(640,plain,
! [SV45: $i] :
( ( ( unordered_pair @ SV45 @ SV45 )
= ( singleton @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(641,plain,
! [SV46: $i] :
( ( ! [SY369: $i] :
( ~ ( subset @ ( singleton @ SV46 ) @ ( singleton @ SY369 ) )
| ( SV46 = SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(642,plain,
! [SV47: $i] :
( ( ! [SY370: $i] : ( subset @ SV47 @ ( set_union2 @ SV47 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(643,plain,
! [SV48: $i] :
( ( ! [SY371: $i,SY372: $i] :
( ~ ( subset @ SV48 @ SY371 )
| ~ ( subset @ SY372 @ SY371 )
| ( subset @ ( set_union2 @ SV48 @ SY372 ) @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(644,plain,
! [SV49: $i] :
( ( ! [SY373: $i] :
( ! [SY374: $i] :
( ( singleton @ SV49 )
!= ( unordered_pair @ SY373 @ SY374 ) )
| ( SV49 = SY373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(645,plain,
! [SV50: $i] :
( ( ! [SY375: $i] :
( ~ ( in @ SV50 @ SY375 )
| ( subset @ SV50 @ ( union @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(646,plain,
! [SV51: $i] :
( ( ( union @ ( powerset @ SV51 ) )
= SV51 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(647,plain,
! [SV52: $i] :
( ( ! [SY376: $i,SY377: $i] :
( ( ( singleton @ SV52 )
!= ( unordered_pair @ SY376 @ SY377 ) )
| ( SY376 = SY377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(648,plain,
! [SV53: $i] :
( ( ! [SY378: $i] :
( ~ ( in @ SV53 @ SY378 )
| ~ ( in @ SY378 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(649,plain,
! [SV54: $i] :
( ( ! [SY379: $i] :
( ( set_union2 @ SV54 @ SY379 )
= ( set_union2 @ SY379 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(650,plain,
! [SV55: $i] :
( ( ! [SY380: $i] :
( ( set_intersection2 @ SV55 @ SY380 )
= ( set_intersection2 @ SY380 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(651,plain,
! [SV56: $i] :
( ( ! [SY381: $i] :
( ( ordered_pair @ SV56 @ SY381 )
= ( unordered_pair @ ( unordered_pair @ SV56 @ SY381 ) @ ( singleton @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(652,plain,
! [SV57: $i] :
( ( ~ ( empty @ ( powerset @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(653,plain,
! [SV58: $i] :
( ( ! [SY382: $i] :
~ ( empty @ ( ordered_pair @ SV58 @ SY382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(654,plain,
! [SV59: $i] :
( ( ~ ( empty @ ( singleton @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(655,plain,
! [SV60: $i] :
( ( ( empty @ SV60 )
| ! [SY383: $i] :
~ ( empty @ ( set_union2 @ SV60 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(656,plain,
! [SV61: $i] :
( ( ! [SY384: $i] :
~ ( empty @ ( unordered_pair @ SV61 @ SY384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(657,plain,
! [SV62: $i] :
( ( ( empty @ SV62 )
| ! [SY385: $i] :
~ ( empty @ ( set_union2 @ SY385 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(658,plain,
! [SV63: $i] :
( ( ! [SY386: $i] :
( ( empty @ SV63 )
| ( empty @ SY386 )
| ~ ( empty @ ( cartesian_product2 @ SV63 @ SY386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(659,plain,
! [SV64: $i] :
( ( ( set_union2 @ SV64 @ SV64 )
= SV64 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(660,plain,
! [SV65: $i] :
( ( ( set_intersection2 @ SV65 @ SV65 )
= SV65 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(661,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(662,plain,
! [SV66: $i] :
( ( subset @ SV66 @ SV66 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(663,plain,
! [SV67: $i] :
( ( ! [SY387: $i] :
( ~ ( disjoint @ SV67 @ SY387 )
| ( disjoint @ SY387 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(664,plain,
! [SV68: $i] :
( ( ! [SY388: $i] :
( ~ ( in @ SV68 @ SY388 )
| ( element @ SV68 @ SY388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(665,plain,
! [SV69: $i] :
( ( ! [SY389: $i] :
( ~ ( element @ SV69 @ SY389 )
| ( empty @ SY389 )
| ( in @ SV69 @ SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(666,plain,
! [SV70: $i] :
( ( ! [SY390: $i,SY391: $i] :
( ~ ( element @ SY390 @ ( powerset @ SY391 ) )
| ~ ( in @ SV70 @ SY390 )
| ( element @ SV70 @ SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(667,plain,
! [SV71: $i] :
( ( ! [SY392: $i,SY393: $i] :
( ~ ( element @ SY392 @ ( powerset @ SY393 ) )
| ~ ( in @ SV71 @ SY392 )
| ~ ( empty @ SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(668,plain,
! [SV72: $i] :
( ( ! [SY394: $i] :
( ~ ( empty @ SY394 )
| ~ ( in @ SV72 @ SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(669,plain,
! [SV73: $i] :
( ( ! [SY395: $i] :
( ( SV73 = SY395 )
| ~ ( empty @ SV73 )
| ~ ( empty @ SY395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(670,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
= $true )
| ( ( ( relation_rng @ sK1_A )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(671,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(672,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK30_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)],[544]) ).
thf(673,plain,
! [SV74: $i] :
( ( ~ ( ~ ! [SY396: $i,SY397: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY396 )
| ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) )
| ~ ( ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY396 )
| ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) ) ) )
| ( SY397
= ( set_intersection2 @ SV74 @ SY396 ) ) )
| ~ ! [SY398: $i,SY399: $i] :
( ( SY399
!= ( set_intersection2 @ SV74 @ SY398 ) )
| ~ ( ~ ! [SY400: $i] :
( ~ ( in @ SY400 @ SV74 )
| ~ ( in @ SY400 @ SY398 )
| ( in @ SY400 @ SY399 ) )
| ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY399 )
| ( in @ SY401 @ SV74 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY399 )
| ( in @ SX3 @ SY398 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(674,plain,
! [SV75: $i] :
( ( ! [SY403: $i] :
~ ( ~ ! [SY404: $i,SY405: $i] :
( ~ ( in @ SV75 @ SY404 )
| ~ ( in @ SY403 @ SY405 )
| ( in @ ( ordered_pair @ SV75 @ SY403 ) @ ( cartesian_product2 @ SY404 @ SY405 ) ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ! [SY407: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SY403 ) @ ( cartesian_product2 @ SY406 @ SY407 ) )
| ( in @ SV75 @ SY406 ) )
| ~ ! [SY408: $i,SY409: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SY403 ) @ ( cartesian_product2 @ SY408 @ SY409 ) )
| ( in @ SY403 @ SY409 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(675,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(676,plain,
! [SV76: $i] :
( ( ~ ( relation @ SV76 )
| ~ ( ~ ! [SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( subset @ SV76 @ SY410 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SY410 ) ) )
| ~ ! [SY411: $i] :
( ~ ( relation @ SY411 )
| ~ ( subset @ SV76 @ SY411 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SY411 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(677,plain,
! [SV77: $i] :
( ( ~ ( relation @ SV77 )
| ! [SY412: $i] :
( ~ ( relation @ SY412 )
| ~ ( ~ ! [SY413: $i] :
( ~ ( relation @ SY413 )
| ~ ( ~ ( ! [SY414: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ SY414 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY414 @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY412 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY413 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK12_SY308 @ SY413 @ SY412 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY412 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY413 ) ) )
| ( SY413
= ( relation_composition @ SV77 @ SY412 ) ) )
| ~ ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ( SY415
!= ( relation_composition @ SV77 @ SY412 ) )
| ~ ( ~ ! [SY416: $i,SY417: $i] :
( ! [SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY416 @ SY418 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY418 @ SY417 ) @ SY412 ) )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SY415 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY415 )
| ~ ( ~ ( in @ ( ordered_pair @ SY419 @ ( sK9_F @ SY420 @ SY419 @ SY415 @ SY412 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY420 @ SY419 @ SY415 @ SY412 @ SV77 ) @ SY420 ) @ SY412 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(678,plain,
! [SV78: $i] :
( ( ~ ( relation @ SV78 )
| ~ ( ~ ! [SY421: $i] :
( ~ ( ~ ( ! [SY422: $i] :
~ ( in @ ( ordered_pair @ SY422 @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SY421 @ SV78 ) @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) ) )
| ( SY421
= ( relation_rng @ SV78 ) ) )
| ~ ! [SY423: $i] :
( ( SY423
!= ( relation_rng @ SV78 ) )
| ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY424 ) @ SV78 )
| ( in @ SY424 @ SY423 ) )
| ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY423 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY426 @ SY423 @ SV78 ) @ SY426 ) @ SV78 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(679,plain,
! [SV79: $i] :
( ( ~ ( ~ ! [SY427: $i,SY428: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
!= SY427 ) ) )
| ~ ( ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
= SV79 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
= SY427 ) ) )
| ( SY428
= ( unordered_pair @ SV79 @ SY427 ) ) )
| ~ ! [SY429: $i,SY430: $i] :
( ( SY430
!= ( unordered_pair @ SV79 @ SY429 ) )
| ~ ( ~ ! [SY431: $i] :
( ~ ( in @ SY431 @ SY430 )
| ( SY431 = SV79 )
| ( SY431 = SY429 ) )
| ~ ~ ( ~ ! [SY432: $i] :
( ( SY432 != SV79 )
| ( in @ SY432 @ SY430 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY429 )
| ( in @ SX3 @ SY430 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(680,plain,
( ( ~ ( empty @ sK35_A )
| ~ ( relation @ sK35_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(681,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)],[553]) ).
thf(682,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK48_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK48_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK46_C @ SX1 @ SX0 ) @ ( sK47_SY328 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(683,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)],[555]) ).
thf(684,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(685,plain,
! [SV80: $i] :
( ( ~ ( ~ ( element @ ( sK6_B @ SV80 ) @ ( powerset @ SV80 ) )
| ~ ( empty @ ( sK6_B @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(686,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)],[558]) ).
thf(687,plain,
! [SV81: $i] :
( ( ~ ( ~ ! [SY434: $i,SY435: $i] :
( ~ ( ~ ( ! [SY436: $i,SY437: $i] :
( ~ ( in @ SY436 @ SV81 )
| ~ ( in @ SY437 @ SY434 )
| ( ( sK23_D @ SY435 @ SY434 @ SV81 )
!= ( ordered_pair @ SY436 @ SY437 ) ) )
| ~ ( in @ ( sK23_D @ SY435 @ SY434 @ SV81 ) @ SY435 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SY435 @ SY434 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SY435 @ SY434 @ SV81 ) @ SY434 ) )
| ( ( sK23_D @ SY435 @ SY434 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SY435 @ SY434 @ SV81 ) @ ( sK25_SY317 @ SY435 @ SY434 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SY435 @ SY434 @ SV81 ) @ SY435 ) ) )
| ( SY435
= ( cartesian_product2 @ SV81 @ SY434 ) ) )
| ~ ! [SY438: $i,SY439: $i] :
( ( SY439
!= ( cartesian_product2 @ SV81 @ SY438 ) )
| ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i,SY442: $i] :
( ~ ( in @ SY441 @ SV81 )
| ~ ( in @ SY442 @ SY438 )
| ( SY440
!= ( ordered_pair @ SY441 @ SY442 ) ) )
| ( in @ SY440 @ SY439 ) )
| ~ ! [SY443: $i] :
( ~ ( in @ SY443 @ SY439 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY443 @ SY439 @ SY438 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY443 @ SY439 @ SY438 @ SV81 ) @ SY438 ) )
| ( SY443
!= ( ordered_pair @ ( sK21_E @ SY443 @ SY439 @ SY438 @ SV81 ) @ ( sK22_SY312 @ SY443 @ SY439 @ SY438 @ SV81 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(688,plain,
! [SV82: $i] :
( ( ! [SY444: $i] :
~ ( ~ ! [SY445: $i,SY446: $i] :
( ~ ( in @ SV82 @ SY445 )
| ~ ( in @ SY444 @ SY446 )
| ( in @ ( ordered_pair @ SV82 @ SY444 ) @ ( cartesian_product2 @ SY445 @ SY446 ) ) )
| ~ ~ ( ~ ! [SY447: $i] :
( ! [SY448: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SY444 ) @ ( cartesian_product2 @ SY447 @ SY448 ) )
| ( in @ SV82 @ SY447 ) )
| ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SY444 ) @ ( cartesian_product2 @ SY449 @ SY450 ) )
| ( in @ SY444 @ SY450 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(689,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)],[561]) ).
thf(690,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(691,plain,
! [SV83: $i] :
( ( ~ ( ~ ! [SY451: $i,SY452: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY451 ) ) )
| ~ ( ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY451 ) ) )
| ( SY452
= ( set_union2 @ SV83 @ SY451 ) ) )
| ~ ! [SY453: $i,SY454: $i] :
( ( SY454
!= ( set_union2 @ SV83 @ SY453 ) )
| ~ ( ~ ! [SY455: $i] :
( ~ ( in @ SY455 @ SY454 )
| ( in @ SY455 @ SV83 )
| ( in @ SY455 @ SY453 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ~ ( in @ SY456 @ SV83 )
| ( in @ SY456 @ SY454 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY453 )
| ( in @ SX3 @ SY454 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(692,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)],[564]) ).
thf(693,plain,
! [SV84: $i] :
( ( ! [SY458: $i] :
~ ( ~ ! [SY459: $i] :
( ! [SY460: $i] :
( ( ordered_pair @ SV84 @ SY458 )
!= ( ordered_pair @ SY459 @ SY460 ) )
| ( SV84 = SY459 ) )
| ~ ! [SY461: $i,SY462: $i] :
( ( ( ordered_pair @ SV84 @ SY458 )
!= ( ordered_pair @ SY461 @ SY462 ) )
| ( SY458 = SY462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(694,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(695,plain,
! [SV85: $i] :
( ( ~ ( ~ ! [SY463: $i] :
( ~ ( subset @ SY463 @ ( sK2_B @ SV85 ) )
| ( are_equipotent @ SY463 @ ( sK2_B @ SV85 ) )
| ( in @ SY463 @ ( sK2_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY464: $i] :
( ~ ( ~ ! [SY465: $i] :
( ~ ( subset @ SY465 @ SY464 )
| ( in @ SY465 @ ( sK3_SY299 @ SY464 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SY464 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SY464 @ ( sK2_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(696,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)],[568]) ).
thf(697,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY311 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY311 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_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 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(698,plain,
! [SV86: $i] :
( ( ~ ( relation @ SV86 )
| ~ ( ~ ! [SY468: $i] :
( ~ ( ~ ( ! [SY469: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ SY469 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ ( sK41_SY325 @ SY468 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) ) )
| ( SY468
= ( relation_dom @ SV86 ) ) )
| ~ ! [SY470: $i] :
( ( SY470
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY471: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY472 ) @ SV86 )
| ( in @ SY471 @ SY470 ) )
| ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ SY470 )
| ( in @ ( ordered_pair @ SY473 @ ( sK39_D @ SY473 @ SY470 @ SV86 ) ) @ SV86 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(699,plain,
( ( ~ ~ ( empty @ sK34_A )
| ~ ( relation @ sK34_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(700,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(701,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(702,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(703,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(704,plain,
! [SV87: $i] :
( ( ~ ( ~ ! [SY474: $i] :
( ~ ( subset @ SY474 @ ( sK32_B @ SV87 ) )
| ( are_equipotent @ SY474 @ ( sK32_B @ SV87 ) )
| ( in @ SY474 @ ( sK32_B @ SV87 ) ) )
| ~ ~ ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ ( sK32_B @ SV87 ) )
| ( in @ ( powerset @ SY475 ) @ ( sK32_B @ SV87 ) ) )
| ~ ~ ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) )
| ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(705,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(706,plain,
! [SV88: $i] :
( ( ( empty @ SV88 )
| ~ ( ~ ( element @ ( sK8_B @ SV88 ) @ ( powerset @ SV88 ) )
| ~ ~ ( empty @ ( sK8_B @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(707,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(708,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(709,plain,
! [SV89: $i] :
( ( ~ ( ~ ! [SY478: $i,SY479: $i] :
( ~ ( in @ SV89 @ SY479 )
| ~ ( in @ SY478 @ SY479 )
| ( subset @ ( unordered_pair @ SV89 @ SY478 ) @ SY479 ) )
| ~ ~ ( ~ ! [SY480: $i,SY481: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY480 ) @ SY481 )
| ( in @ SV89 @ SY481 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY482 ) @ SY483 )
| ( in @ SY482 @ SY483 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(710,plain,
! [SV90: $i] :
( ( ~ ( relation @ SV90 )
| ~ ( ~ ! [SY484: $i] :
( ~ ( relation @ SY484 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) ) )
| ( SY484
= ( relation_inverse @ SV90 ) ) )
| ~ ! [SY485: $i] :
( ~ ( relation @ SY485 )
| ( SY485
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY486: $i,SY487: $i] :
( ~ ( in @ ( ordered_pair @ SY486 @ SY487 ) @ SY485 )
| ( in @ ( ordered_pair @ SY487 @ SY486 ) @ SV90 ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( in @ ( ordered_pair @ SY489 @ SY488 ) @ SV90 )
| ( in @ ( ordered_pair @ SY488 @ SY489 ) @ SY485 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(711,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK29_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK29_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK29_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)],[583]) ).
thf(712,plain,
! [SV91: $i] :
( ( ! [SY490: $i] :
( ~ ( ~ ( in @ ( sK33_C @ SY490 @ SV91 ) @ SV91 )
| ~ ~ ( in @ ( sK33_C @ SY490 @ SV91 ) @ SY490 ) )
| ( element @ SV91 @ ( powerset @ SY490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(713,plain,
! [SV92: $i] :
( ( ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( relation @ SY492 )
| ~ ( in @ ( ordered_pair @ SV92 @ SY491 ) @ SY492 )
| ( in @ SV92 @ ( relation_field @ SY492 ) ) )
| ~ ! [SY493: $i,SY494: $i] :
( ~ ( relation @ SY494 )
| ~ ( in @ ( ordered_pair @ SV92 @ SY493 ) @ SY494 )
| ( in @ SY493 @ ( relation_field @ SY494 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(714,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(715,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK31_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK31_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)],[587]) ).
thf(716,plain,
! [SV93: $i] :
( ( ~ ( ~ ! [SY495: $i,SY496: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY495 )
| ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY495 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) ) ) )
| ( SY496
= ( set_difference @ SV93 @ SY495 ) ) )
| ~ ! [SY497: $i,SY498: $i] :
( ( SY498
!= ( set_difference @ SV93 @ SY497 ) )
| ~ ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV93 )
| ( in @ SY499 @ SY497 )
| ( in @ SY499 @ SY498 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SY498 )
| ( in @ SY500 @ SV93 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY498 )
| ~ ( in @ SX3 @ SY497 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(717,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(718,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(719,plain,
! [SV94: $i] :
( ( ! [SY502: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_C @ SY502 @ SV94 ) @ SV94 )
| ~ ( in @ ( sK4_C @ SY502 @ SV94 ) @ SY502 ) )
| ~ ( ( in @ ( sK4_C @ SY502 @ SV94 ) @ SV94 )
| ( in @ ( sK4_C @ SY502 @ SV94 ) @ SY502 ) ) )
| ( SV94 = SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(720,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY326 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK43_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)],[592]) ).
thf(721,plain,
! [SV95: $i] :
( ( ~ ( ~ ! [SY503: $i,SY504: $i] :
( ~ ( relation @ SY504 )
| ~ ( in @ ( ordered_pair @ SV95 @ SY503 ) @ SY504 )
| ( in @ SV95 @ ( relation_dom @ SY504 ) ) )
| ~ ! [SY505: $i,SY506: $i] :
( ~ ( relation @ SY506 )
| ~ ( in @ ( ordered_pair @ SV95 @ SY505 ) @ SY506 )
| ( in @ SY505 @ ( relation_rng @ SY506 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(722,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(723,plain,
! [SV96: $i] :
( ( ~ ( ~ ! [SY507: $i] :
( ~ ( subset @ SV96 @ SY507 )
| ! [SY508: $i] : ( subset @ ( cartesian_product2 @ SV96 @ SY508 ) @ ( cartesian_product2 @ SY507 @ SY508 ) ) )
| ~ ! [SY509: $i] :
( ~ ( subset @ SV96 @ SY509 )
| ! [SY510: $i] : ( subset @ ( cartesian_product2 @ SY510 @ SV96 ) @ ( cartesian_product2 @ SY510 @ SY509 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(724,plain,
! [SV1: $i] :
( ( ( singleton @ SV1 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(725,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( subset @ SV2 @ ( cartesian_product2 @ ( relation_dom @ SV2 ) @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(726,plain,
! [SV4: $i] :
( ( ( ~ ( subset @ SV4 @ empty_set ) )
= $true )
| ( ( SV4 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(727,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ! [SY332: $i] :
( ~ ( relation @ SY332 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SY332 ) ) @ ( relation_dom @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(728,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ! [SY333: $i] :
( ~ ( relation @ SY333 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SY333 ) ) @ ( relation_rng @ SY333 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(729,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( relation @ SY334 )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SY334 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SY334 ) )
= ( relation_dom @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(730,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ! [SY335: $i] :
( ~ ( relation @ SY335 )
| ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SY335 ) )
| ( ( relation_rng @ ( relation_composition @ SY335 @ SV8 ) )
= ( relation_rng @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(731,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK49_B @ SV9 ) @ ( sK50_SY331 @ SV9 ) ) @ SV9 )
| ( SV9 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(732,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $true )
| ( ( relation @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(733,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(734,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(735,plain,
! [SV97: $i,SV13: $i] :
( ( ~ ( relation @ SV13 )
| ~ ( relation @ SV97 )
| ( relation @ ( relation_composition @ SV13 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(736,plain,
! [SV98: $i,SV14: $i] :
( ( ~ ( relation @ SV14 )
| ~ ( relation @ SV98 )
| ( relation @ ( set_union2 @ SV14 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(737,plain,
! [SV15: $i] :
( ( ( ( empty @ SV15 )
| ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(738,plain,
! [SV16: $i] :
( ( ( ( empty @ SV16 )
| ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(739,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(740,plain,
! [SV22: $i] :
( ( ( ~ ( empty @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(741,plain,
! [SV99: $i,SV23: $i] :
( ( ~ ( in @ SV23 @ SV99 )
| ( ( set_union2 @ ( singleton @ SV23 ) @ SV99 )
= SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(742,plain,
! [SV100: $i,SV24: $i] :
( ( ~ ( disjoint @ ( singleton @ SV24 ) @ SV100 )
| ~ ( in @ SV24 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(743,plain,
! [SV101: $i,SV25: $i] :
( ( ( in @ SV25 @ SV101 )
| ( disjoint @ ( singleton @ SV25 ) @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(744,plain,
! [SV26: $i,SV102: $i] :
( ( ~ ( element @ SV102 @ ( powerset @ SV26 ) )
| ! [SY511: $i] :
( ~ ( in @ SY511 @ SV102 )
| ( in @ SY511 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(745,plain,
! [SV103: $i,SV27: $i] :
( ( ~ ( subset @ SV27 @ SV103 )
| ! [SY512: $i] :
( ( in @ SY512 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SY512 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(746,plain,
! [SV104: $i,SV28: $i] :
( ( ~ ( in @ SV28 @ SV104 )
| ( subset @ SV28 @ ( union @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(747,plain,
! [SV105: $i,SV29: $i] :
( ( ! [SY513: $i,SY514: $i] :
( ~ ( subset @ SV29 @ SV105 )
| ~ ( subset @ SY513 @ SY514 )
| ( subset @ ( cartesian_product2 @ SV29 @ SY513 ) @ ( cartesian_product2 @ SV105 @ SY514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(748,plain,
! [SV106: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV106 )
| ( ( set_union2 @ SV30 @ SV106 )
= SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(749,plain,
! [SV107: $i,SV31: $i] :
( ( subset @ ( set_intersection2 @ SV31 @ SV107 ) @ SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(750,plain,
! [SV108: $i,SV32: $i] :
( ( ! [SY515: $i] :
( ~ ( subset @ SV32 @ SV108 )
| ~ ( subset @ SV32 @ SY515 )
| ( subset @ SV32 @ ( set_intersection2 @ SV108 @ SY515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(751,plain,
! [SV109: $i,SV33: $i] :
( ( ! [SY516: $i] :
( ~ ( subset @ SV33 @ SV109 )
| ~ ( subset @ SV109 @ SY516 )
| ( subset @ SV33 @ SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(752,plain,
! [SV110: $i,SV34: $i] :
( ( ~ ( subset @ SV34 @ SV110 )
| ! [SY517: $i] : ( subset @ ( set_intersection2 @ SV34 @ SY517 ) @ ( set_intersection2 @ SV110 @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(753,plain,
! [SV111: $i,SV35: $i] :
( ( ~ ( subset @ SV35 @ SV111 )
| ( ( set_intersection2 @ SV35 @ SV111 )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(754,plain,
! [SV112: $i,SV36: $i] :
( ( ~ ( subset @ SV36 @ SV112 )
| ! [SY518: $i] : ( subset @ ( set_difference @ SV36 @ SY518 ) @ ( set_difference @ SV112 @ SY518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(755,plain,
! [SV113: $i,SV37: $i] :
( ( subset @ ( set_difference @ SV37 @ SV113 ) @ SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(756,plain,
! [SV114: $i,SV38: $i] :
( ( ( set_union2 @ SV38 @ ( set_difference @ SV114 @ SV38 ) )
= ( set_union2 @ SV38 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(757,plain,
! [SV115: $i,SV39: $i] :
( ( ( set_difference @ ( set_union2 @ SV39 @ SV115 ) @ SV115 )
= ( set_difference @ SV39 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(758,plain,
! [SV116: $i,SV40: $i] :
( ( ~ ( subset @ SV40 @ SV116 )
| ( SV116
= ( set_union2 @ SV40 @ ( set_difference @ SV116 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(759,plain,
! [SV117: $i,SV41: $i] :
( ( ~ ( in @ SV41 @ SV117 )
| ( ( set_union2 @ ( singleton @ SV41 ) @ SV117 )
= SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(760,plain,
! [SV118: $i,SV42: $i] :
( ( ( set_difference @ SV42 @ ( set_difference @ SV42 @ SV118 ) )
= ( set_intersection2 @ SV42 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(761,plain,
! [SV43: $i,SV119: $i] :
( ( ~ ( proper_subset @ SV119 @ SV43 )
| ~ ( subset @ SV43 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(762,plain,
! [SV44: $i,SV120: $i] :
( ( ! [SY519: $i] :
( ~ ( disjoint @ SV120 @ SY519 )
| ~ ( subset @ SV44 @ SV120 )
| ( disjoint @ SV44 @ SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(763,plain,
! [SV121: $i,SV46: $i] :
( ( ~ ( subset @ ( singleton @ SV46 ) @ ( singleton @ SV121 ) )
| ( SV46 = SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(764,plain,
! [SV122: $i,SV47: $i] :
( ( subset @ SV47 @ ( set_union2 @ SV47 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(765,plain,
! [SV123: $i,SV48: $i] :
( ( ! [SY520: $i] :
( ~ ( subset @ SV48 @ SV123 )
| ~ ( subset @ SY520 @ SV123 )
| ( subset @ ( set_union2 @ SV48 @ SY520 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(766,plain,
! [SV124: $i,SV49: $i] :
( ( ! [SY521: $i] :
( ( singleton @ SV49 )
!= ( unordered_pair @ SV124 @ SY521 ) )
| ( SV49 = SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(767,plain,
! [SV125: $i,SV50: $i] :
( ( ~ ( in @ SV50 @ SV125 )
| ( subset @ SV50 @ ( union @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(768,plain,
! [SV126: $i,SV52: $i] :
( ( ! [SY522: $i] :
( ( ( singleton @ SV52 )
!= ( unordered_pair @ SV126 @ SY522 ) )
| ( SV126 = SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(769,plain,
! [SV127: $i,SV53: $i] :
( ( ~ ( in @ SV53 @ SV127 )
| ~ ( in @ SV127 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(770,plain,
! [SV128: $i,SV54: $i] :
( ( ( set_union2 @ SV54 @ SV128 )
= ( set_union2 @ SV128 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(771,plain,
! [SV129: $i,SV55: $i] :
( ( ( set_intersection2 @ SV55 @ SV129 )
= ( set_intersection2 @ SV129 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(772,plain,
! [SV130: $i,SV56: $i] :
( ( ( ordered_pair @ SV56 @ SV130 )
= ( unordered_pair @ ( unordered_pair @ SV56 @ SV130 ) @ ( singleton @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(773,plain,
! [SV57: $i] :
( ( empty @ ( powerset @ SV57 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(774,plain,
! [SV131: $i,SV58: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV58 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(775,plain,
! [SV59: $i] :
( ( empty @ ( singleton @ SV59 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(776,plain,
! [SV60: $i] :
( ( ( empty @ SV60 )
= $true )
| ( ( ! [SY383: $i] :
~ ( empty @ ( set_union2 @ SV60 @ SY383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(777,plain,
! [SV132: $i,SV61: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV61 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(778,plain,
! [SV62: $i] :
( ( ( empty @ SV62 )
= $true )
| ( ( ! [SY385: $i] :
~ ( empty @ ( set_union2 @ SY385 @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(779,plain,
! [SV133: $i,SV63: $i] :
( ( ( empty @ SV63 )
| ( empty @ SV133 )
| ~ ( empty @ ( cartesian_product2 @ SV63 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(780,plain,
! [SV134: $i,SV67: $i] :
( ( ~ ( disjoint @ SV67 @ SV134 )
| ( disjoint @ SV134 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(781,plain,
! [SV135: $i,SV68: $i] :
( ( ~ ( in @ SV68 @ SV135 )
| ( element @ SV68 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(782,plain,
! [SV136: $i,SV69: $i] :
( ( ~ ( element @ SV69 @ SV136 )
| ( empty @ SV136 )
| ( in @ SV69 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(783,plain,
! [SV70: $i,SV137: $i] :
( ( ! [SY523: $i] :
( ~ ( element @ SV137 @ ( powerset @ SY523 ) )
| ~ ( in @ SV70 @ SV137 )
| ( element @ SV70 @ SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(784,plain,
! [SV71: $i,SV138: $i] :
( ( ! [SY524: $i] :
( ~ ( element @ SV138 @ ( powerset @ SY524 ) )
| ~ ( in @ SV71 @ SV138 )
| ~ ( empty @ SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(785,plain,
! [SV72: $i,SV139: $i] :
( ( ~ ( empty @ SV139 )
| ~ ( in @ SV72 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(786,plain,
! [SV140: $i,SV73: $i] :
( ( ( SV73 = SV140 )
| ~ ( empty @ SV73 )
| ~ ( empty @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(787,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(788,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(789,plain,
! [SV74: $i] :
( ( ~ ! [SY396: $i,SY397: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY396 )
| ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) )
| ~ ( ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY396 )
| ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) ) ) )
| ( SY397
= ( set_intersection2 @ SV74 @ SY396 ) ) )
| ~ ! [SY398: $i,SY399: $i] :
( ( SY399
!= ( set_intersection2 @ SV74 @ SY398 ) )
| ~ ( ~ ! [SY400: $i] :
( ~ ( in @ SY400 @ SV74 )
| ~ ( in @ SY400 @ SY398 )
| ( in @ SY400 @ SY399 ) )
| ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY399 )
| ( in @ SY401 @ SV74 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY399 )
| ( in @ SX3 @ SY398 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(790,plain,
! [SV141: $i,SV75: $i] :
( ( ~ ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( in @ SV75 @ SY525 )
| ~ ( in @ SV141 @ SY526 )
| ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY525 @ SY526 ) ) )
| ~ ~ ( ~ ! [SY527: $i] :
( ! [SY528: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY527 @ SY528 ) )
| ( in @ SV75 @ SY527 ) )
| ~ ! [SY529: $i,SY530: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY529 @ SY530 ) )
| ( in @ SV141 @ SY530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(791,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(792,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(793,plain,
! [SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( subset @ SV76 @ SY410 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SY410 ) ) )
| ~ ! [SY411: $i] :
( ~ ( relation @ SY411 )
| ~ ( subset @ SV76 @ SY411 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SY411 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(794,plain,
! [SV77: $i] :
( ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ! [SY412: $i] :
( ~ ( relation @ SY412 )
| ~ ( ~ ! [SY413: $i] :
( ~ ( relation @ SY413 )
| ~ ( ~ ( ! [SY414: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ SY414 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY414 @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY412 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY413 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK12_SY308 @ SY413 @ SY412 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY412 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY413 ) ) )
| ( SY413
= ( relation_composition @ SV77 @ SY412 ) ) )
| ~ ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ( SY415
!= ( relation_composition @ SV77 @ SY412 ) )
| ~ ( ~ ! [SY416: $i,SY417: $i] :
( ! [SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY416 @ SY418 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY418 @ SY417 ) @ SY412 ) )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SY415 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY415 )
| ~ ( ~ ( in @ ( ordered_pair @ SY419 @ ( sK9_F @ SY420 @ SY419 @ SY415 @ SY412 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY420 @ SY419 @ SY415 @ SY412 @ SV77 ) @ SY420 ) @ SY412 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(795,plain,
! [SV78: $i] :
( ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( ~ ! [SY421: $i] :
( ~ ( ~ ( ! [SY422: $i] :
~ ( in @ ( ordered_pair @ SY422 @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SY421 @ SV78 ) @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) ) )
| ( SY421
= ( relation_rng @ SV78 ) ) )
| ~ ! [SY423: $i] :
( ( SY423
!= ( relation_rng @ SV78 ) )
| ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY424 ) @ SV78 )
| ( in @ SY424 @ SY423 ) )
| ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY423 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY426 @ SY423 @ SV78 ) @ SY426 ) @ SV78 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(796,plain,
! [SV79: $i] :
( ( ~ ! [SY427: $i,SY428: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
!= SY427 ) ) )
| ~ ( ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
= SV79 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
= SY427 ) ) )
| ( SY428
= ( unordered_pair @ SV79 @ SY427 ) ) )
| ~ ! [SY429: $i,SY430: $i] :
( ( SY430
!= ( unordered_pair @ SV79 @ SY429 ) )
| ~ ( ~ ! [SY431: $i] :
( ~ ( in @ SY431 @ SY430 )
| ( SY431 = SV79 )
| ( SY431 = SY429 ) )
| ~ ~ ( ~ ! [SY432: $i] :
( ( SY432 != SV79 )
| ( in @ SY432 @ SY430 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY429 )
| ( in @ SX3 @ SY430 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(797,plain,
( ( ~ ( empty @ sK35_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(798,plain,
( ( ~ ( relation @ sK35_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(799,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)],[681]) ).
thf(800,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)],[681]) ).
thf(801,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK48_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK48_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(802,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK46_C @ SX1 @ SX0 ) @ ( sK47_SY328 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(803,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(804,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(805,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(806,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(807,plain,
! [SV80: $i] :
( ( ~ ( element @ ( sK6_B @ SV80 ) @ ( powerset @ SV80 ) )
| ~ ( empty @ ( sK6_B @ SV80 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(808,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(809,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(810,plain,
! [SV81: $i] :
( ( ~ ! [SY434: $i,SY435: $i] :
( ~ ( ~ ( ! [SY436: $i,SY437: $i] :
( ~ ( in @ SY436 @ SV81 )
| ~ ( in @ SY437 @ SY434 )
| ( ( sK23_D @ SY435 @ SY434 @ SV81 )
!= ( ordered_pair @ SY436 @ SY437 ) ) )
| ~ ( in @ ( sK23_D @ SY435 @ SY434 @ SV81 ) @ SY435 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SY435 @ SY434 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SY435 @ SY434 @ SV81 ) @ SY434 ) )
| ( ( sK23_D @ SY435 @ SY434 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SY435 @ SY434 @ SV81 ) @ ( sK25_SY317 @ SY435 @ SY434 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SY435 @ SY434 @ SV81 ) @ SY435 ) ) )
| ( SY435
= ( cartesian_product2 @ SV81 @ SY434 ) ) )
| ~ ! [SY438: $i,SY439: $i] :
( ( SY439
!= ( cartesian_product2 @ SV81 @ SY438 ) )
| ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i,SY442: $i] :
( ~ ( in @ SY441 @ SV81 )
| ~ ( in @ SY442 @ SY438 )
| ( SY440
!= ( ordered_pair @ SY441 @ SY442 ) ) )
| ( in @ SY440 @ SY439 ) )
| ~ ! [SY443: $i] :
( ~ ( in @ SY443 @ SY439 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY443 @ SY439 @ SY438 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY443 @ SY439 @ SY438 @ SV81 ) @ SY438 ) )
| ( SY443
!= ( ordered_pair @ ( sK21_E @ SY443 @ SY439 @ SY438 @ SV81 ) @ ( sK22_SY312 @ SY443 @ SY439 @ SY438 @ SV81 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(811,plain,
! [SV142: $i,SV82: $i] :
( ( ~ ( ~ ! [SY531: $i,SY532: $i] :
( ~ ( in @ SV82 @ SY531 )
| ~ ( in @ SV142 @ SY532 )
| ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY531 @ SY532 ) ) )
| ~ ~ ( ~ ! [SY533: $i] :
( ! [SY534: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY533 @ SY534 ) )
| ( in @ SV82 @ SY533 ) )
| ~ ! [SY535: $i,SY536: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY535 @ SY536 ) )
| ( in @ SV142 @ SY536 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(812,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)],[689]) ).
thf(813,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)],[689]) ).
thf(814,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(815,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(816,plain,
! [SV83: $i] :
( ( ~ ! [SY451: $i,SY452: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY451 ) ) )
| ~ ( ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY451 ) ) )
| ( SY452
= ( set_union2 @ SV83 @ SY451 ) ) )
| ~ ! [SY453: $i,SY454: $i] :
( ( SY454
!= ( set_union2 @ SV83 @ SY453 ) )
| ~ ( ~ ! [SY455: $i] :
( ~ ( in @ SY455 @ SY454 )
| ( in @ SY455 @ SV83 )
| ( in @ SY455 @ SY453 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ~ ( in @ SY456 @ SV83 )
| ( in @ SY456 @ SY454 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY453 )
| ( in @ SX3 @ SY454 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(817,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)],[692]) ).
thf(818,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(819,plain,
! [SV143: $i,SV84: $i] :
( ( ~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SY537 @ SY538 ) )
| ( SV84 = SY537 ) )
| ~ ! [SY539: $i,SY540: $i] :
( ( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SY539 @ SY540 ) )
| ( SV143 = SY540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(820,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(821,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(822,plain,
! [SV85: $i] :
( ( ~ ! [SY463: $i] :
( ~ ( subset @ SY463 @ ( sK2_B @ SV85 ) )
| ( are_equipotent @ SY463 @ ( sK2_B @ SV85 ) )
| ( in @ SY463 @ ( sK2_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY464: $i] :
( ~ ( ~ ! [SY465: $i] :
( ~ ( subset @ SY465 @ SY464 )
| ( in @ SY465 @ ( sK3_SY299 @ SY464 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SY464 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SY464 @ ( sK2_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(823,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(824,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(825,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY311 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY311 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(826,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 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(827,plain,
! [SV86: $i] :
( ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY468: $i] :
( ~ ( ~ ( ! [SY469: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ SY469 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ ( sK41_SY325 @ SY468 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) ) )
| ( SY468
= ( relation_dom @ SV86 ) ) )
| ~ ! [SY470: $i] :
( ( SY470
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY471: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY472 ) @ SV86 )
| ( in @ SY471 @ SY470 ) )
| ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ SY470 )
| ( in @ ( ordered_pair @ SY473 @ ( sK39_D @ SY473 @ SY470 @ SV86 ) ) @ SV86 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(828,plain,
( ( ~ ~ ( empty @ sK34_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(829,plain,
( ( ~ ( relation @ sK34_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(830,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(831,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(832,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(833,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(834,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(835,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(836,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(837,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(838,plain,
! [SV87: $i] :
( ( ~ ! [SY474: $i] :
( ~ ( subset @ SY474 @ ( sK32_B @ SV87 ) )
| ( are_equipotent @ SY474 @ ( sK32_B @ SV87 ) )
| ( in @ SY474 @ ( sK32_B @ SV87 ) ) )
| ~ ~ ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ ( sK32_B @ SV87 ) )
| ( in @ ( powerset @ SY475 ) @ ( sK32_B @ SV87 ) ) )
| ~ ~ ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) )
| ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(839,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(840,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(841,plain,
! [SV88: $i] :
( ( ( empty @ SV88 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_B @ SV88 ) @ ( powerset @ SV88 ) )
| ~ ~ ( empty @ ( sK8_B @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(842,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(843,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(844,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(845,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(846,plain,
! [SV89: $i] :
( ( ~ ! [SY478: $i,SY479: $i] :
( ~ ( in @ SV89 @ SY479 )
| ~ ( in @ SY478 @ SY479 )
| ( subset @ ( unordered_pair @ SV89 @ SY478 ) @ SY479 ) )
| ~ ~ ( ~ ! [SY480: $i,SY481: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY480 ) @ SY481 )
| ( in @ SV89 @ SY481 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY482 ) @ SY483 )
| ( in @ SY482 @ SY483 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(847,plain,
! [SV90: $i] :
( ( ( ~ ( relation @ SV90 ) )
= $true )
| ( ( ~ ( ~ ! [SY484: $i] :
( ~ ( relation @ SY484 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) ) )
| ( SY484
= ( relation_inverse @ SV90 ) ) )
| ~ ! [SY485: $i] :
( ~ ( relation @ SY485 )
| ( SY485
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY486: $i,SY487: $i] :
( ~ ( in @ ( ordered_pair @ SY486 @ SY487 ) @ SY485 )
| ( in @ ( ordered_pair @ SY487 @ SY486 ) @ SV90 ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( in @ ( ordered_pair @ SY489 @ SY488 ) @ SV90 )
| ( in @ ( ordered_pair @ SY488 @ SY489 ) @ SY485 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(848,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK29_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK29_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(849,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)],[711]) ).
thf(850,plain,
! [SV91: $i,SV144: $i] :
( ( ~ ( ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV91 )
| ~ ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV144 ) )
| ( element @ SV91 @ ( powerset @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(851,plain,
! [SV92: $i] :
( ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( relation @ SY492 )
| ~ ( in @ ( ordered_pair @ SV92 @ SY491 ) @ SY492 )
| ( in @ SV92 @ ( relation_field @ SY492 ) ) )
| ~ ! [SY493: $i,SY494: $i] :
( ~ ( relation @ SY494 )
| ~ ( in @ ( ordered_pair @ SV92 @ SY493 ) @ SY494 )
| ( in @ SY493 @ ( relation_field @ SY494 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(852,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(853,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(854,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK31_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK31_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(855,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(856,plain,
! [SV93: $i] :
( ( ~ ! [SY495: $i,SY496: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY495 )
| ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY495 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) ) ) )
| ( SY496
= ( set_difference @ SV93 @ SY495 ) ) )
| ~ ! [SY497: $i,SY498: $i] :
( ( SY498
!= ( set_difference @ SV93 @ SY497 ) )
| ~ ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV93 )
| ( in @ SY499 @ SY497 )
| ( in @ SY499 @ SY498 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SY498 )
| ( in @ SY500 @ SV93 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY498 )
| ~ ( in @ SX3 @ SY497 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(857,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(858,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(859,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(860,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(861,plain,
! [SV94: $i,SV145: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) )
| ~ ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) ) )
| ( SV94 = SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(862,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY326 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK43_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)],[720]) ).
thf(863,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)],[720]) ).
thf(864,plain,
! [SV95: $i] :
( ( ~ ! [SY503: $i,SY504: $i] :
( ~ ( relation @ SY504 )
| ~ ( in @ ( ordered_pair @ SV95 @ SY503 ) @ SY504 )
| ( in @ SV95 @ ( relation_dom @ SY504 ) ) )
| ~ ! [SY505: $i,SY506: $i] :
( ~ ( relation @ SY506 )
| ~ ( in @ ( ordered_pair @ SV95 @ SY505 ) @ SY506 )
| ( in @ SY505 @ ( relation_rng @ SY506 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(865,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(866,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(867,plain,
! [SV96: $i] :
( ( ~ ! [SY507: $i] :
( ~ ( subset @ SV96 @ SY507 )
| ! [SY508: $i] : ( subset @ ( cartesian_product2 @ SV96 @ SY508 ) @ ( cartesian_product2 @ SY507 @ SY508 ) ) )
| ~ ! [SY509: $i] :
( ~ ( subset @ SV96 @ SY509 )
| ! [SY510: $i] : ( subset @ ( cartesian_product2 @ SY510 @ SV96 ) @ ( cartesian_product2 @ SY510 @ SY509 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(868,plain,
! [SV2: $i] :
( ( ( relation @ SV2 )
= $false )
| ( ( subset @ SV2 @ ( cartesian_product2 @ ( relation_dom @ SV2 ) @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(869,plain,
! [SV4: $i] :
( ( ( subset @ SV4 @ empty_set )
= $false )
| ( ( SV4 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(870,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ! [SY332: $i] :
( ~ ( relation @ SY332 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SY332 ) ) @ ( relation_dom @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(871,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ! [SY333: $i] :
( ~ ( relation @ SY333 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SY333 ) ) @ ( relation_rng @ SY333 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(872,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ! [SY334: $i] :
( ~ ( relation @ SY334 )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SY334 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SY334 ) )
= ( relation_dom @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(873,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ! [SY335: $i] :
( ~ ( relation @ SY335 )
| ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SY335 ) )
| ( ( relation_rng @ ( relation_composition @ SY335 @ SV8 ) )
= ( relation_rng @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(874,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK49_B @ SV9 ) @ ( sK50_SY331 @ SV9 ) ) @ SV9 )
| ( SV9 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(875,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $false )
| ( ( relation @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(876,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(877,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( relation @ ( relation_inverse @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(878,plain,
! [SV97: $i,SV13: $i] :
( ( ( ~ ( relation @ SV13 )
| ~ ( relation @ SV97 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV13 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(879,plain,
! [SV98: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 )
| ~ ( relation @ SV98 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV14 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(880,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $true )
| ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(881,plain,
! [SV16: $i] :
( ( ( empty @ SV16 )
= $true )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(882,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(883,plain,
! [SV22: $i] :
( ( ( empty @ SV22 )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(884,plain,
! [SV99: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV99 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV23 ) @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(885,plain,
! [SV100: $i,SV24: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV24 ) @ SV100 ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(886,plain,
! [SV101: $i,SV25: $i] :
( ( ( in @ SV25 @ SV101 )
= $true )
| ( ( disjoint @ ( singleton @ SV25 ) @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(887,plain,
! [SV26: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( ! [SY511: $i] :
( ~ ( in @ SY511 @ SV102 )
| ( in @ SY511 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(888,plain,
! [SV103: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV103 ) )
= $true )
| ( ( ! [SY512: $i] :
( ( in @ SY512 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SY512 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(889,plain,
! [SV104: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV104 ) )
= $true )
| ( ( subset @ SV28 @ ( union @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(890,plain,
! [SV146: $i,SV105: $i,SV29: $i] :
( ( ! [SY541: $i] :
( ~ ( subset @ SV29 @ SV105 )
| ~ ( subset @ SV146 @ SY541 )
| ( subset @ ( cartesian_product2 @ SV29 @ SV146 ) @ ( cartesian_product2 @ SV105 @ SY541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(891,plain,
! [SV106: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV106 ) )
= $true )
| ( ( ( set_union2 @ SV30 @ SV106 )
= SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(892,plain,
! [SV147: $i,SV108: $i,SV32: $i] :
( ( ~ ( subset @ SV32 @ SV108 )
| ~ ( subset @ SV32 @ SV147 )
| ( subset @ SV32 @ ( set_intersection2 @ SV108 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(893,plain,
! [SV148: $i,SV109: $i,SV33: $i] :
( ( ~ ( subset @ SV33 @ SV109 )
| ~ ( subset @ SV109 @ SV148 )
| ( subset @ SV33 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(894,plain,
! [SV110: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV110 ) )
= $true )
| ( ( ! [SY517: $i] : ( subset @ ( set_intersection2 @ SV34 @ SY517 ) @ ( set_intersection2 @ SV110 @ SY517 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(895,plain,
! [SV111: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV111 ) )
= $true )
| ( ( ( set_intersection2 @ SV35 @ SV111 )
= SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(896,plain,
! [SV112: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV112 ) )
= $true )
| ( ( ! [SY518: $i] : ( subset @ ( set_difference @ SV36 @ SY518 ) @ ( set_difference @ SV112 @ SY518 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(897,plain,
! [SV116: $i,SV40: $i] :
( ( ( ~ ( subset @ SV40 @ SV116 ) )
= $true )
| ( ( SV116
= ( set_union2 @ SV40 @ ( set_difference @ SV116 @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(898,plain,
! [SV117: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV117 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV41 ) @ SV117 )
= SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(899,plain,
! [SV43: $i,SV119: $i] :
( ( ( ~ ( proper_subset @ SV119 @ SV43 ) )
= $true )
| ( ( ~ ( subset @ SV43 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(900,plain,
! [SV44: $i,SV149: $i,SV120: $i] :
( ( ~ ( disjoint @ SV120 @ SV149 )
| ~ ( subset @ SV44 @ SV120 )
| ( disjoint @ SV44 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(901,plain,
! [SV121: $i,SV46: $i] :
( ( ( ~ ( subset @ ( singleton @ SV46 ) @ ( singleton @ SV121 ) ) )
= $true )
| ( ( SV46 = SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(902,plain,
! [SV150: $i,SV123: $i,SV48: $i] :
( ( ~ ( subset @ SV48 @ SV123 )
| ~ ( subset @ SV150 @ SV123 )
| ( subset @ ( set_union2 @ SV48 @ SV150 ) @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(903,plain,
! [SV124: $i,SV49: $i] :
( ( ( ! [SY521: $i] :
( ( singleton @ SV49 )
!= ( unordered_pair @ SV124 @ SY521 ) ) )
= $true )
| ( ( SV49 = SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(904,plain,
! [SV125: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ SV125 ) )
= $true )
| ( ( subset @ SV50 @ ( union @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(905,plain,
! [SV151: $i,SV126: $i,SV52: $i] :
( ( ( ( singleton @ SV52 )
!= ( unordered_pair @ SV126 @ SV151 ) )
| ( SV126 = SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(906,plain,
! [SV127: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV127 ) )
= $true )
| ( ( ~ ( in @ SV127 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(907,plain,
! [SV131: $i,SV58: $i] :
( ( empty @ ( ordered_pair @ SV58 @ SV131 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(908,plain,
! [SV152: $i,SV60: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV60 @ SV152 ) ) )
= $true )
| ( ( empty @ SV60 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(909,plain,
! [SV132: $i,SV61: $i] :
( ( empty @ ( unordered_pair @ SV61 @ SV132 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(910,plain,
! [SV62: $i,SV153: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV153 @ SV62 ) ) )
= $true )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(911,plain,
! [SV133: $i,SV63: $i] :
( ( ( ( empty @ SV63 )
| ( empty @ SV133 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV63 @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(912,plain,
! [SV134: $i,SV67: $i] :
( ( ( ~ ( disjoint @ SV67 @ SV134 ) )
= $true )
| ( ( disjoint @ SV134 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(913,plain,
! [SV135: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ SV135 ) )
= $true )
| ( ( element @ SV68 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(914,plain,
! [SV136: $i,SV69: $i] :
( ( ( ~ ( element @ SV69 @ SV136 ) )
= $true )
| ( ( ( empty @ SV136 )
| ( in @ SV69 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(915,plain,
! [SV70: $i,SV154: $i,SV137: $i] :
( ( ~ ( element @ SV137 @ ( powerset @ SV154 ) )
| ~ ( in @ SV70 @ SV137 )
| ( element @ SV70 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(916,plain,
! [SV71: $i,SV155: $i,SV138: $i] :
( ( ~ ( element @ SV138 @ ( powerset @ SV155 ) )
| ~ ( in @ SV71 @ SV138 )
| ~ ( empty @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(917,plain,
! [SV72: $i,SV139: $i] :
( ( ( ~ ( empty @ SV139 ) )
= $true )
| ( ( ~ ( in @ SV72 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(918,plain,
! [SV140: $i,SV73: $i] :
( ( ( ( SV73 = SV140 )
| ~ ( empty @ SV73 ) )
= $true )
| ( ( ~ ( empty @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(919,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(920,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[788]) ).
thf(921,plain,
! [SV74: $i] :
( ( ~ ! [SY396: $i,SY397: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY396 )
| ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) )
| ~ ( ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY396 )
| ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) ) ) )
| ( SY397
= ( set_intersection2 @ SV74 @ SY396 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(922,plain,
! [SV74: $i] :
( ( ~ ! [SY398: $i,SY399: $i] :
( ( SY399
!= ( set_intersection2 @ SV74 @ SY398 ) )
| ~ ( ~ ! [SY400: $i] :
( ~ ( in @ SY400 @ SV74 )
| ~ ( in @ SY400 @ SY398 )
| ( in @ SY400 @ SY399 ) )
| ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY399 )
| ( in @ SY401 @ SV74 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY399 )
| ( in @ SX3 @ SY398 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(923,plain,
! [SV141: $i,SV75: $i] :
( ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( in @ SV75 @ SY525 )
| ~ ( in @ SV141 @ SY526 )
| ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY525 @ SY526 ) ) )
| ~ ~ ( ~ ! [SY527: $i] :
( ! [SY528: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY527 @ SY528 ) )
| ( in @ SV75 @ SY527 ) )
| ~ ! [SY529: $i,SY530: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY529 @ SY530 ) )
| ( in @ SV141 @ SY530 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(924,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(925,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(926,plain,
! [SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( ~ ( ~ ! [SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( subset @ SV76 @ SY410 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SY410 ) ) )
| ~ ! [SY411: $i] :
( ~ ( relation @ SY411 )
| ~ ( subset @ SV76 @ SY411 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SY411 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(927,plain,
! [SV77: $i] :
( ( ( relation @ SV77 )
= $false )
| ( ( ! [SY412: $i] :
( ~ ( relation @ SY412 )
| ~ ( ~ ! [SY413: $i] :
( ~ ( relation @ SY413 )
| ~ ( ~ ( ! [SY414: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ SY414 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY414 @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY412 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY413 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK12_SY308 @ SY413 @ SY412 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY412 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY413 @ SY412 @ SV77 ) @ ( sK11_SY304 @ SY413 @ SY412 @ SV77 ) ) @ SY413 ) ) )
| ( SY413
= ( relation_composition @ SV77 @ SY412 ) ) )
| ~ ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ( SY415
!= ( relation_composition @ SV77 @ SY412 ) )
| ~ ( ~ ! [SY416: $i,SY417: $i] :
( ! [SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY416 @ SY418 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY418 @ SY417 ) @ SY412 ) )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SY415 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY415 )
| ~ ( ~ ( in @ ( ordered_pair @ SY419 @ ( sK9_F @ SY420 @ SY419 @ SY415 @ SY412 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY420 @ SY419 @ SY415 @ SY412 @ SV77 ) @ SY420 ) @ SY412 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(928,plain,
! [SV78: $i] :
( ( ( relation @ SV78 )
= $false )
| ( ( ~ ( ~ ! [SY421: $i] :
( ~ ( ~ ( ! [SY422: $i] :
~ ( in @ ( ordered_pair @ SY422 @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SY421 @ SV78 ) @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) ) )
| ( SY421
= ( relation_rng @ SV78 ) ) )
| ~ ! [SY423: $i] :
( ( SY423
!= ( relation_rng @ SV78 ) )
| ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY424 ) @ SV78 )
| ( in @ SY424 @ SY423 ) )
| ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY423 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY426 @ SY423 @ SV78 ) @ SY426 ) @ SV78 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(929,plain,
! [SV79: $i] :
( ( ~ ! [SY427: $i,SY428: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
!= SY427 ) ) )
| ~ ( ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
= SV79 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
= SY427 ) ) )
| ( SY428
= ( unordered_pair @ SV79 @ SY427 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(930,plain,
! [SV79: $i] :
( ( ~ ! [SY429: $i,SY430: $i] :
( ( SY430
!= ( unordered_pair @ SV79 @ SY429 ) )
| ~ ( ~ ! [SY431: $i] :
( ~ ( in @ SY431 @ SY430 )
| ( SY431 = SV79 )
| ( SY431 = SY429 ) )
| ~ ~ ( ~ ! [SY432: $i] :
( ( SY432 != SV79 )
| ( in @ SY432 @ SY430 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY429 )
| ( in @ SX3 @ SY430 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(931,plain,
( ( empty @ sK35_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(932,plain,
( ( relation @ sK35_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(933,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)],[799]) ).
thf(934,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)],[800]) ).
thf(935,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK48_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK48_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(936,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK46_C @ SX1 @ SX0 ) @ ( sK47_SY328 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(937,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(938,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(939,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(940,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(941,plain,
! [SV80: $i] :
( ( ~ ( element @ ( sK6_B @ SV80 ) @ ( powerset @ SV80 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(942,plain,
! [SV80: $i] :
( ( ~ ( empty @ ( sK6_B @ SV80 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(943,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(944,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(945,plain,
! [SV81: $i] :
( ( ~ ! [SY434: $i,SY435: $i] :
( ~ ( ~ ( ! [SY436: $i,SY437: $i] :
( ~ ( in @ SY436 @ SV81 )
| ~ ( in @ SY437 @ SY434 )
| ( ( sK23_D @ SY435 @ SY434 @ SV81 )
!= ( ordered_pair @ SY436 @ SY437 ) ) )
| ~ ( in @ ( sK23_D @ SY435 @ SY434 @ SV81 ) @ SY435 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SY435 @ SY434 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SY435 @ SY434 @ SV81 ) @ SY434 ) )
| ( ( sK23_D @ SY435 @ SY434 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SY435 @ SY434 @ SV81 ) @ ( sK25_SY317 @ SY435 @ SY434 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SY435 @ SY434 @ SV81 ) @ SY435 ) ) )
| ( SY435
= ( cartesian_product2 @ SV81 @ SY434 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[810]) ).
thf(946,plain,
! [SV81: $i] :
( ( ~ ! [SY438: $i,SY439: $i] :
( ( SY439
!= ( cartesian_product2 @ SV81 @ SY438 ) )
| ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i,SY442: $i] :
( ~ ( in @ SY441 @ SV81 )
| ~ ( in @ SY442 @ SY438 )
| ( SY440
!= ( ordered_pair @ SY441 @ SY442 ) ) )
| ( in @ SY440 @ SY439 ) )
| ~ ! [SY443: $i] :
( ~ ( in @ SY443 @ SY439 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY443 @ SY439 @ SY438 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY443 @ SY439 @ SY438 @ SV81 ) @ SY438 ) )
| ( SY443
!= ( ordered_pair @ ( sK21_E @ SY443 @ SY439 @ SY438 @ SV81 ) @ ( sK22_SY312 @ SY443 @ SY439 @ SY438 @ SV81 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[810]) ).
thf(947,plain,
! [SV142: $i,SV82: $i] :
( ( ~ ! [SY531: $i,SY532: $i] :
( ~ ( in @ SV82 @ SY531 )
| ~ ( in @ SV142 @ SY532 )
| ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY531 @ SY532 ) ) )
| ~ ~ ( ~ ! [SY533: $i] :
( ! [SY534: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY533 @ SY534 ) )
| ( in @ SV82 @ SY533 ) )
| ~ ! [SY535: $i,SY536: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY535 @ SY536 ) )
| ( in @ SV142 @ SY536 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(948,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)],[812]) ).
thf(949,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)],[813]) ).
thf(950,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(951,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(952,plain,
! [SV83: $i] :
( ( ~ ! [SY451: $i,SY452: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY451 ) ) )
| ~ ( ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY451 ) ) )
| ( SY452
= ( set_union2 @ SV83 @ SY451 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[816]) ).
thf(953,plain,
! [SV83: $i] :
( ( ~ ! [SY453: $i,SY454: $i] :
( ( SY454
!= ( set_union2 @ SV83 @ SY453 ) )
| ~ ( ~ ! [SY455: $i] :
( ~ ( in @ SY455 @ SY454 )
| ( in @ SY455 @ SV83 )
| ( in @ SY455 @ SY453 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ~ ( in @ SY456 @ SV83 )
| ( in @ SY456 @ SY454 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY453 )
| ( in @ SX3 @ SY454 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[816]) ).
thf(954,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)],[817]) ).
thf(955,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(956,plain,
! [SV143: $i,SV84: $i] :
( ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SY537 @ SY538 ) )
| ( SV84 = SY537 ) )
| ~ ! [SY539: $i,SY540: $i] :
( ( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SY539 @ SY540 ) )
| ( SV143 = SY540 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(957,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(958,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(959,plain,
! [SV85: $i] :
( ( ~ ! [SY463: $i] :
( ~ ( subset @ SY463 @ ( sK2_B @ SV85 ) )
| ( are_equipotent @ SY463 @ ( sK2_B @ SV85 ) )
| ( in @ SY463 @ ( sK2_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(960,plain,
! [SV85: $i] :
( ( ~ ~ ( ~ ! [SY464: $i] :
( ~ ( ~ ! [SY465: $i] :
( ~ ( subset @ SY465 @ SY464 )
| ( in @ SY465 @ ( sK3_SY299 @ SY464 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SY464 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SY464 @ ( sK2_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(961,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(962,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(963,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY311 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY311 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(964,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 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(965,plain,
! [SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( ~ ( ~ ! [SY468: $i] :
( ~ ( ~ ( ! [SY469: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ SY469 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ ( sK41_SY325 @ SY468 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) ) )
| ( SY468
= ( relation_dom @ SV86 ) ) )
| ~ ! [SY470: $i] :
( ( SY470
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY471: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY472 ) @ SV86 )
| ( in @ SY471 @ SY470 ) )
| ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ SY470 )
| ( in @ ( ordered_pair @ SY473 @ ( sK39_D @ SY473 @ SY470 @ SV86 ) ) @ SV86 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(966,plain,
( ( ~ ( empty @ sK34_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(967,plain,
( ( relation @ sK34_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(968,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(969,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(970,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(971,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(972,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(973,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(974,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(975,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(976,plain,
! [SV87: $i] :
( ( ~ ! [SY474: $i] :
( ~ ( subset @ SY474 @ ( sK32_B @ SV87 ) )
| ( are_equipotent @ SY474 @ ( sK32_B @ SV87 ) )
| ( in @ SY474 @ ( sK32_B @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(977,plain,
! [SV87: $i] :
( ( ~ ~ ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ ( sK32_B @ SV87 ) )
| ( in @ ( powerset @ SY475 ) @ ( sK32_B @ SV87 ) ) )
| ~ ~ ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) )
| ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(978,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(979,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(980,plain,
! [SV88: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV88 ) @ ( powerset @ SV88 ) )
| ~ ~ ( empty @ ( sK8_B @ SV88 ) ) )
= $false )
| ( ( empty @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(981,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(982,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(983,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[844]) ).
thf(984,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(985,plain,
! [SV89: $i] :
( ( ~ ! [SY478: $i,SY479: $i] :
( ~ ( in @ SV89 @ SY479 )
| ~ ( in @ SY478 @ SY479 )
| ( subset @ ( unordered_pair @ SV89 @ SY478 ) @ SY479 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(986,plain,
! [SV89: $i] :
( ( ~ ~ ( ~ ! [SY480: $i,SY481: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY480 ) @ SY481 )
| ( in @ SV89 @ SY481 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY482 ) @ SY483 )
| ( in @ SY482 @ SY483 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(987,plain,
! [SV90: $i] :
( ( ( relation @ SV90 )
= $false )
| ( ( ~ ( ~ ! [SY484: $i] :
( ~ ( relation @ SY484 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) ) )
| ( SY484
= ( relation_inverse @ SV90 ) ) )
| ~ ! [SY485: $i] :
( ~ ( relation @ SY485 )
| ( SY485
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY486: $i,SY487: $i] :
( ~ ( in @ ( ordered_pair @ SY486 @ SY487 ) @ SY485 )
| ( in @ ( ordered_pair @ SY487 @ SY486 ) @ SV90 ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( in @ ( ordered_pair @ SY489 @ SY488 ) @ SV90 )
| ( in @ ( ordered_pair @ SY488 @ SY489 ) @ SY485 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(988,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK29_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK29_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(989,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)],[849]) ).
thf(990,plain,
! [SV91: $i,SV144: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV91 )
| ~ ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV144 ) ) )
= $true )
| ( ( element @ SV91 @ ( powerset @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(991,plain,
! [SV92: $i] :
( ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( relation @ SY492 )
| ~ ( in @ ( ordered_pair @ SV92 @ SY491 ) @ SY492 )
| ( in @ SV92 @ ( relation_field @ SY492 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(992,plain,
! [SV92: $i] :
( ( ~ ! [SY493: $i,SY494: $i] :
( ~ ( relation @ SY494 )
| ~ ( in @ ( ordered_pair @ SV92 @ SY493 ) @ SY494 )
| ( in @ SY493 @ ( relation_field @ SY494 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(993,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(994,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(995,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK31_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK31_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(996,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(997,plain,
! [SV93: $i] :
( ( ~ ! [SY495: $i,SY496: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY495 )
| ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY495 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) ) ) )
| ( SY496
= ( set_difference @ SV93 @ SY495 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(998,plain,
! [SV93: $i] :
( ( ~ ! [SY497: $i,SY498: $i] :
( ( SY498
!= ( set_difference @ SV93 @ SY497 ) )
| ~ ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV93 )
| ( in @ SY499 @ SY497 )
| ( in @ SY499 @ SY498 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SY498 )
| ( in @ SY500 @ SV93 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY498 )
| ~ ( in @ SX3 @ SY497 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(999,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(1000,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(1001,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(1002,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(1003,plain,
! [SV94: $i,SV145: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) )
| ~ ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) ) ) )
= $true )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(1004,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY326 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK43_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)],[862]) ).
thf(1005,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)],[863]) ).
thf(1006,plain,
! [SV95: $i] :
( ( ~ ! [SY503: $i,SY504: $i] :
( ~ ( relation @ SY504 )
| ~ ( in @ ( ordered_pair @ SV95 @ SY503 ) @ SY504 )
| ( in @ SV95 @ ( relation_dom @ SY504 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(1007,plain,
! [SV95: $i] :
( ( ~ ! [SY505: $i,SY506: $i] :
( ~ ( relation @ SY506 )
| ~ ( in @ ( ordered_pair @ SV95 @ SY505 ) @ SY506 )
| ( in @ SY505 @ ( relation_rng @ SY506 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(1008,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(1009,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(1010,plain,
! [SV96: $i] :
( ( ~ ! [SY507: $i] :
( ~ ( subset @ SV96 @ SY507 )
| ! [SY508: $i] : ( subset @ ( cartesian_product2 @ SV96 @ SY508 ) @ ( cartesian_product2 @ SY507 @ SY508 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[867]) ).
thf(1011,plain,
! [SV96: $i] :
( ( ~ ! [SY509: $i] :
( ~ ( subset @ SV96 @ SY509 )
| ! [SY510: $i] : ( subset @ ( cartesian_product2 @ SY510 @ SV96 ) @ ( cartesian_product2 @ SY510 @ SY509 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[867]) ).
thf(1012,plain,
! [SV5: $i,SV156: $i] :
( ( ( ~ ( relation @ SV156 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SV156 ) ) @ ( relation_dom @ SV5 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1013,plain,
! [SV6: $i,SV157: $i] :
( ( ( ~ ( relation @ SV157 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SV157 ) ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1014,plain,
! [SV7: $i,SV158: $i] :
( ( ( ~ ( relation @ SV158 )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SV158 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SV158 ) )
= ( relation_dom @ SV7 ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1015,plain,
! [SV8: $i,SV159: $i] :
( ( ( ~ ( relation @ SV159 )
| ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SV159 ) )
| ( ( relation_rng @ ( relation_composition @ SV159 @ SV8 ) )
= ( relation_rng @ SV8 ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1016,plain,
! [SV9: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_B @ SV9 ) @ ( sK50_SY331 @ SV9 ) ) @ SV9 )
= $true )
| ( ( SV9 = empty_set )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(1017,plain,
! [SV97: $i,SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV13 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(1018,plain,
! [SV98: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV14 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(1019,plain,
! [SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(1020,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( empty @ SV16 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(1021,plain,
! [SV99: $i,SV23: $i] :
( ( ( in @ SV23 @ SV99 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV23 ) @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(1022,plain,
! [SV100: $i,SV24: $i] :
( ( ( disjoint @ ( singleton @ SV24 ) @ SV100 )
= $false )
| ( ( ~ ( in @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(1023,plain,
! [SV26: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV26 ) )
= $false )
| ( ( ! [SY511: $i] :
( ~ ( in @ SY511 @ SV102 )
| ( in @ SY511 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(1024,plain,
! [SV103: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV103 )
= $false )
| ( ( ! [SY512: $i] :
( ( in @ SY512 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SY512 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(1025,plain,
! [SV104: $i,SV28: $i] :
( ( ( in @ SV28 @ SV104 )
= $false )
| ( ( subset @ SV28 @ ( union @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(1026,plain,
! [SV160: $i,SV146: $i,SV105: $i,SV29: $i] :
( ( ~ ( subset @ SV29 @ SV105 )
| ~ ( subset @ SV146 @ SV160 )
| ( subset @ ( cartesian_product2 @ SV29 @ SV146 ) @ ( cartesian_product2 @ SV105 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1027,plain,
! [SV106: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV106 )
= $false )
| ( ( ( set_union2 @ SV30 @ SV106 )
= SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(1028,plain,
! [SV147: $i,SV108: $i,SV32: $i] :
( ( ( ~ ( subset @ SV32 @ SV108 )
| ~ ( subset @ SV32 @ SV147 ) )
= $true )
| ( ( subset @ SV32 @ ( set_intersection2 @ SV108 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(1029,plain,
! [SV148: $i,SV109: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV109 )
| ~ ( subset @ SV109 @ SV148 ) )
= $true )
| ( ( subset @ SV33 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(1030,plain,
! [SV110: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV110 )
= $false )
| ( ( ! [SY517: $i] : ( subset @ ( set_intersection2 @ SV34 @ SY517 ) @ ( set_intersection2 @ SV110 @ SY517 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(1031,plain,
! [SV111: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV111 )
= $false )
| ( ( ( set_intersection2 @ SV35 @ SV111 )
= SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(1032,plain,
! [SV112: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV112 )
= $false )
| ( ( ! [SY518: $i] : ( subset @ ( set_difference @ SV36 @ SY518 ) @ ( set_difference @ SV112 @ SY518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(1033,plain,
! [SV116: $i,SV40: $i] :
( ( ( subset @ SV40 @ SV116 )
= $false )
| ( ( SV116
= ( set_union2 @ SV40 @ ( set_difference @ SV116 @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(1034,plain,
! [SV117: $i,SV41: $i] :
( ( ( in @ SV41 @ SV117 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV41 ) @ SV117 )
= SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(1035,plain,
! [SV43: $i,SV119: $i] :
( ( ( proper_subset @ SV119 @ SV43 )
= $false )
| ( ( ~ ( subset @ SV43 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(1036,plain,
! [SV44: $i,SV149: $i,SV120: $i] :
( ( ( ~ ( disjoint @ SV120 @ SV149 )
| ~ ( subset @ SV44 @ SV120 ) )
= $true )
| ( ( disjoint @ SV44 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(1037,plain,
! [SV121: $i,SV46: $i] :
( ( ( subset @ ( singleton @ SV46 ) @ ( singleton @ SV121 ) )
= $false )
| ( ( SV46 = SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(1038,plain,
! [SV150: $i,SV123: $i,SV48: $i] :
( ( ( ~ ( subset @ SV48 @ SV123 )
| ~ ( subset @ SV150 @ SV123 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV48 @ SV150 ) @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1039,plain,
! [SV161: $i,SV124: $i,SV49: $i] :
( ( ( ( ( singleton @ SV49 )
!= ( unordered_pair @ SV124 @ SV161 ) ) )
= $true )
| ( ( SV49 = SV124 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1040,plain,
! [SV125: $i,SV50: $i] :
( ( ( in @ SV50 @ SV125 )
= $false )
| ( ( subset @ SV50 @ ( union @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(1041,plain,
! [SV151: $i,SV126: $i,SV52: $i] :
( ( ( ( ( singleton @ SV52 )
!= ( unordered_pair @ SV126 @ SV151 ) ) )
= $true )
| ( ( SV126 = SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(1042,plain,
! [SV127: $i,SV53: $i] :
( ( ( in @ SV53 @ SV127 )
= $false )
| ( ( ~ ( in @ SV127 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(1043,plain,
! [SV152: $i,SV60: $i] :
( ( ( empty @ ( set_union2 @ SV60 @ SV152 ) )
= $false )
| ( ( empty @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1044,plain,
! [SV62: $i,SV153: $i] :
( ( ( empty @ ( set_union2 @ SV153 @ SV62 ) )
= $false )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(1045,plain,
! [SV133: $i,SV63: $i] :
( ( ( empty @ SV63 )
= $true )
| ( ( empty @ SV133 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV63 @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1046,plain,
! [SV134: $i,SV67: $i] :
( ( ( disjoint @ SV67 @ SV134 )
= $false )
| ( ( disjoint @ SV134 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1047,plain,
! [SV135: $i,SV68: $i] :
( ( ( in @ SV68 @ SV135 )
= $false )
| ( ( element @ SV68 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(1048,plain,
! [SV136: $i,SV69: $i] :
( ( ( element @ SV69 @ SV136 )
= $false )
| ( ( ( empty @ SV136 )
| ( in @ SV69 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1049,plain,
! [SV70: $i,SV154: $i,SV137: $i] :
( ( ( ~ ( element @ SV137 @ ( powerset @ SV154 ) )
| ~ ( in @ SV70 @ SV137 ) )
= $true )
| ( ( element @ SV70 @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1050,plain,
! [SV71: $i,SV155: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ ( powerset @ SV155 ) )
| ~ ( in @ SV71 @ SV138 ) )
= $true )
| ( ( ~ ( empty @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1051,plain,
! [SV72: $i,SV139: $i] :
( ( ( empty @ SV139 )
= $false )
| ( ( ~ ( in @ SV72 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1052,plain,
! [SV140: $i,SV73: $i] :
( ( ( SV73 = SV140 )
= $true )
| ( ( ~ ( empty @ SV73 ) )
= $true )
| ( ( ~ ( empty @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1053,plain,
! [SV162: $i] :
( ( ! [SY542: $i] :
( ( disjoint @ SV162 @ SY542 )
| ( in @ ( sK30_C @ SY542 @ SV162 ) @ ( set_intersection2 @ SV162 @ SY542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1054,plain,
! [SV163: $i] :
( ( ! [SY543: $i] :
( ! [SY544: $i] :
~ ( in @ SY544 @ ( set_intersection2 @ SV163 @ SY543 ) )
| ~ ( disjoint @ SV163 @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1055,plain,
! [SV74: $i] :
( ( ! [SY396: $i,SY397: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY396 )
| ~ ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) )
| ~ ( ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY396 )
| ( in @ ( sK19_D @ SY397 @ SY396 @ SV74 ) @ SY397 ) ) ) )
| ( SY397
= ( set_intersection2 @ SV74 @ SY396 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(1056,plain,
! [SV74: $i] :
( ( ! [SY398: $i,SY399: $i] :
( ( SY399
!= ( set_intersection2 @ SV74 @ SY398 ) )
| ~ ( ~ ! [SY400: $i] :
( ~ ( in @ SY400 @ SV74 )
| ~ ( in @ SY400 @ SY398 )
| ( in @ SY400 @ SY399 ) )
| ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY399 )
| ( in @ SY401 @ SV74 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY399 )
| ( in @ SX3 @ SY398 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(1057,plain,
! [SV141: $i,SV75: $i] :
( ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( in @ SV75 @ SY525 )
| ~ ( in @ SV141 @ SY526 )
| ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY525 @ SY526 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(1058,plain,
! [SV141: $i,SV75: $i] :
( ( ~ ~ ( ~ ! [SY527: $i] :
( ! [SY528: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY527 @ SY528 ) )
| ( in @ SV75 @ SY527 ) )
| ~ ! [SY529: $i,SY530: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY529 @ SY530 ) )
| ( in @ SV141 @ SY530 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(1059,plain,
! [SV164: $i] :
( ( ! [SY545: $i] :
( ( ( set_difference @ SV164 @ SY545 )
!= empty_set )
| ( subset @ SV164 @ SY545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1060,plain,
! [SV165: $i] :
( ( ! [SY546: $i] :
( ~ ( subset @ SV165 @ SY546 )
| ( ( set_difference @ SV165 @ SY546 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1061,plain,
! [SV76: $i] :
( ( ( ~ ! [SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( subset @ SV76 @ SY410 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SY410 ) ) )
| ~ ! [SY411: $i] :
( ~ ( relation @ SY411 )
| ~ ( subset @ SV76 @ SY411 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SY411 ) ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1062,plain,
! [SV77: $i,SV166: $i] :
( ( ( ~ ( relation @ SV166 )
| ~ ( ~ ! [SY547: $i] :
( ~ ( relation @ SY547 )
| ~ ( ~ ( ! [SY548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ SY548 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY548 @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) ) )
| ( SY547
= ( relation_composition @ SV77 @ SV166 ) ) )
| ~ ! [SY549: $i] :
( ~ ( relation @ SY549 )
| ( SY549
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY550: $i,SY551: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY550 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY551 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY550 @ SY551 ) @ SY549 ) )
| ~ ! [SY553: $i,SY554: $i] :
( ~ ( in @ ( ordered_pair @ SY553 @ SY554 ) @ SY549 )
| ~ ( ~ ( in @ ( ordered_pair @ SY553 @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) @ SY554 ) @ SV166 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1063,plain,
! [SV78: $i] :
( ( ( ~ ! [SY421: $i] :
( ~ ( ~ ( ! [SY422: $i] :
~ ( in @ ( ordered_pair @ SY422 @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SY421 @ SV78 ) @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) ) )
| ( SY421
= ( relation_rng @ SV78 ) ) )
| ~ ! [SY423: $i] :
( ( SY423
!= ( relation_rng @ SV78 ) )
| ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY424 ) @ SV78 )
| ( in @ SY424 @ SY423 ) )
| ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY423 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY426 @ SY423 @ SV78 ) @ SY426 ) @ SV78 ) ) ) ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1064,plain,
! [SV79: $i] :
( ( ! [SY427: $i,SY428: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
!= SY427 ) ) )
| ~ ( ( in @ ( sK27_D @ SY428 @ SY427 @ SV79 ) @ SY428 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
= SV79 )
| ( ( sK27_D @ SY428 @ SY427 @ SV79 )
= SY427 ) ) )
| ( SY428
= ( unordered_pair @ SV79 @ SY427 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(1065,plain,
! [SV79: $i] :
( ( ! [SY429: $i,SY430: $i] :
( ( SY430
!= ( unordered_pair @ SV79 @ SY429 ) )
| ~ ( ~ ! [SY431: $i] :
( ~ ( in @ SY431 @ SY430 )
| ( SY431 = SV79 )
| ( SY431 = SY429 ) )
| ~ ~ ( ~ ! [SY432: $i] :
( ( SY432 != SV79 )
| ( in @ SY432 @ SY430 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY429 )
| ( in @ SX3 @ SY430 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(1066,plain,
! [SV167: $i] :
( ( ! [SY555: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SY555 @ SV167 ) @ SY555 )
| ~ ( subset @ ( sK28_C @ SY555 @ SV167 ) @ SV167 ) )
| ~ ( ( in @ ( sK28_C @ SY555 @ SV167 ) @ SY555 )
| ( subset @ ( sK28_C @ SY555 @ SV167 ) @ SV167 ) ) )
| ( SY555
= ( powerset @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1067,plain,
! [SV168: $i] :
( ( ! [SY556: $i] :
( ( SY556
!= ( powerset @ SV168 ) )
| ~ ( ~ ! [SY557: $i] :
( ~ ( in @ SY557 @ SY556 )
| ( subset @ SY557 @ SV168 ) )
| ~ ! [SY558: $i] :
( ~ ( subset @ SY558 @ SV168 )
| ( in @ SY558 @ SY556 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1068,plain,
! [SV169: $i] :
( ( ~ ( ~ ! [SY559: $i,SY560: $i] :
( ( sK48_B @ SV169 )
!= ( ordered_pair @ SY559 @ SY560 ) )
| ~ ( in @ ( sK48_B @ SV169 ) @ SV169 ) )
| ( relation @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1069,plain,
! [SV170: $i] :
( ( ~ ( relation @ SV170 )
| ! [SY561: $i] :
( ( SY561
= ( ordered_pair @ ( sK46_C @ SY561 @ SV170 ) @ ( sK47_SY328 @ SY561 @ SV170 ) ) )
| ~ ( in @ SY561 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1070,plain,
! [SV171: $i] :
( ( ! [SY562: $i] :
( ( ( set_difference @ SV171 @ ( singleton @ SY562 ) )
!= SV171 )
| ~ ( in @ SY562 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1071,plain,
! [SV172: $i] :
( ( ! [SY563: $i] :
( ( in @ SY563 @ SV172 )
| ( ( set_difference @ SV172 @ ( singleton @ SY563 ) )
= SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1072,plain,
! [SV173: $i] :
( ( ! [SY564: $i] :
( ~ ( subset @ SV173 @ ( singleton @ SY564 ) )
| ( SV173 = empty_set )
| ( SV173
= ( singleton @ SY564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1073,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1074,plain,
! [SV80: $i] :
( ( element @ ( sK6_B @ SV80 ) @ ( powerset @ SV80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(1075,plain,
! [SV80: $i] :
( ( empty @ ( sK6_B @ SV80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1076,plain,
! [SV174: $i] :
( ( ! [SY565: $i] :
( ~ ( in @ SV174 @ SY565 )
| ( subset @ ( singleton @ SV174 ) @ SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1077,plain,
! [SV175: $i] :
( ( ! [SY566: $i] :
( ~ ( subset @ ( singleton @ SV175 ) @ SY566 )
| ( in @ SV175 @ SY566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1078,plain,
! [SV81: $i] :
( ( ! [SY434: $i,SY435: $i] :
( ~ ( ~ ( ! [SY436: $i,SY437: $i] :
( ~ ( in @ SY436 @ SV81 )
| ~ ( in @ SY437 @ SY434 )
| ( ( sK23_D @ SY435 @ SY434 @ SV81 )
!= ( ordered_pair @ SY436 @ SY437 ) ) )
| ~ ( in @ ( sK23_D @ SY435 @ SY434 @ SV81 ) @ SY435 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SY435 @ SY434 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SY435 @ SY434 @ SV81 ) @ SY434 ) )
| ( ( sK23_D @ SY435 @ SY434 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SY435 @ SY434 @ SV81 ) @ ( sK25_SY317 @ SY435 @ SY434 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SY435 @ SY434 @ SV81 ) @ SY435 ) ) )
| ( SY435
= ( cartesian_product2 @ SV81 @ SY434 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(1079,plain,
! [SV81: $i] :
( ( ! [SY438: $i,SY439: $i] :
( ( SY439
!= ( cartesian_product2 @ SV81 @ SY438 ) )
| ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i,SY442: $i] :
( ~ ( in @ SY441 @ SV81 )
| ~ ( in @ SY442 @ SY438 )
| ( SY440
!= ( ordered_pair @ SY441 @ SY442 ) ) )
| ( in @ SY440 @ SY439 ) )
| ~ ! [SY443: $i] :
( ~ ( in @ SY443 @ SY439 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY443 @ SY439 @ SY438 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY443 @ SY439 @ SY438 @ SV81 ) @ SY438 ) )
| ( SY443
!= ( ordered_pair @ ( sK21_E @ SY443 @ SY439 @ SY438 @ SV81 ) @ ( sK22_SY312 @ SY443 @ SY439 @ SY438 @ SV81 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(1080,plain,
! [SV142: $i,SV82: $i] :
( ( ~ ! [SY531: $i,SY532: $i] :
( ~ ( in @ SV82 @ SY531 )
| ~ ( in @ SV142 @ SY532 )
| ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY531 @ SY532 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1081,plain,
! [SV142: $i,SV82: $i] :
( ( ~ ~ ( ~ ! [SY533: $i] :
( ! [SY534: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY533 @ SY534 ) )
| ( in @ SV82 @ SY533 ) )
| ~ ! [SY535: $i,SY536: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY535 @ SY536 ) )
| ( in @ SV142 @ SY536 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1082,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)],[948]) ).
thf(1083,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)],[949]) ).
thf(1084,plain,
! [SV176: $i] :
( ( ~ ( relation @ SV176 )
| ( ( relation_rng @ SV176 )
= ( relation_dom @ ( relation_inverse @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1085,plain,
! [SV177: $i] :
( ( ~ ( relation @ SV177 )
| ( ( relation_dom @ SV177 )
= ( relation_rng @ ( relation_inverse @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1086,plain,
! [SV83: $i] :
( ( ! [SY451: $i,SY452: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ~ ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY451 ) ) )
| ~ ( ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY452 )
| ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SY452 @ SY451 @ SV83 ) @ SY451 ) ) )
| ( SY452
= ( set_union2 @ SV83 @ SY451 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(1087,plain,
! [SV83: $i] :
( ( ! [SY453: $i,SY454: $i] :
( ( SY454
!= ( set_union2 @ SV83 @ SY453 ) )
| ~ ( ~ ! [SY455: $i] :
( ~ ( in @ SY455 @ SY454 )
| ( in @ SY455 @ SV83 )
| ( in @ SY455 @ SY453 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ~ ( in @ SY456 @ SV83 )
| ( in @ SY456 @ SY454 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY453 )
| ( in @ SX3 @ SY454 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(1088,plain,
! [SV178: $i] :
( ( ! [SY567: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SY567 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( sK20_C @ SY567 @ SV178 ) @ SY567 ) )
| ( subset @ SV178 @ SY567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1089,plain,
! [SV179: $i] :
( ( ! [SY568: $i] :
( ~ ( subset @ SV179 @ SY568 )
| ! [SY569: $i] :
( ~ ( in @ SY569 @ SV179 )
| ( in @ SY569 @ SY568 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1090,plain,
! [SV143: $i,SV84: $i] :
( ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SY537 @ SY538 ) )
| ( SV84 = SY537 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(1091,plain,
! [SV143: $i,SV84: $i] :
( ( ~ ! [SY539: $i,SY540: $i] :
( ( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SY539 @ SY540 ) )
| ( SV143 = SY540 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(1092,plain,
! [SV180: $i] :
( ( ~ ( empty @ SV180 )
| ( empty @ ( relation_rng @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1093,plain,
! [SV181: $i] :
( ( ~ ( empty @ SV181 )
| ( relation @ ( relation_rng @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1094,plain,
! [SV85: $i] :
( ( ! [SY463: $i] :
( ~ ( subset @ SY463 @ ( sK2_B @ SV85 ) )
| ( are_equipotent @ SY463 @ ( sK2_B @ SV85 ) )
| ( in @ SY463 @ ( sK2_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(1095,plain,
! [SV85: $i] :
( ( ~ ( ~ ! [SY464: $i] :
( ~ ( ~ ! [SY465: $i] :
( ~ ( subset @ SY465 @ SY464 )
| ( in @ SY465 @ ( sK3_SY299 @ SY464 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SY464 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SY464 @ ( sK2_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(1096,plain,
! [SV182: $i] :
( ( ! [SY570: $i] :
( ~ ( in @ SV182 @ SY570 )
| ( subset @ ( singleton @ SV182 ) @ SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1097,plain,
! [SV183: $i] :
( ( ! [SY571: $i] :
( ~ ( subset @ ( singleton @ SV183 ) @ SY571 )
| ( in @ SV183 @ SY571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1098,plain,
! [SV184: $i] :
( ( ! [SY572: $i] :
( ~ ( ~ ( ! [SY573: $i] :
( ~ ( in @ ( sK17_C @ SY572 @ SV184 ) @ SY573 )
| ~ ( in @ SY573 @ SV184 ) )
| ~ ( in @ ( sK17_C @ SY572 @ SV184 ) @ SY572 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SY572 @ SV184 ) @ ( sK18_SY311 @ SY572 @ SV184 ) )
| ~ ( in @ ( sK18_SY311 @ SY572 @ SV184 ) @ SV184 ) )
| ( in @ ( sK17_C @ SY572 @ SV184 ) @ SY572 ) ) )
| ( SY572
= ( union @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1099,plain,
! [SV185: $i] :
( ( ! [SY574: $i] :
( ( SY574
!= ( union @ SV185 ) )
| ~ ( ~ ! [SY575: $i] :
( ! [SY576: $i] :
( ~ ( in @ SY575 @ SY576 )
| ~ ( in @ SY576 @ SV185 ) )
| ( in @ SY575 @ SY574 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ SY574 )
| ~ ( ~ ( in @ SY577 @ ( sK16_D @ SY577 @ SY574 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SY577 @ SY574 @ SV185 ) @ SV185 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1100,plain,
! [SV86: $i] :
( ( ( ~ ! [SY468: $i] :
( ~ ( ~ ( ! [SY469: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ SY469 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ ( sK41_SY325 @ SY468 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) ) )
| ( SY468
= ( relation_dom @ SV86 ) ) )
| ~ ! [SY470: $i] :
( ( SY470
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY471: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY472 ) @ SV86 )
| ( in @ SY471 @ SY470 ) )
| ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ SY470 )
| ( in @ ( ordered_pair @ SY473 @ ( sK39_D @ SY473 @ SY470 @ SV86 ) ) @ SV86 ) ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1101,plain,
( ( empty @ sK34_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1102,plain,
! [SV186: $i] :
( ( ! [SY578: $i] :
( ( ( set_intersection2 @ SV186 @ SY578 )
!= empty_set )
| ( disjoint @ SV186 @ SY578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1103,plain,
! [SV187: $i] :
( ( ! [SY579: $i] :
( ~ ( disjoint @ SV187 @ SY579 )
| ( ( set_intersection2 @ SV187 @ SY579 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1104,plain,
! [SV188: $i] :
( ( ! [SY580: $i] :
( ( SV188 = SY580 )
| ~ ( subset @ SV188 @ SY580 )
| ( proper_subset @ SV188 @ SY580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1105,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1106,plain,
! [SV87: $i] :
( ( ! [SY474: $i] :
( ~ ( subset @ SY474 @ ( sK32_B @ SV87 ) )
| ( are_equipotent @ SY474 @ ( sK32_B @ SV87 ) )
| ( in @ SY474 @ ( sK32_B @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1107,plain,
! [SV87: $i] :
( ( ~ ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ ( sK32_B @ SV87 ) )
| ( in @ ( powerset @ SY475 ) @ ( sK32_B @ SV87 ) ) )
| ~ ~ ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) )
| ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(1108,plain,
! [SV189: $i] :
( ( ~ ( empty @ SV189 )
| ( empty @ ( relation_dom @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1109,plain,
! [SV190: $i] :
( ( ~ ( empty @ SV190 )
| ( relation @ ( relation_dom @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1110,plain,
! [SV88: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV88 ) @ ( powerset @ SV88 ) ) )
= $false )
| ( ( empty @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1111,plain,
! [SV88: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV88 ) ) )
= $false )
| ( ( empty @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1112,plain,
! [SV191: $i] :
( ( ! [SY581: $i] :
( ~ ( subset @ SV191 @ ( singleton @ SY581 ) )
| ( SV191 = empty_set )
| ( SV191
= ( singleton @ SY581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1113,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1114,plain,
! [SV192: $i] :
( ( ! [SY582: $i] :
( ( ( set_difference @ SV192 @ SY582 )
!= SV192 )
| ( disjoint @ SV192 @ SY582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1115,plain,
! [SV193: $i] :
( ( ! [SY583: $i] :
( ~ ( disjoint @ SV193 @ SY583 )
| ( ( set_difference @ SV193 @ SY583 )
= SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1116,plain,
! [SV89: $i] :
( ( ! [SY478: $i,SY479: $i] :
( ~ ( in @ SV89 @ SY479 )
| ~ ( in @ SY478 @ SY479 )
| ( subset @ ( unordered_pair @ SV89 @ SY478 ) @ SY479 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1117,plain,
! [SV89: $i] :
( ( ~ ( ~ ! [SY480: $i,SY481: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY480 ) @ SY481 )
| ( in @ SV89 @ SY481 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY482 ) @ SY483 )
| ( in @ SY482 @ SY483 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1118,plain,
! [SV90: $i] :
( ( ( ~ ! [SY484: $i] :
( ~ ( relation @ SY484 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) ) )
| ( SY484
= ( relation_inverse @ SV90 ) ) )
| ~ ! [SY485: $i] :
( ~ ( relation @ SY485 )
| ( SY485
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY486: $i,SY487: $i] :
( ~ ( in @ ( ordered_pair @ SY486 @ SY487 ) @ SY485 )
| ( in @ ( ordered_pair @ SY487 @ SY486 ) @ SV90 ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( in @ ( ordered_pair @ SY489 @ SY488 ) @ SV90 )
| ( in @ ( ordered_pair @ SY488 @ SY489 ) @ SY485 ) ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1119,plain,
! [SV194: $i] :
( ( ! [SY584: $i] :
( ~ ( ~ ( ( ( sK29_C @ SY584 @ SV194 )
!= SV194 )
| ~ ( in @ ( sK29_C @ SY584 @ SV194 ) @ SY584 ) )
| ~ ( ( ( sK29_C @ SY584 @ SV194 )
= SV194 )
| ( in @ ( sK29_C @ SY584 @ SV194 ) @ SY584 ) ) )
| ( SY584
= ( singleton @ SV194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1120,plain,
! [SV195: $i] :
( ( ! [SY585: $i] :
( ( SY585
!= ( singleton @ SV195 ) )
| ~ ( ~ ! [SY586: $i] :
( ( SY586 != SV195 )
| ( in @ SY586 @ SY585 ) )
| ~ ! [SY587: $i] :
( ~ ( in @ SY587 @ SY585 )
| ( SY587 = SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1121,plain,
! [SV91: $i,SV144: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV91 )
| ~ ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV144 ) )
= $false )
| ( ( element @ SV91 @ ( powerset @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1122,plain,
! [SV92: $i] :
( ( ! [SY491: $i,SY492: $i] :
( ~ ( relation @ SY492 )
| ~ ( in @ ( ordered_pair @ SV92 @ SY491 ) @ SY492 )
| ( in @ SV92 @ ( relation_field @ SY492 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1123,plain,
! [SV92: $i] :
( ( ! [SY493: $i,SY494: $i] :
( ~ ( relation @ SY494 )
| ~ ( in @ ( ordered_pair @ SV92 @ SY493 ) @ SY494 )
| ( in @ SY493 @ ( relation_field @ SY494 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1124,plain,
! [SV196: $i] :
( ( ! [SY588: $i] :
( ~ ( subset @ SV196 @ SY588 )
| ~ ( subset @ SY588 @ SV196 )
| ( SV196 = SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1125,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1126,plain,
! [SV197: $i] :
( ( ! [SY589: $i] :
( ( disjoint @ SV197 @ SY589 )
| ~ ( ~ ( in @ ( sK31_C @ SY589 @ SV197 ) @ SV197 )
| ~ ( in @ ( sK31_C @ SY589 @ SV197 ) @ SY589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1127,plain,
! [SV198: $i] :
( ( ! [SY590: $i] :
( ! [SY591: $i] :
( ~ ( in @ SY591 @ SV198 )
| ~ ( in @ SY591 @ SY590 ) )
| ~ ( disjoint @ SV198 @ SY590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1128,plain,
! [SV93: $i] :
( ( ! [SY495: $i,SY496: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY495 )
| ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY495 )
| ( in @ ( sK15_D @ SY496 @ SY495 @ SV93 ) @ SY496 ) ) ) )
| ( SY496
= ( set_difference @ SV93 @ SY495 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1129,plain,
! [SV93: $i] :
( ( ! [SY497: $i,SY498: $i] :
( ( SY498
!= ( set_difference @ SV93 @ SY497 ) )
| ~ ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV93 )
| ( in @ SY499 @ SY497 )
| ( in @ SY499 @ SY498 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SY498 )
| ( in @ SY500 @ SV93 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY498 )
| ~ ( in @ SX3 @ SY497 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1130,plain,
! [SV199: $i] :
( ( ! [SY592: $i] :
( ~ ( element @ SV199 @ ( powerset @ SY592 ) )
| ( subset @ SV199 @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1131,plain,
! [SV200: $i] :
( ( ! [SY593: $i] :
( ~ ( subset @ SV200 @ SY593 )
| ( element @ SV200 @ ( powerset @ SY593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1132,plain,
! [SV201: $i] :
( ( ! [SY594: $i] :
( ( ( set_difference @ SV201 @ SY594 )
!= empty_set )
| ( subset @ SV201 @ SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1133,plain,
! [SV202: $i] :
( ( ! [SY595: $i] :
( ~ ( subset @ SV202 @ SY595 )
| ( ( set_difference @ SV202 @ SY595 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1134,plain,
! [SV94: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) )
| ~ ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) ) )
= $false )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1135,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY326 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK43_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)],[1004]) ).
thf(1136,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)],[1005]) ).
thf(1137,plain,
! [SV95: $i] :
( ( ! [SY503: $i,SY504: $i] :
( ~ ( relation @ SY504 )
| ~ ( in @ ( ordered_pair @ SV95 @ SY503 ) @ SY504 )
| ( in @ SV95 @ ( relation_dom @ SY504 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1138,plain,
! [SV95: $i] :
( ( ! [SY505: $i,SY506: $i] :
( ~ ( relation @ SY506 )
| ~ ( in @ ( ordered_pair @ SV95 @ SY505 ) @ SY506 )
| ( in @ SY505 @ ( relation_rng @ SY506 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1007]) ).
thf(1139,plain,
! [SV203: $i] :
( ( ( in @ ( sK42_B @ SV203 ) @ SV203 )
| ( SV203 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1140,plain,
! [SV204: $i] :
( ( ( SV204 != empty_set )
| ! [SY596: $i] :
~ ( in @ SY596 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1141,plain,
! [SV96: $i] :
( ( ! [SY507: $i] :
( ~ ( subset @ SV96 @ SY507 )
| ! [SY508: $i] : ( subset @ ( cartesian_product2 @ SV96 @ SY508 ) @ ( cartesian_product2 @ SY507 @ SY508 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1142,plain,
! [SV96: $i] :
( ( ! [SY509: $i] :
( ~ ( subset @ SV96 @ SY509 )
| ! [SY510: $i] : ( subset @ ( cartesian_product2 @ SY510 @ SV96 ) @ ( cartesian_product2 @ SY510 @ SY509 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1143,plain,
! [SV5: $i,SV156: $i] :
( ( ( ~ ( relation @ SV156 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SV156 ) ) @ ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1144,plain,
! [SV6: $i,SV157: $i] :
( ( ( ~ ( relation @ SV157 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SV157 ) ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1145,plain,
! [SV7: $i,SV158: $i] :
( ( ( ~ ( relation @ SV158 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SV158 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SV158 ) )
= ( relation_dom @ SV7 ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1146,plain,
! [SV8: $i,SV159: $i] :
( ( ( ~ ( relation @ SV159 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SV159 ) )
| ( ( relation_rng @ ( relation_composition @ SV159 @ SV8 ) )
= ( relation_rng @ SV8 ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1147,plain,
! [SV97: $i,SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV13 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1148,plain,
! [SV98: $i,SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV14 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1149,plain,
! [SV15: $i] :
( ( ( empty @ ( relation_dom @ SV15 ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1150,plain,
! [SV16: $i] :
( ( ( empty @ ( relation_rng @ SV16 ) )
= $false )
| ( ( empty @ SV16 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1151,plain,
! [SV100: $i,SV24: $i] :
( ( ( in @ SV24 @ SV100 )
= $false )
| ( ( disjoint @ ( singleton @ SV24 ) @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1152,plain,
! [SV26: $i,SV102: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV102 )
| ( in @ SV205 @ SV26 ) )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1153,plain,
! [SV103: $i,SV27: $i,SV206: $i] :
( ( ( ( in @ SV206 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SV206 ) ) ) )
= $true )
| ( ( subset @ SV27 @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1154,plain,
! [SV160: $i,SV146: $i,SV105: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV105 )
| ~ ( subset @ SV146 @ SV160 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV29 @ SV146 ) @ ( cartesian_product2 @ SV105 @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1155,plain,
! [SV147: $i,SV108: $i,SV32: $i] :
( ( ( ~ ( subset @ SV32 @ SV108 ) )
= $true )
| ( ( ~ ( subset @ SV32 @ SV147 ) )
= $true )
| ( ( subset @ SV32 @ ( set_intersection2 @ SV108 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1156,plain,
! [SV148: $i,SV109: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV109 ) )
= $true )
| ( ( ~ ( subset @ SV109 @ SV148 ) )
= $true )
| ( ( subset @ SV33 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1157,plain,
! [SV110: $i,SV207: $i,SV34: $i] :
( ( ( subset @ ( set_intersection2 @ SV34 @ SV207 ) @ ( set_intersection2 @ SV110 @ SV207 ) )
= $true )
| ( ( subset @ SV34 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1158,plain,
! [SV112: $i,SV208: $i,SV36: $i] :
( ( ( subset @ ( set_difference @ SV36 @ SV208 ) @ ( set_difference @ SV112 @ SV208 ) )
= $true )
| ( ( subset @ SV36 @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1159,plain,
! [SV119: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV119 )
= $false )
| ( ( proper_subset @ SV119 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1160,plain,
! [SV44: $i,SV149: $i,SV120: $i] :
( ( ( ~ ( disjoint @ SV120 @ SV149 ) )
= $true )
| ( ( ~ ( subset @ SV44 @ SV120 ) )
= $true )
| ( ( disjoint @ SV44 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1161,plain,
! [SV150: $i,SV123: $i,SV48: $i] :
( ( ( ~ ( subset @ SV48 @ SV123 ) )
= $true )
| ( ( ~ ( subset @ SV150 @ SV123 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV48 @ SV150 ) @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1162,plain,
! [SV161: $i,SV124: $i,SV49: $i] :
( ( ( ( singleton @ SV49 )
= ( unordered_pair @ SV124 @ SV161 ) )
= $false )
| ( ( SV49 = SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1163,plain,
! [SV151: $i,SV126: $i,SV52: $i] :
( ( ( ( singleton @ SV52 )
= ( unordered_pair @ SV126 @ SV151 ) )
= $false )
| ( ( SV126 = SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1164,plain,
! [SV53: $i,SV127: $i] :
( ( ( in @ SV127 @ SV53 )
= $false )
| ( ( in @ SV53 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1165,plain,
! [SV133: $i,SV63: $i] :
( ( ( empty @ ( cartesian_product2 @ SV63 @ SV133 ) )
= $false )
| ( ( empty @ SV133 )
= $true )
| ( ( empty @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1166,plain,
! [SV69: $i,SV136: $i] :
( ( ( empty @ SV136 )
= $true )
| ( ( in @ SV69 @ SV136 )
= $true )
| ( ( element @ SV69 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1167,plain,
! [SV70: $i,SV154: $i,SV137: $i] :
( ( ( ~ ( element @ SV137 @ ( powerset @ SV154 ) ) )
= $true )
| ( ( ~ ( in @ SV70 @ SV137 ) )
= $true )
| ( ( element @ SV70 @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1168,plain,
! [SV71: $i,SV155: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ ( powerset @ SV155 ) ) )
= $true )
| ( ( ~ ( in @ SV71 @ SV138 ) )
= $true )
| ( ( ~ ( empty @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1169,plain,
! [SV139: $i,SV72: $i] :
( ( ( in @ SV72 @ SV139 )
= $false )
| ( ( empty @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1170,plain,
! [SV140: $i,SV73: $i] :
( ( ( empty @ SV73 )
= $false )
| ( ( SV73 = SV140 )
= $true )
| ( ( ~ ( empty @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1171,plain,
! [SV209: $i,SV162: $i] :
( ( ( disjoint @ SV162 @ SV209 )
| ( in @ ( sK30_C @ SV209 @ SV162 ) @ ( set_intersection2 @ SV162 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1172,plain,
! [SV210: $i,SV163: $i] :
( ( ! [SY597: $i] :
~ ( in @ SY597 @ ( set_intersection2 @ SV163 @ SV210 ) )
| ~ ( disjoint @ SV163 @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1173,plain,
! [SV74: $i,SV211: $i] :
( ( ! [SY598: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY598 @ SV211 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SY598 @ SV211 @ SV74 ) @ SV211 )
| ~ ( in @ ( sK19_D @ SY598 @ SV211 @ SV74 ) @ SY598 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY598 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SY598 @ SV211 @ SV74 ) @ SY598 ) )
| ~ ( ( in @ ( sK19_D @ SY598 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SY598 @ SV211 @ SV74 ) @ SY598 ) ) ) )
| ( SY598
= ( set_intersection2 @ SV74 @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1174,plain,
! [SV212: $i,SV74: $i] :
( ( ! [SY599: $i] :
( ( SY599
!= ( set_intersection2 @ SV74 @ SV212 ) )
| ~ ( ~ ! [SY600: $i] :
( ~ ( in @ SY600 @ SV74 )
| ~ ( in @ SY600 @ SV212 )
| ( in @ SY600 @ SY599 ) )
| ~ ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SY599 )
| ( in @ SY401 @ SV74 ) )
| ~ ! [SY602: $i] :
( ~ ( in @ SY602 @ SY599 )
| ( in @ SY602 @ SV212 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1175,plain,
! [SV141: $i,SV75: $i] :
( ( ! [SY525: $i,SY526: $i] :
( ~ ( in @ SV75 @ SY525 )
| ~ ( in @ SV141 @ SY526 )
| ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY525 @ SY526 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1176,plain,
! [SV141: $i,SV75: $i] :
( ( ~ ( ~ ! [SY527: $i] :
( ! [SY528: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY527 @ SY528 ) )
| ( in @ SV75 @ SY527 ) )
| ~ ! [SY529: $i,SY530: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY529 @ SY530 ) )
| ( in @ SV141 @ SY530 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1177,plain,
! [SV213: $i,SV164: $i] :
( ( ( ( set_difference @ SV164 @ SV213 )
!= empty_set )
| ( subset @ SV164 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1178,plain,
! [SV214: $i,SV165: $i] :
( ( ~ ( subset @ SV165 @ SV214 )
| ( ( set_difference @ SV165 @ SV214 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1179,plain,
! [SV76: $i] :
( ( ( ~ ! [SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( subset @ SV76 @ SY410 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SY410 ) ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1180,plain,
! [SV76: $i] :
( ( ( ~ ! [SY411: $i] :
( ~ ( relation @ SY411 )
| ~ ( subset @ SV76 @ SY411 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SY411 ) ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1181,plain,
! [SV77: $i,SV166: $i] :
( ( ( ~ ( relation @ SV166 ) )
= $true )
| ( ( ~ ( ~ ! [SY547: $i] :
( ~ ( relation @ SY547 )
| ~ ( ~ ( ! [SY548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ SY548 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY548 @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) ) )
| ( SY547
= ( relation_composition @ SV77 @ SV166 ) ) )
| ~ ! [SY549: $i] :
( ~ ( relation @ SY549 )
| ( SY549
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY550: $i,SY551: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY550 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY551 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY550 @ SY551 ) @ SY549 ) )
| ~ ! [SY553: $i,SY554: $i] :
( ~ ( in @ ( ordered_pair @ SY553 @ SY554 ) @ SY549 )
| ~ ( ~ ( in @ ( ordered_pair @ SY553 @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) @ SY554 ) @ SV166 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1182,plain,
! [SV78: $i] :
( ( ( ~ ! [SY421: $i] :
( ~ ( ~ ( ! [SY422: $i] :
~ ( in @ ( ordered_pair @ SY422 @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SY421 @ SV78 ) @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) ) )
| ( SY421
= ( relation_rng @ SV78 ) ) ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1183,plain,
! [SV78: $i] :
( ( ( ~ ! [SY423: $i] :
( ( SY423
!= ( relation_rng @ SV78 ) )
| ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY424 ) @ SV78 )
| ( in @ SY424 @ SY423 ) )
| ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY423 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY426 @ SY423 @ SV78 ) @ SY426 ) @ SV78 ) ) ) ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1184,plain,
! [SV79: $i,SV215: $i] :
( ( ! [SY603: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY603 @ SV215 @ SV79 ) @ SY603 )
| ( ( sK27_D @ SY603 @ SV215 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY603 @ SV215 @ SV79 ) @ SY603 )
| ( ( sK27_D @ SY603 @ SV215 @ SV79 )
!= SV215 ) ) )
| ~ ( ( in @ ( sK27_D @ SY603 @ SV215 @ SV79 ) @ SY603 )
| ( ( sK27_D @ SY603 @ SV215 @ SV79 )
= SV79 )
| ( ( sK27_D @ SY603 @ SV215 @ SV79 )
= SV215 ) ) )
| ( SY603
= ( unordered_pair @ SV79 @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1185,plain,
! [SV216: $i,SV79: $i] :
( ( ! [SY604: $i] :
( ( SY604
!= ( unordered_pair @ SV79 @ SV216 ) )
| ~ ( ~ ! [SY605: $i] :
( ~ ( in @ SY605 @ SY604 )
| ( SY605 = SV79 )
| ( SY605 = SV216 ) )
| ~ ~ ( ~ ! [SY432: $i] :
( ( SY432 != SV79 )
| ( in @ SY432 @ SY604 ) )
| ~ ! [SY607: $i] :
( ( SY607 != SV216 )
| ( in @ SY607 @ SY604 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1186,plain,
! [SV167: $i,SV217: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ~ ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) )
| ~ ( ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) ) )
| ( SV217
= ( powerset @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1187,plain,
! [SV168: $i,SV218: $i] :
( ( ( SV218
!= ( powerset @ SV168 ) )
| ~ ( ~ ! [SY608: $i] :
( ~ ( in @ SY608 @ SV218 )
| ( subset @ SY608 @ SV168 ) )
| ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV168 )
| ( in @ SY609 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1188,plain,
! [SV169: $i] :
( ( ( ~ ( ~ ! [SY559: $i,SY560: $i] :
( ( sK48_B @ SV169 )
!= ( ordered_pair @ SY559 @ SY560 ) )
| ~ ( in @ ( sK48_B @ SV169 ) @ SV169 ) ) )
= $true )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1189,plain,
! [SV170: $i] :
( ( ( ~ ( relation @ SV170 ) )
= $true )
| ( ( ! [SY561: $i] :
( ( SY561
= ( ordered_pair @ ( sK46_C @ SY561 @ SV170 ) @ ( sK47_SY328 @ SY561 @ SV170 ) ) )
| ~ ( in @ SY561 @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1190,plain,
! [SV219: $i,SV171: $i] :
( ( ( ( set_difference @ SV171 @ ( singleton @ SV219 ) )
!= SV171 )
| ~ ( in @ SV219 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1191,plain,
! [SV172: $i,SV220: $i] :
( ( ( in @ SV220 @ SV172 )
| ( ( set_difference @ SV172 @ ( singleton @ SV220 ) )
= SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1192,plain,
! [SV221: $i,SV173: $i] :
( ( ~ ( subset @ SV173 @ ( singleton @ SV221 ) )
| ( SV173 = empty_set )
| ( SV173
= ( singleton @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1193,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1194,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1195,plain,
! [SV222: $i,SV174: $i] :
( ( ~ ( in @ SV174 @ SV222 )
| ( subset @ ( singleton @ SV174 ) @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1196,plain,
! [SV223: $i,SV175: $i] :
( ( ~ ( subset @ ( singleton @ SV175 ) @ SV223 )
| ( in @ SV175 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1197,plain,
! [SV224: $i,SV81: $i] :
( ( ! [SY610: $i] :
( ~ ( ~ ( ! [SY611: $i,SY612: $i] :
( ~ ( in @ SY611 @ SV81 )
| ~ ( in @ SY612 @ SV224 )
| ( ( sK23_D @ SY610 @ SV224 @ SV81 )
!= ( ordered_pair @ SY611 @ SY612 ) ) )
| ~ ( in @ ( sK23_D @ SY610 @ SV224 @ SV81 ) @ SY610 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SY610 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SY610 @ SV224 @ SV81 ) @ SV224 ) )
| ( ( sK23_D @ SY610 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SY610 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SY610 @ SV224 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SY610 @ SV224 @ SV81 ) @ SY610 ) ) )
| ( SY610
= ( cartesian_product2 @ SV81 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1198,plain,
! [SV225: $i,SV81: $i] :
( ( ! [SY613: $i] :
( ( SY613
!= ( cartesian_product2 @ SV81 @ SV225 ) )
| ~ ( ~ ! [SY614: $i] :
( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SY615 @ SV81 )
| ~ ( in @ SY616 @ SV225 )
| ( SY614
!= ( ordered_pair @ SY615 @ SY616 ) ) )
| ( in @ SY614 @ SY613 ) )
| ~ ! [SY617: $i] :
( ~ ( in @ SY617 @ SY613 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY617 @ SY613 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY617 @ SY613 @ SV225 @ SV81 ) @ SV225 ) )
| ( SY617
!= ( ordered_pair @ ( sK21_E @ SY617 @ SY613 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SY617 @ SY613 @ SV225 @ SV81 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1199,plain,
! [SV142: $i,SV82: $i] :
( ( ! [SY531: $i,SY532: $i] :
( ~ ( in @ SV82 @ SY531 )
| ~ ( in @ SV142 @ SY532 )
| ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY531 @ SY532 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1200,plain,
! [SV142: $i,SV82: $i] :
( ( ~ ( ~ ! [SY533: $i] :
( ! [SY534: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY533 @ SY534 ) )
| ( in @ SV82 @ SY533 ) )
| ~ ! [SY535: $i,SY536: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY535 @ SY536 ) )
| ( in @ SV142 @ SY536 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1201,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1202,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1203,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1204,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1205,plain,
! [SV176: $i] :
( ( ( ~ ( relation @ SV176 ) )
= $true )
| ( ( ( relation_rng @ SV176 )
= ( relation_dom @ ( relation_inverse @ SV176 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1206,plain,
! [SV177: $i] :
( ( ( ~ ( relation @ SV177 ) )
= $true )
| ( ( ( relation_dom @ SV177 )
= ( relation_rng @ ( relation_inverse @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1207,plain,
! [SV83: $i,SV226: $i] :
( ( ! [SY618: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY618 @ SV226 @ SV83 ) @ SY618 )
| ~ ( in @ ( sK26_D @ SY618 @ SV226 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY618 @ SV226 @ SV83 ) @ SY618 )
| ~ ( in @ ( sK26_D @ SY618 @ SV226 @ SV83 ) @ SV226 ) ) )
| ~ ( ( in @ ( sK26_D @ SY618 @ SV226 @ SV83 ) @ SY618 )
| ( in @ ( sK26_D @ SY618 @ SV226 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SY618 @ SV226 @ SV83 ) @ SV226 ) ) )
| ( SY618
= ( set_union2 @ SV83 @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1208,plain,
! [SV227: $i,SV83: $i] :
( ( ! [SY619: $i] :
( ( SY619
!= ( set_union2 @ SV83 @ SV227 ) )
| ~ ( ~ ! [SY620: $i] :
( ~ ( in @ SY620 @ SY619 )
| ( in @ SY620 @ SV83 )
| ( in @ SY620 @ SV227 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ~ ( in @ SY456 @ SV83 )
| ( in @ SY456 @ SY619 ) )
| ~ ! [SY622: $i] :
( ~ ( in @ SY622 @ SV227 )
| ( in @ SY622 @ SY619 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1209,plain,
! [SV178: $i,SV228: $i] :
( ( ~ ( ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV228 ) )
| ( subset @ SV178 @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1210,plain,
! [SV229: $i,SV179: $i] :
( ( ~ ( subset @ SV179 @ SV229 )
| ! [SY623: $i] :
( ~ ( in @ SY623 @ SV179 )
| ( in @ SY623 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1211,plain,
! [SV143: $i,SV84: $i] :
( ( ! [SY537: $i] :
( ! [SY538: $i] :
( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SY537 @ SY538 ) )
| ( SV84 = SY537 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1212,plain,
! [SV143: $i,SV84: $i] :
( ( ! [SY539: $i,SY540: $i] :
( ( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SY539 @ SY540 ) )
| ( SV143 = SY540 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1213,plain,
! [SV180: $i] :
( ( ( ~ ( empty @ SV180 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1214,plain,
! [SV181: $i] :
( ( ( ~ ( empty @ SV181 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1215,plain,
! [SV85: $i,SV230: $i] :
( ( ~ ( subset @ SV230 @ ( sK2_B @ SV85 ) )
| ( are_equipotent @ SV230 @ ( sK2_B @ SV85 ) )
| ( in @ SV230 @ ( sK2_B @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1216,plain,
! [SV85: $i] :
( ( ~ ! [SY464: $i] :
( ~ ( ~ ! [SY465: $i] :
( ~ ( subset @ SY465 @ SY464 )
| ( in @ SY465 @ ( sK3_SY299 @ SY464 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SY464 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SY464 @ ( sK2_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1217,plain,
! [SV231: $i,SV182: $i] :
( ( ~ ( in @ SV182 @ SV231 )
| ( subset @ ( singleton @ SV182 ) @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1218,plain,
! [SV232: $i,SV183: $i] :
( ( ~ ( subset @ ( singleton @ SV183 ) @ SV232 )
| ( in @ SV183 @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1219,plain,
! [SV184: $i,SV233: $i] :
( ( ~ ( ~ ( ! [SY624: $i] :
( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SY624 )
| ~ ( in @ SY624 @ SV184 ) )
| ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) )
| ~ ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 ) )
| ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) ) )
| ( SV233
= ( union @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1220,plain,
! [SV185: $i,SV234: $i] :
( ( ( SV234
!= ( union @ SV185 ) )
| ~ ( ~ ! [SY625: $i] :
( ! [SY576: $i] :
( ~ ( in @ SY625 @ SY576 )
| ~ ( in @ SY576 @ SV185 ) )
| ( in @ SY625 @ SV234 ) )
| ~ ! [SY627: $i] :
( ~ ( in @ SY627 @ SV234 )
| ~ ( ~ ( in @ SY627 @ ( sK16_D @ SY627 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SY627 @ SV234 @ SV185 ) @ SV185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1221,plain,
! [SV86: $i] :
( ( ( ~ ! [SY468: $i] :
( ~ ( ~ ( ! [SY469: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ SY469 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ ( sK41_SY325 @ SY468 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) ) )
| ( SY468
= ( relation_dom @ SV86 ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1222,plain,
! [SV86: $i] :
( ( ( ~ ! [SY470: $i] :
( ( SY470
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY471: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY472 ) @ SV86 )
| ( in @ SY471 @ SY470 ) )
| ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ SY470 )
| ( in @ ( ordered_pair @ SY473 @ ( sK39_D @ SY473 @ SY470 @ SV86 ) ) @ SV86 ) ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1223,plain,
! [SV235: $i,SV186: $i] :
( ( ( ( set_intersection2 @ SV186 @ SV235 )
!= empty_set )
| ( disjoint @ SV186 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1224,plain,
! [SV236: $i,SV187: $i] :
( ( ~ ( disjoint @ SV187 @ SV236 )
| ( ( set_intersection2 @ SV187 @ SV236 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1225,plain,
! [SV237: $i,SV188: $i] :
( ( ( SV188 = SV237 )
| ~ ( subset @ SV188 @ SV237 )
| ( proper_subset @ SV188 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1227,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1228,plain,
! [SV87: $i,SV238: $i] :
( ( ~ ( subset @ SV238 @ ( sK32_B @ SV87 ) )
| ( are_equipotent @ SV238 @ ( sK32_B @ SV87 ) )
| ( in @ SV238 @ ( sK32_B @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1229,plain,
! [SV87: $i] :
( ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ ( sK32_B @ SV87 ) )
| ( in @ ( powerset @ SY475 ) @ ( sK32_B @ SV87 ) ) )
| ~ ~ ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) )
| ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1230,plain,
! [SV189: $i] :
( ( ( ~ ( empty @ SV189 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1231,plain,
! [SV190: $i] :
( ( ( ~ ( empty @ SV190 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1232,plain,
! [SV88: $i] :
( ( ( element @ ( sK8_B @ SV88 ) @ ( powerset @ SV88 ) )
= $true )
| ( ( empty @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1233,plain,
! [SV88: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV88 ) ) )
= $true )
| ( ( empty @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1234,plain,
! [SV239: $i,SV191: $i] :
( ( ~ ( subset @ SV191 @ ( singleton @ SV239 ) )
| ( SV191 = empty_set )
| ( SV191
= ( singleton @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1235,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1236,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1237,plain,
! [SV240: $i,SV192: $i] :
( ( ( ( set_difference @ SV192 @ SV240 )
!= SV192 )
| ( disjoint @ SV192 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1238,plain,
! [SV241: $i,SV193: $i] :
( ( ~ ( disjoint @ SV193 @ SV241 )
| ( ( set_difference @ SV193 @ SV241 )
= SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1239,plain,
! [SV242: $i,SV89: $i] :
( ( ! [SY628: $i] :
( ~ ( in @ SV89 @ SY628 )
| ~ ( in @ SV242 @ SY628 )
| ( subset @ ( unordered_pair @ SV89 @ SV242 ) @ SY628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1240,plain,
! [SV89: $i] :
( ( ~ ! [SY480: $i,SY481: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY480 ) @ SY481 )
| ( in @ SV89 @ SY481 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY482 ) @ SY483 )
| ( in @ SY482 @ SY483 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1241,plain,
! [SV90: $i] :
( ( ( ~ ! [SY484: $i] :
( ~ ( relation @ SY484 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) ) )
| ( SY484
= ( relation_inverse @ SV90 ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1242,plain,
! [SV90: $i] :
( ( ( ~ ! [SY485: $i] :
( ~ ( relation @ SY485 )
| ( SY485
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY486: $i,SY487: $i] :
( ~ ( in @ ( ordered_pair @ SY486 @ SY487 ) @ SY485 )
| ( in @ ( ordered_pair @ SY487 @ SY486 ) @ SV90 ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( in @ ( ordered_pair @ SY489 @ SY488 ) @ SV90 )
| ( in @ ( ordered_pair @ SY488 @ SY489 ) @ SY485 ) ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1243,plain,
! [SV194: $i,SV243: $i] :
( ( ~ ( ~ ( ( ( sK29_C @ SV243 @ SV194 )
!= SV194 )
| ~ ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) )
| ~ ( ( ( sK29_C @ SV243 @ SV194 )
= SV194 )
| ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) ) )
| ( SV243
= ( singleton @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1244,plain,
! [SV195: $i,SV244: $i] :
( ( ( SV244
!= ( singleton @ SV195 ) )
| ~ ( ~ ! [SY629: $i] :
( ( SY629 != SV195 )
| ( in @ SY629 @ SV244 ) )
| ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ SV244 )
| ( SY630 = SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1245,plain,
! [SV91: $i,SV144: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV91 ) )
= $false )
| ( ( element @ SV91 @ ( powerset @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1246,plain,
! [SV91: $i,SV144: $i] :
( ( ( ~ ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV144 ) )
= $false )
| ( ( element @ SV91 @ ( powerset @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1247,plain,
! [SV245: $i,SV92: $i] :
( ( ! [SY631: $i] :
( ~ ( relation @ SY631 )
| ~ ( in @ ( ordered_pair @ SV92 @ SV245 ) @ SY631 )
| ( in @ SV92 @ ( relation_field @ SY631 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1248,plain,
! [SV246: $i,SV92: $i] :
( ( ! [SY632: $i] :
( ~ ( relation @ SY632 )
| ~ ( in @ ( ordered_pair @ SV92 @ SV246 ) @ SY632 )
| ( in @ SV246 @ ( relation_field @ SY632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1249,plain,
! [SV247: $i,SV196: $i] :
( ( ~ ( subset @ SV196 @ SV247 )
| ~ ( subset @ SV247 @ SV196 )
| ( SV196 = SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1250,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1251,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1252,plain,
! [SV248: $i,SV197: $i] :
( ( ( disjoint @ SV197 @ SV248 )
| ~ ( ~ ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV197 )
| ~ ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1253,plain,
! [SV249: $i,SV198: $i] :
( ( ! [SY633: $i] :
( ~ ( in @ SY633 @ SV198 )
| ~ ( in @ SY633 @ SV249 ) )
| ~ ( disjoint @ SV198 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1254,plain,
! [SV93: $i,SV250: $i] :
( ( ! [SY634: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY634 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY634 @ SV250 @ SV93 ) @ SV250 )
| ~ ( in @ ( sK15_D @ SY634 @ SV250 @ SV93 ) @ SY634 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY634 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SY634 @ SV250 @ SV93 ) @ SY634 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY634 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SY634 @ SV250 @ SV93 ) @ SY634 ) ) ) )
| ( SY634
= ( set_difference @ SV93 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1255,plain,
! [SV251: $i,SV93: $i] :
( ( ! [SY635: $i] :
( ( SY635
!= ( set_difference @ SV93 @ SV251 ) )
| ~ ( ~ ! [SY636: $i] :
( ~ ( in @ SY636 @ SV93 )
| ( in @ SY636 @ SV251 )
| ( in @ SY636 @ SY635 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SY635 )
| ( in @ SY500 @ SV93 ) )
| ~ ! [SY638: $i] :
( ~ ( in @ SY638 @ SY635 )
| ~ ( in @ SY638 @ SV251 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1256,plain,
! [SV252: $i,SV199: $i] :
( ( ~ ( element @ SV199 @ ( powerset @ SV252 ) )
| ( subset @ SV199 @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1257,plain,
! [SV253: $i,SV200: $i] :
( ( ~ ( subset @ SV200 @ SV253 )
| ( element @ SV200 @ ( powerset @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1258,plain,
! [SV254: $i,SV201: $i] :
( ( ( ( set_difference @ SV201 @ SV254 )
!= empty_set )
| ( subset @ SV201 @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1259,plain,
! [SV255: $i,SV202: $i] :
( ( ~ ( subset @ SV202 @ SV255 )
| ( ( set_difference @ SV202 @ SV255 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1260,plain,
! [SV94: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) ) )
= $false )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1134]) ).
thf(1261,plain,
! [SV94: $i,SV145: $i] :
( ( ( ~ ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) ) )
= $false )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1134]) ).
thf(1262,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY326 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1135]) ).
thf(1263,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK43_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)],[1135]) ).
thf(1264,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1265,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1266,plain,
! [SV256: $i,SV95: $i] :
( ( ! [SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( in @ ( ordered_pair @ SV95 @ SV256 ) @ SY639 )
| ( in @ SV95 @ ( relation_dom @ SY639 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1267,plain,
! [SV257: $i,SV95: $i] :
( ( ! [SY640: $i] :
( ~ ( relation @ SY640 )
| ~ ( in @ ( ordered_pair @ SV95 @ SV257 ) @ SY640 )
| ( in @ SV257 @ ( relation_rng @ SY640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1268,plain,
! [SV203: $i] :
( ( ( in @ ( sK42_B @ SV203 ) @ SV203 )
= $true )
| ( ( SV203 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1269,plain,
! [SV204: $i] :
( ( ( ( SV204 != empty_set ) )
= $true )
| ( ( ! [SY596: $i] :
~ ( in @ SY596 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1270,plain,
! [SV258: $i,SV96: $i] :
( ( ~ ( subset @ SV96 @ SV258 )
| ! [SY641: $i] : ( subset @ ( cartesian_product2 @ SV96 @ SY641 ) @ ( cartesian_product2 @ SV258 @ SY641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1271,plain,
! [SV259: $i,SV96: $i] :
( ( ~ ( subset @ SV96 @ SV259 )
| ! [SY642: $i] : ( subset @ ( cartesian_product2 @ SY642 @ SV96 ) @ ( cartesian_product2 @ SY642 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1272,plain,
! [SV5: $i,SV156: $i] :
( ( ( relation @ SV156 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SV156 ) ) @ ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1273,plain,
! [SV6: $i,SV157: $i] :
( ( ( relation @ SV157 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SV157 ) ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1274,plain,
! [SV7: $i,SV158: $i] :
( ( ( relation @ SV158 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SV158 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SV158 ) )
= ( relation_dom @ SV7 ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1275,plain,
! [SV8: $i,SV159: $i] :
( ( ( relation @ SV159 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SV159 ) )
| ( ( relation_rng @ ( relation_composition @ SV159 @ SV8 ) )
= ( relation_rng @ SV8 ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1276,plain,
! [SV13: $i,SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( relation @ ( relation_composition @ SV13 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1277,plain,
! [SV14: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV14 )
= $false )
| ( ( relation @ ( set_union2 @ SV14 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1278,plain,
! [SV26: $i,SV102: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV102 ) )
= $true )
| ( ( in @ SV205 @ SV26 )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1279,plain,
! [SV103: $i,SV27: $i,SV206: $i] :
( ( ( in @ SV206 @ SV27 )
= $true )
| ( ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SV206 ) ) )
= $true )
| ( ( subset @ SV27 @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1280,plain,
! [SV160: $i,SV146: $i,SV105: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV105 ) )
= $true )
| ( ( ~ ( subset @ SV146 @ SV160 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV29 @ SV146 ) @ ( cartesian_product2 @ SV105 @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1281,plain,
! [SV147: $i,SV108: $i,SV32: $i] :
( ( ( subset @ SV32 @ SV108 )
= $false )
| ( ( ~ ( subset @ SV32 @ SV147 ) )
= $true )
| ( ( subset @ SV32 @ ( set_intersection2 @ SV108 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1282,plain,
! [SV148: $i,SV109: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV109 )
= $false )
| ( ( ~ ( subset @ SV109 @ SV148 ) )
= $true )
| ( ( subset @ SV33 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1283,plain,
! [SV44: $i,SV149: $i,SV120: $i] :
( ( ( disjoint @ SV120 @ SV149 )
= $false )
| ( ( ~ ( subset @ SV44 @ SV120 ) )
= $true )
| ( ( disjoint @ SV44 @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1284,plain,
! [SV150: $i,SV123: $i,SV48: $i] :
( ( ( subset @ SV48 @ SV123 )
= $false )
| ( ( ~ ( subset @ SV150 @ SV123 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV48 @ SV150 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1285,plain,
! [SV70: $i,SV154: $i,SV137: $i] :
( ( ( element @ SV137 @ ( powerset @ SV154 ) )
= $false )
| ( ( ~ ( in @ SV70 @ SV137 ) )
= $true )
| ( ( element @ SV70 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1286,plain,
! [SV71: $i,SV155: $i,SV138: $i] :
( ( ( element @ SV138 @ ( powerset @ SV155 ) )
= $false )
| ( ( ~ ( in @ SV71 @ SV138 ) )
= $true )
| ( ( ~ ( empty @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1287,plain,
! [SV73: $i,SV140: $i] :
( ( ( empty @ SV140 )
= $false )
| ( ( SV73 = SV140 )
= $true )
| ( ( empty @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1288,plain,
! [SV209: $i,SV162: $i] :
( ( ( disjoint @ SV162 @ SV209 )
= $true )
| ( ( in @ ( sK30_C @ SV209 @ SV162 ) @ ( set_intersection2 @ SV162 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1289,plain,
! [SV210: $i,SV163: $i] :
( ( ( ! [SY597: $i] :
~ ( in @ SY597 @ ( set_intersection2 @ SV163 @ SV210 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV163 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1290,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) ) )
| ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1291,plain,
! [SV212: $i,SV74: $i,SV261: $i] :
( ( ( SV261
!= ( set_intersection2 @ SV74 @ SV212 ) )
| ~ ( ~ ! [SY643: $i] :
( ~ ( in @ SY643 @ SV74 )
| ~ ( in @ SY643 @ SV212 )
| ( in @ SY643 @ SV261 ) )
| ~ ~ ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1292,plain,
! [SV141: $i,SV262: $i,SV75: $i] :
( ( ! [SY646: $i] :
( ~ ( in @ SV75 @ SV262 )
| ~ ( in @ SV141 @ SY646 )
| ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV262 @ SY646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1293,plain,
! [SV141: $i,SV75: $i] :
( ( ~ ! [SY527: $i] :
( ! [SY528: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY527 @ SY528 ) )
| ( in @ SV75 @ SY527 ) )
| ~ ! [SY529: $i,SY530: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY529 @ SY530 ) )
| ( in @ SV141 @ SY530 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1294,plain,
! [SV213: $i,SV164: $i] :
( ( ( ( ( set_difference @ SV164 @ SV213 )
!= empty_set ) )
= $true )
| ( ( subset @ SV164 @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1295,plain,
! [SV214: $i,SV165: $i] :
( ( ( ~ ( subset @ SV165 @ SV214 ) )
= $true )
| ( ( ( set_difference @ SV165 @ SV214 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1296,plain,
! [SV76: $i] :
( ( ( ! [SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( subset @ SV76 @ SY410 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SY410 ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1297,plain,
! [SV76: $i] :
( ( ( ! [SY411: $i] :
( ~ ( relation @ SY411 )
| ~ ( subset @ SV76 @ SY411 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SY411 ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1298,plain,
! [SV77: $i,SV166: $i] :
( ( ( relation @ SV166 )
= $false )
| ( ( ~ ( ~ ! [SY547: $i] :
( ~ ( relation @ SY547 )
| ~ ( ~ ( ! [SY548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ SY548 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY548 @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) ) )
| ( SY547
= ( relation_composition @ SV77 @ SV166 ) ) )
| ~ ! [SY549: $i] :
( ~ ( relation @ SY549 )
| ( SY549
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY550: $i,SY551: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY550 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY551 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY550 @ SY551 ) @ SY549 ) )
| ~ ! [SY553: $i,SY554: $i] :
( ~ ( in @ ( ordered_pair @ SY553 @ SY554 ) @ SY549 )
| ~ ( ~ ( in @ ( ordered_pair @ SY553 @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) @ SY554 ) @ SV166 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1299,plain,
! [SV78: $i] :
( ( ( ! [SY421: $i] :
( ~ ( ~ ( ! [SY422: $i] :
~ ( in @ ( ordered_pair @ SY422 @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SY421 @ SV78 ) @ ( sK37_C @ SY421 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SY421 @ SV78 ) @ SY421 ) ) )
| ( SY421
= ( relation_rng @ SV78 ) ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1300,plain,
! [SV78: $i] :
( ( ( ! [SY423: $i] :
( ( SY423
!= ( relation_rng @ SV78 ) )
| ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY424 ) @ SV78 )
| ( in @ SY424 @ SY423 ) )
| ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY423 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY426 @ SY423 @ SV78 ) @ SY426 ) @ SV78 ) ) ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1301,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) ) )
| ~ ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV79 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV215 ) ) )
| ( SV263
= ( unordered_pair @ SV79 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1302,plain,
! [SV216: $i,SV79: $i,SV264: $i] :
( ( ( SV264
!= ( unordered_pair @ SV79 @ SV216 ) )
| ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV264 )
| ( SY647 = SV79 )
| ( SY647 = SV216 ) )
| ~ ~ ( ~ ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) )
| ~ ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1303,plain,
! [SV167: $i,SV217: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ~ ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) )
| ~ ( ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) ) ) )
= $true )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1304,plain,
! [SV168: $i,SV218: $i] :
( ( ( ( SV218
!= ( powerset @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY608: $i] :
( ~ ( in @ SY608 @ SV218 )
| ( subset @ SY608 @ SV168 ) )
| ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV168 )
| ( in @ SY609 @ SV218 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1305,plain,
! [SV169: $i] :
( ( ( ~ ! [SY559: $i,SY560: $i] :
( ( sK48_B @ SV169 )
!= ( ordered_pair @ SY559 @ SY560 ) )
| ~ ( in @ ( sK48_B @ SV169 ) @ SV169 ) )
= $false )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1306,plain,
! [SV170: $i] :
( ( ( relation @ SV170 )
= $false )
| ( ( ! [SY561: $i] :
( ( SY561
= ( ordered_pair @ ( sK46_C @ SY561 @ SV170 ) @ ( sK47_SY328 @ SY561 @ SV170 ) ) )
| ~ ( in @ SY561 @ SV170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1307,plain,
! [SV219: $i,SV171: $i] :
( ( ( ( ( set_difference @ SV171 @ ( singleton @ SV219 ) )
!= SV171 ) )
= $true )
| ( ( ~ ( in @ SV219 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1308,plain,
! [SV172: $i,SV220: $i] :
( ( ( in @ SV220 @ SV172 )
= $true )
| ( ( ( set_difference @ SV172 @ ( singleton @ SV220 ) )
= SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1309,plain,
! [SV221: $i,SV173: $i] :
( ( ( ~ ( subset @ SV173 @ ( singleton @ SV221 ) ) )
= $true )
| ( ( ( SV173 = empty_set )
| ( SV173
= ( singleton @ SV221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1310,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1311,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1312,plain,
! [SV222: $i,SV174: $i] :
( ( ( ~ ( in @ SV174 @ SV222 ) )
= $true )
| ( ( subset @ ( singleton @ SV174 ) @ SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1313,plain,
! [SV223: $i,SV175: $i] :
( ( ( ~ ( subset @ ( singleton @ SV175 ) @ SV223 ) )
= $true )
| ( ( in @ SV175 @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1314,plain,
! [SV265: $i,SV224: $i,SV81: $i] :
( ( ~ ( ~ ( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV81 )
| ~ ( in @ SY651 @ SV224 )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) ) )
| ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1315,plain,
! [SV225: $i,SV81: $i,SV266: $i] :
( ( ( SV266
!= ( cartesian_product2 @ SV81 @ SV225 ) )
| ~ ( ~ ! [SY652: $i] :
( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SY615 @ SV81 )
| ~ ( in @ SY616 @ SV225 )
| ( SY652
!= ( ordered_pair @ SY615 @ SY616 ) ) )
| ( in @ SY652 @ SV266 ) )
| ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV266 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SY655
!= ( ordered_pair @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1316,plain,
! [SV142: $i,SV267: $i,SV82: $i] :
( ( ! [SY656: $i] :
( ~ ( in @ SV82 @ SV267 )
| ~ ( in @ SV142 @ SY656 )
| ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV267 @ SY656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1317,plain,
! [SV142: $i,SV82: $i] :
( ( ~ ! [SY533: $i] :
( ! [SY534: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY533 @ SY534 ) )
| ( in @ SV82 @ SY533 ) )
| ~ ! [SY535: $i,SY536: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY535 @ SY536 ) )
| ( in @ SV142 @ SY536 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1318,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1319,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1202]) ).
thf(1320,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1321,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1204]) ).
thf(1322,plain,
! [SV176: $i] :
( ( ( relation @ SV176 )
= $false )
| ( ( ( relation_rng @ SV176 )
= ( relation_dom @ ( relation_inverse @ SV176 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1323,plain,
! [SV177: $i] :
( ( ( relation @ SV177 )
= $false )
| ( ( ( relation_dom @ SV177 )
= ( relation_rng @ ( relation_inverse @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1324,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) )
| ~ ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) )
| ( SV268
= ( set_union2 @ SV83 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1325,plain,
! [SV227: $i,SV83: $i,SV269: $i] :
( ( ( SV269
!= ( set_union2 @ SV83 @ SV227 ) )
| ~ ( ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV269 )
| ( in @ SY657 @ SV83 )
| ( in @ SY657 @ SV227 ) )
| ~ ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1326,plain,
! [SV178: $i,SV228: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV228 ) ) )
= $true )
| ( ( subset @ SV178 @ SV228 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1327,plain,
! [SV229: $i,SV179: $i] :
( ( ( ~ ( subset @ SV179 @ SV229 ) )
= $true )
| ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV179 )
| ( in @ SY623 @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1328,plain,
! [SV270: $i,SV143: $i,SV84: $i] :
( ( ! [SY660: $i] :
( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SV270 @ SY660 ) )
| ( SV84 = SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1329,plain,
! [SV271: $i,SV143: $i,SV84: $i] :
( ( ! [SY661: $i] :
( ( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SV271 @ SY661 ) )
| ( SV143 = SY661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1330,plain,
! [SV180: $i] :
( ( ( empty @ SV180 )
= $false )
| ( ( empty @ ( relation_rng @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1331,plain,
! [SV181: $i] :
( ( ( empty @ SV181 )
= $false )
| ( ( relation @ ( relation_rng @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1332,plain,
! [SV85: $i,SV230: $i] :
( ( ( ~ ( subset @ SV230 @ ( sK2_B @ SV85 ) )
| ( are_equipotent @ SV230 @ ( sK2_B @ SV85 ) ) )
= $true )
| ( ( in @ SV230 @ ( sK2_B @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1333,plain,
! [SV85: $i] :
( ( ~ ! [SY464: $i] :
( ~ ( ~ ! [SY465: $i] :
( ~ ( subset @ SY465 @ SY464 )
| ( in @ SY465 @ ( sK3_SY299 @ SY464 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SY464 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SY464 @ ( sK2_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1334,plain,
! [SV85: $i] :
( ( ~ ~ ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1335,plain,
! [SV231: $i,SV182: $i] :
( ( ( ~ ( in @ SV182 @ SV231 ) )
= $true )
| ( ( subset @ ( singleton @ SV182 ) @ SV231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1336,plain,
! [SV232: $i,SV183: $i] :
( ( ( ~ ( subset @ ( singleton @ SV183 ) @ SV232 ) )
= $true )
| ( ( in @ SV183 @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1337,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( ~ ( ! [SY624: $i] :
( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SY624 )
| ~ ( in @ SY624 @ SV184 ) )
| ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) )
| ~ ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 ) )
| ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) ) ) )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1338,plain,
! [SV185: $i,SV234: $i] :
( ( ( ( SV234
!= ( union @ SV185 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY625: $i] :
( ! [SY576: $i] :
( ~ ( in @ SY625 @ SY576 )
| ~ ( in @ SY576 @ SV185 ) )
| ( in @ SY625 @ SV234 ) )
| ~ ! [SY627: $i] :
( ~ ( in @ SY627 @ SV234 )
| ~ ( ~ ( in @ SY627 @ ( sK16_D @ SY627 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SY627 @ SV234 @ SV185 ) @ SV185 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1339,plain,
! [SV86: $i] :
( ( ( ! [SY468: $i] :
( ~ ( ~ ( ! [SY469: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ SY469 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY468 @ SV86 ) @ ( sK41_SY325 @ SY468 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY468 @ SV86 ) @ SY468 ) ) )
| ( SY468
= ( relation_dom @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1340,plain,
! [SV86: $i] :
( ( ( ! [SY470: $i] :
( ( SY470
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY471: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY472 ) @ SV86 )
| ( in @ SY471 @ SY470 ) )
| ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ SY470 )
| ( in @ ( ordered_pair @ SY473 @ ( sK39_D @ SY473 @ SY470 @ SV86 ) ) @ SV86 ) ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1341,plain,
! [SV235: $i,SV186: $i] :
( ( ( ( ( set_intersection2 @ SV186 @ SV235 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV186 @ SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1342,plain,
! [SV236: $i,SV187: $i] :
( ( ( ~ ( disjoint @ SV187 @ SV236 ) )
= $true )
| ( ( ( set_intersection2 @ SV187 @ SV236 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1343,plain,
! [SV237: $i,SV188: $i] :
( ( ( ( SV188 = SV237 )
| ~ ( subset @ SV188 @ SV237 ) )
= $true )
| ( ( proper_subset @ SV188 @ SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1344,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1345,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1346,plain,
! [SV87: $i,SV238: $i] :
( ( ( ~ ( subset @ SV238 @ ( sK32_B @ SV87 ) )
| ( are_equipotent @ SV238 @ ( sK32_B @ SV87 ) ) )
= $true )
| ( ( in @ SV238 @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1347,plain,
! [SV87: $i] :
( ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ ( sK32_B @ SV87 ) )
| ( in @ ( powerset @ SY475 ) @ ( sK32_B @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1348,plain,
! [SV87: $i] :
( ( ~ ~ ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) )
| ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1349,plain,
! [SV189: $i] :
( ( ( empty @ SV189 )
= $false )
| ( ( empty @ ( relation_dom @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1350,plain,
! [SV190: $i] :
( ( ( empty @ SV190 )
= $false )
| ( ( relation @ ( relation_dom @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1351,plain,
! [SV88: $i] :
( ( ( empty @ ( sK8_B @ SV88 ) )
= $false )
| ( ( empty @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1352,plain,
! [SV239: $i,SV191: $i] :
( ( ( ~ ( subset @ SV191 @ ( singleton @ SV239 ) ) )
= $true )
| ( ( ( SV191 = empty_set )
| ( SV191
= ( singleton @ SV239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1353,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1354,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1355,plain,
! [SV240: $i,SV192: $i] :
( ( ( ( ( set_difference @ SV192 @ SV240 )
!= SV192 ) )
= $true )
| ( ( disjoint @ SV192 @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1356,plain,
! [SV241: $i,SV193: $i] :
( ( ( ~ ( disjoint @ SV193 @ SV241 ) )
= $true )
| ( ( ( set_difference @ SV193 @ SV241 )
= SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1357,plain,
! [SV242: $i,SV272: $i,SV89: $i] :
( ( ~ ( in @ SV89 @ SV272 )
| ~ ( in @ SV242 @ SV272 )
| ( subset @ ( unordered_pair @ SV89 @ SV242 ) @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1358,plain,
! [SV89: $i] :
( ( ~ ! [SY480: $i,SY481: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY480 ) @ SY481 )
| ( in @ SV89 @ SY481 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1359,plain,
! [SV89: $i] :
( ( ~ ! [SY482: $i,SY483: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY482 ) @ SY483 )
| ( in @ SY482 @ SY483 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1360,plain,
! [SV90: $i] :
( ( ( ! [SY484: $i] :
( ~ ( relation @ SY484 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY484 @ SV90 ) @ ( sK14_SY309 @ SY484 @ SV90 ) ) @ SY484 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SY484 @ SV90 ) @ ( sK13_C @ SY484 @ SV90 ) ) @ SV90 ) ) )
| ( SY484
= ( relation_inverse @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1361,plain,
! [SV90: $i] :
( ( ( ! [SY485: $i] :
( ~ ( relation @ SY485 )
| ( SY485
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY486: $i,SY487: $i] :
( ~ ( in @ ( ordered_pair @ SY486 @ SY487 ) @ SY485 )
| ( in @ ( ordered_pair @ SY487 @ SY486 ) @ SV90 ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( in @ ( ordered_pair @ SY489 @ SY488 ) @ SV90 )
| ( in @ ( ordered_pair @ SY488 @ SY489 ) @ SY485 ) ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1362,plain,
! [SV194: $i,SV243: $i] :
( ( ( ~ ( ~ ( ( ( sK29_C @ SV243 @ SV194 )
!= SV194 )
| ~ ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) )
| ~ ( ( ( sK29_C @ SV243 @ SV194 )
= SV194 )
| ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) ) ) )
= $true )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1363,plain,
! [SV195: $i,SV244: $i] :
( ( ( ( SV244
!= ( singleton @ SV195 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY629: $i] :
( ( SY629 != SV195 )
| ( in @ SY629 @ SV244 ) )
| ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ SV244 )
| ( SY630 = SV195 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1364,plain,
! [SV91: $i,SV144: $i] :
( ( ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV91 )
= $true )
| ( ( element @ SV91 @ ( powerset @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1365,plain,
! [SV91: $i,SV144: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV144 ) )
= $true )
| ( ( element @ SV91 @ ( powerset @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1366,plain,
! [SV245: $i,SV92: $i,SV273: $i] :
( ( ~ ( relation @ SV273 )
| ~ ( in @ ( ordered_pair @ SV92 @ SV245 ) @ SV273 )
| ( in @ SV92 @ ( relation_field @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1367,plain,
! [SV246: $i,SV92: $i,SV274: $i] :
( ( ~ ( relation @ SV274 )
| ~ ( in @ ( ordered_pair @ SV92 @ SV246 ) @ SV274 )
| ( in @ SV246 @ ( relation_field @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1368,plain,
! [SV247: $i,SV196: $i] :
( ( ( ~ ( subset @ SV196 @ SV247 )
| ~ ( subset @ SV247 @ SV196 ) )
= $true )
| ( ( SV196 = SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1369,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1370,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1371,plain,
! [SV248: $i,SV197: $i] :
( ( ( disjoint @ SV197 @ SV248 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV197 )
| ~ ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1372,plain,
! [SV249: $i,SV198: $i] :
( ( ( ! [SY633: $i] :
( ~ ( in @ SY633 @ SV198 )
| ~ ( in @ SY633 @ SV249 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV198 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1373,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) ) )
| ( SV275
= ( set_difference @ SV93 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1374,plain,
! [SV251: $i,SV93: $i,SV276: $i] :
( ( ( SV276
!= ( set_difference @ SV93 @ SV251 ) )
| ~ ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV93 )
| ( in @ SY662 @ SV251 )
| ( in @ SY662 @ SV276 ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) )
| ~ ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1375,plain,
! [SV252: $i,SV199: $i] :
( ( ( ~ ( element @ SV199 @ ( powerset @ SV252 ) ) )
= $true )
| ( ( subset @ SV199 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1376,plain,
! [SV253: $i,SV200: $i] :
( ( ( ~ ( subset @ SV200 @ SV253 ) )
= $true )
| ( ( element @ SV200 @ ( powerset @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1377,plain,
! [SV254: $i,SV201: $i] :
( ( ( ( ( set_difference @ SV201 @ SV254 )
!= empty_set ) )
= $true )
| ( ( subset @ SV201 @ SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1378,plain,
! [SV255: $i,SV202: $i] :
( ( ( ~ ( subset @ SV202 @ SV255 ) )
= $true )
| ( ( ( set_difference @ SV202 @ SV255 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1379,plain,
! [SV94: $i,SV145: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) )
= $true )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1380,plain,
! [SV94: $i,SV145: $i] :
( ( ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
| ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) )
= $true )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1381,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY326 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1382,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK43_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1383,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1384,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1385,plain,
! [SV256: $i,SV95: $i,SV277: $i] :
( ( ~ ( relation @ SV277 )
| ~ ( in @ ( ordered_pair @ SV95 @ SV256 ) @ SV277 )
| ( in @ SV95 @ ( relation_dom @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1386,plain,
! [SV257: $i,SV95: $i,SV278: $i] :
( ( ~ ( relation @ SV278 )
| ~ ( in @ ( ordered_pair @ SV95 @ SV257 ) @ SV278 )
| ( in @ SV257 @ ( relation_rng @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1387,plain,
! [SV204: $i] :
( ( ( SV204 = empty_set )
= $false )
| ( ( ! [SY596: $i] :
~ ( in @ SY596 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1388,plain,
! [SV258: $i,SV96: $i] :
( ( ( ~ ( subset @ SV96 @ SV258 ) )
= $true )
| ( ( ! [SY641: $i] : ( subset @ ( cartesian_product2 @ SV96 @ SY641 ) @ ( cartesian_product2 @ SV258 @ SY641 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1389,plain,
! [SV259: $i,SV96: $i] :
( ( ( ~ ( subset @ SV96 @ SV259 ) )
= $true )
| ( ( ! [SY642: $i] : ( subset @ ( cartesian_product2 @ SY642 @ SV96 ) @ ( cartesian_product2 @ SY642 @ SV259 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1390,plain,
! [SV158: $i,SV7: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SV158 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV7 @ SV158 ) )
= ( relation_dom @ SV7 ) )
= $true )
| ( ( relation @ SV158 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1391,plain,
! [SV159: $i,SV8: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SV159 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV159 @ SV8 ) )
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV159 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1392,plain,
! [SV26: $i,SV102: $i,SV205: $i] :
( ( ( in @ SV205 @ SV102 )
= $false )
| ( ( in @ SV205 @ SV26 )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1393,plain,
! [SV160: $i,SV146: $i,SV105: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV105 )
= $false )
| ( ( ~ ( subset @ SV146 @ SV160 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV29 @ SV146 ) @ ( cartesian_product2 @ SV105 @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1394,plain,
! [SV108: $i,SV147: $i,SV32: $i] :
( ( ( subset @ SV32 @ SV147 )
= $false )
| ( ( subset @ SV32 @ SV108 )
= $false )
| ( ( subset @ SV32 @ ( set_intersection2 @ SV108 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1395,plain,
! [SV33: $i,SV148: $i,SV109: $i] :
( ( ( subset @ SV109 @ SV148 )
= $false )
| ( ( subset @ SV33 @ SV109 )
= $false )
| ( ( subset @ SV33 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1396,plain,
! [SV149: $i,SV120: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV120 )
= $false )
| ( ( disjoint @ SV120 @ SV149 )
= $false )
| ( ( disjoint @ SV44 @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1397,plain,
! [SV48: $i,SV123: $i,SV150: $i] :
( ( ( subset @ SV150 @ SV123 )
= $false )
| ( ( subset @ SV48 @ SV123 )
= $false )
| ( ( subset @ ( set_union2 @ SV48 @ SV150 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1398,plain,
! [SV154: $i,SV137: $i,SV70: $i] :
( ( ( in @ SV70 @ SV137 )
= $false )
| ( ( element @ SV137 @ ( powerset @ SV154 ) )
= $false )
| ( ( element @ SV70 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1399,plain,
! [SV155: $i,SV138: $i,SV71: $i] :
( ( ( in @ SV71 @ SV138 )
= $false )
| ( ( element @ SV138 @ ( powerset @ SV155 ) )
= $false )
| ( ( ~ ( empty @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1400,plain,
! [SV210: $i,SV163: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ ( set_intersection2 @ SV163 @ SV210 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV163 @ SV210 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1401,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) ) ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1402,plain,
! [SV212: $i,SV74: $i,SV261: $i] :
( ( ( ( SV261
!= ( set_intersection2 @ SV74 @ SV212 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY643: $i] :
( ~ ( in @ SY643 @ SV74 )
| ~ ( in @ SY643 @ SV212 )
| ( in @ SY643 @ SV261 ) )
| ~ ~ ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1403,plain,
! [SV280: $i,SV141: $i,SV262: $i,SV75: $i] :
( ( ~ ( in @ SV75 @ SV262 )
| ~ ( in @ SV141 @ SV280 )
| ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV262 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1404,plain,
! [SV141: $i,SV75: $i] :
( ( ~ ! [SY527: $i] :
( ! [SY528: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY527 @ SY528 ) )
| ( in @ SV75 @ SY527 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1405,plain,
! [SV141: $i,SV75: $i] :
( ( ~ ! [SY529: $i,SY530: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY529 @ SY530 ) )
| ( in @ SV141 @ SY530 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1406,plain,
! [SV213: $i,SV164: $i] :
( ( ( ( set_difference @ SV164 @ SV213 )
= empty_set )
= $false )
| ( ( subset @ SV164 @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1407,plain,
! [SV214: $i,SV165: $i] :
( ( ( subset @ SV165 @ SV214 )
= $false )
| ( ( ( set_difference @ SV165 @ SV214 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1408,plain,
! [SV76: $i,SV281: $i] :
( ( ( ~ ( relation @ SV281 )
| ~ ( subset @ SV76 @ SV281 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SV281 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1409,plain,
! [SV76: $i,SV282: $i] :
( ( ( ~ ( relation @ SV282 )
| ~ ( subset @ SV76 @ SV282 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SV282 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1410,plain,
! [SV77: $i,SV166: $i] :
( ( ( ~ ! [SY547: $i] :
( ~ ( relation @ SY547 )
| ~ ( ~ ( ! [SY548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ SY548 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY548 @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) ) )
| ( SY547
= ( relation_composition @ SV77 @ SV166 ) ) )
| ~ ! [SY549: $i] :
( ~ ( relation @ SY549 )
| ( SY549
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY550: $i,SY551: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY550 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY551 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY550 @ SY551 ) @ SY549 ) )
| ~ ! [SY553: $i,SY554: $i] :
( ~ ( in @ ( ordered_pair @ SY553 @ SY554 ) @ SY549 )
| ~ ( ~ ( in @ ( ordered_pair @ SY553 @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) @ SY554 ) @ SV166 ) ) ) ) ) )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1411,plain,
! [SV78: $i,SV283: $i] :
( ( ( ~ ( ~ ( ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY665 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SV283 @ SV78 ) @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) ) )
| ( SV283
= ( relation_rng @ SV78 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1412,plain,
! [SV78: $i,SV284: $i] :
( ( ( ( SV284
!= ( relation_rng @ SV78 ) )
| ~ ( ~ ! [SY666: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY666 ) @ SV78 )
| ( in @ SY666 @ SV284 ) )
| ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV284 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY668 @ SV284 @ SV78 ) @ SY668 ) @ SV78 ) ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1413,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) ) )
| ~ ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV79 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV215 ) ) ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1414,plain,
! [SV216: $i,SV79: $i,SV264: $i] :
( ( ( ( SV264
!= ( unordered_pair @ SV79 @ SV216 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV264 )
| ( SY647 = SV79 )
| ( SY647 = SV216 ) )
| ~ ~ ( ~ ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) )
| ~ ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1415,plain,
! [SV167: $i,SV217: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ~ ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) )
| ~ ( ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) ) )
= $false )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1416,plain,
! [SV168: $i,SV218: $i] :
( ( ( SV218
= ( powerset @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY608: $i] :
( ~ ( in @ SY608 @ SV218 )
| ( subset @ SY608 @ SV168 ) )
| ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV168 )
| ( in @ SY609 @ SV218 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1417,plain,
! [SV169: $i] :
( ( ( ~ ! [SY559: $i,SY560: $i] :
( ( sK48_B @ SV169 )
!= ( ordered_pair @ SY559 @ SY560 ) ) )
= $false )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1305]) ).
thf(1418,plain,
! [SV169: $i] :
( ( ( ~ ( in @ ( sK48_B @ SV169 ) @ SV169 ) )
= $false )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1305]) ).
thf(1419,plain,
! [SV170: $i,SV285: $i] :
( ( ( ( SV285
= ( ordered_pair @ ( sK46_C @ SV285 @ SV170 ) @ ( sK47_SY328 @ SV285 @ SV170 ) ) )
| ~ ( in @ SV285 @ SV170 ) )
= $true )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1420,plain,
! [SV219: $i,SV171: $i] :
( ( ( ( set_difference @ SV171 @ ( singleton @ SV219 ) )
= SV171 )
= $false )
| ( ( ~ ( in @ SV219 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1421,plain,
! [SV221: $i,SV173: $i] :
( ( ( subset @ SV173 @ ( singleton @ SV221 ) )
= $false )
| ( ( ( SV173 = empty_set )
| ( SV173
= ( singleton @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1422,plain,
! [SV286: $i] :
( ( ( SV286 != empty_set )
| ! [SY669: $i] : ( subset @ SV286 @ ( singleton @ SY669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1423,plain,
! [SV287: $i] :
( ( ! [SY670: $i] :
( ( SV287
!= ( singleton @ SY670 ) )
| ( subset @ SV287 @ ( singleton @ SY670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1424,plain,
! [SV222: $i,SV174: $i] :
( ( ( in @ SV174 @ SV222 )
= $false )
| ( ( subset @ ( singleton @ SV174 ) @ SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1425,plain,
! [SV223: $i,SV175: $i] :
( ( ( subset @ ( singleton @ SV175 ) @ SV223 )
= $false )
| ( ( in @ SV175 @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1426,plain,
! [SV265: $i,SV224: $i,SV81: $i] :
( ( ( ~ ( ~ ( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV81 )
| ~ ( in @ SY651 @ SV224 )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) ) ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1427,plain,
! [SV225: $i,SV81: $i,SV266: $i] :
( ( ( ( SV266
!= ( cartesian_product2 @ SV81 @ SV225 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY652: $i] :
( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SY615 @ SV81 )
| ~ ( in @ SY616 @ SV225 )
| ( SY652
!= ( ordered_pair @ SY615 @ SY616 ) ) )
| ( in @ SY652 @ SV266 ) )
| ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV266 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SY655
!= ( ordered_pair @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1428,plain,
! [SV288: $i,SV142: $i,SV267: $i,SV82: $i] :
( ( ~ ( in @ SV82 @ SV267 )
| ~ ( in @ SV142 @ SV288 )
| ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV267 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1429,plain,
! [SV142: $i,SV82: $i] :
( ( ~ ! [SY533: $i] :
( ! [SY534: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY533 @ SY534 ) )
| ( in @ SV82 @ SY533 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1317]) ).
thf(1430,plain,
! [SV142: $i,SV82: $i] :
( ( ~ ! [SY535: $i,SY536: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY535 @ SY536 ) )
| ( in @ SV142 @ SY536 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1317]) ).
thf(1431,plain,
! [SV289: $i] :
( ( ( empty @ SV289 )
| ! [SY671: $i] :
( ~ ( element @ SY671 @ SV289 )
| ( in @ SY671 @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1432,plain,
! [SV290: $i] :
( ( ( empty @ SV290 )
| ! [SY672: $i] :
( ~ ( in @ SY672 @ SV290 )
| ( element @ SY672 @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1433,plain,
! [SV291: $i] :
( ( ~ ( empty @ SV291 )
| ! [SY673: $i] :
( ~ ( element @ SY673 @ SV291 )
| ( empty @ SY673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1434,plain,
! [SV292: $i] :
( ( ~ ( empty @ SV292 )
| ! [SY674: $i] :
( ~ ( empty @ SY674 )
| ( element @ SY674 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1435,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) )
| ~ ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1436,plain,
! [SV227: $i,SV83: $i,SV269: $i] :
( ( ( ( SV269
!= ( set_union2 @ SV83 @ SV227 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV269 )
| ( in @ SY657 @ SV83 )
| ( in @ SY657 @ SV227 ) )
| ~ ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1437,plain,
! [SV178: $i,SV228: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV228 ) )
= $false )
| ( ( subset @ SV178 @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1438,plain,
! [SV229: $i,SV179: $i] :
( ( ( subset @ SV179 @ SV229 )
= $false )
| ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV179 )
| ( in @ SY623 @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1439,plain,
! [SV270: $i,SV143: $i,SV84: $i] :
( ( ( ! [SY660: $i] :
( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SV270 @ SY660 ) ) )
= $true )
| ( ( SV84 = SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1440,plain,
! [SV293: $i,SV271: $i,SV143: $i,SV84: $i] :
( ( ( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SV271 @ SV293 ) )
| ( SV143 = SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1441,plain,
! [SV85: $i,SV230: $i] :
( ( ( ~ ( subset @ SV230 @ ( sK2_B @ SV85 ) ) )
= $true )
| ( ( are_equipotent @ SV230 @ ( sK2_B @ SV85 ) )
= $true )
| ( ( in @ SV230 @ ( sK2_B @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1442,plain,
! [SV85: $i] :
( ( ! [SY464: $i] :
( ~ ( ~ ! [SY465: $i] :
( ~ ( subset @ SY465 @ SY464 )
| ( in @ SY465 @ ( sK3_SY299 @ SY464 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SY464 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SY464 @ ( sK2_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1443,plain,
! [SV85: $i] :
( ( ~ ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1444,plain,
! [SV231: $i,SV182: $i] :
( ( ( in @ SV182 @ SV231 )
= $false )
| ( ( subset @ ( singleton @ SV182 ) @ SV231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1445,plain,
! [SV232: $i,SV183: $i] :
( ( ( subset @ ( singleton @ SV183 ) @ SV232 )
= $false )
| ( ( in @ SV183 @ SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1446,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( ! [SY624: $i] :
( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SY624 )
| ~ ( in @ SY624 @ SV184 ) )
| ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) )
| ~ ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 ) )
| ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) ) )
= $false )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1447,plain,
! [SV185: $i,SV234: $i] :
( ( ( SV234
= ( union @ SV185 ) )
= $false )
| ( ( ~ ( ~ ! [SY625: $i] :
( ! [SY576: $i] :
( ~ ( in @ SY625 @ SY576 )
| ~ ( in @ SY576 @ SV185 ) )
| ( in @ SY625 @ SV234 ) )
| ~ ! [SY627: $i] :
( ~ ( in @ SY627 @ SV234 )
| ~ ( ~ ( in @ SY627 @ ( sK16_D @ SY627 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SY627 @ SV234 @ SV185 ) @ SV185 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1448,plain,
! [SV86: $i,SV294: $i] :
( ( ( ~ ( ~ ( ! [SY675: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SY675 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ ( sK41_SY325 @ SV294 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) ) )
| ( SV294
= ( relation_dom @ SV86 ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1449,plain,
! [SV86: $i,SV295: $i] :
( ( ( ( SV295
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY676: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY676 @ SY472 ) @ SV86 )
| ( in @ SY676 @ SV295 ) )
| ~ ! [SY678: $i] :
( ~ ( in @ SY678 @ SV295 )
| ( in @ ( ordered_pair @ SY678 @ ( sK39_D @ SY678 @ SV295 @ SV86 ) ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1450,plain,
! [SV235: $i,SV186: $i] :
( ( ( ( set_intersection2 @ SV186 @ SV235 )
= empty_set )
= $false )
| ( ( disjoint @ SV186 @ SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1451,plain,
! [SV236: $i,SV187: $i] :
( ( ( disjoint @ SV187 @ SV236 )
= $false )
| ( ( ( set_intersection2 @ SV187 @ SV236 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1452,plain,
! [SV237: $i,SV188: $i] :
( ( ( SV188 = SV237 )
= $true )
| ( ( ~ ( subset @ SV188 @ SV237 ) )
= $true )
| ( ( proper_subset @ SV188 @ SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1453,plain,
! [SV296: $i] :
( ( ! [SY679: $i] :
( ~ ( proper_subset @ SV296 @ SY679 )
| ( SV296 != SY679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1454,plain,
! [SV297: $i] :
( ( ! [SY680: $i] :
( ~ ( proper_subset @ SV297 @ SY680 )
| ( subset @ SV297 @ SY680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1455,plain,
! [SV87: $i,SV238: $i] :
( ( ( ~ ( subset @ SV238 @ ( sK32_B @ SV87 ) ) )
= $true )
| ( ( are_equipotent @ SV238 @ ( sK32_B @ SV87 ) )
= $true )
| ( ( in @ SV238 @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1456,plain,
! [SV87: $i] :
( ( ! [SY475: $i] :
( ~ ( in @ SY475 @ ( sK32_B @ SV87 ) )
| ( in @ ( powerset @ SY475 ) @ ( sK32_B @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1457,plain,
! [SV87: $i] :
( ( ~ ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) )
| ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1458,plain,
! [SV239: $i,SV191: $i] :
( ( ( subset @ SV191 @ ( singleton @ SV239 ) )
= $false )
| ( ( ( SV191 = empty_set )
| ( SV191
= ( singleton @ SV239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1459,plain,
! [SV298: $i] :
( ( ( SV298 != empty_set )
| ! [SY681: $i] : ( subset @ SV298 @ ( singleton @ SY681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1460,plain,
! [SV299: $i] :
( ( ! [SY682: $i] :
( ( SV299
!= ( singleton @ SY682 ) )
| ( subset @ SV299 @ ( singleton @ SY682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1461,plain,
! [SV240: $i,SV192: $i] :
( ( ( ( set_difference @ SV192 @ SV240 )
= SV192 )
= $false )
| ( ( disjoint @ SV192 @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1462,plain,
! [SV241: $i,SV193: $i] :
( ( ( disjoint @ SV193 @ SV241 )
= $false )
| ( ( ( set_difference @ SV193 @ SV241 )
= SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1463,plain,
! [SV242: $i,SV272: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV272 )
| ~ ( in @ SV242 @ SV272 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV89 @ SV242 ) @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1464,plain,
! [SV89: $i] :
( ( ! [SY480: $i,SY481: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY480 ) @ SY481 )
| ( in @ SV89 @ SY481 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1465,plain,
! [SV89: $i] :
( ( ! [SY482: $i,SY483: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SY482 ) @ SY483 )
| ( in @ SY482 @ SY483 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1466,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( relation @ SV300 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) ) )
| ( SV300
= ( relation_inverse @ SV90 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1467,plain,
! [SV90: $i,SV301: $i] :
( ( ( ~ ( relation @ SV301 )
| ( SV301
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY683: $i,SY684: $i] :
( ~ ( in @ ( ordered_pair @ SY683 @ SY684 ) @ SV301 )
| ( in @ ( ordered_pair @ SY684 @ SY683 ) @ SV90 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY686 @ SY685 ) @ SV90 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV301 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1468,plain,
! [SV194: $i,SV243: $i] :
( ( ( ~ ( ( ( sK29_C @ SV243 @ SV194 )
!= SV194 )
| ~ ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) )
| ~ ( ( ( sK29_C @ SV243 @ SV194 )
= SV194 )
| ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) ) )
= $false )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1469,plain,
! [SV195: $i,SV244: $i] :
( ( ( SV244
= ( singleton @ SV195 ) )
= $false )
| ( ( ~ ( ~ ! [SY629: $i] :
( ( SY629 != SV195 )
| ( in @ SY629 @ SV244 ) )
| ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ SV244 )
| ( SY630 = SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1470,plain,
! [SV91: $i,SV144: $i] :
( ( ( in @ ( sK33_C @ SV144 @ SV91 ) @ SV144 )
= $false )
| ( ( element @ SV91 @ ( powerset @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1471,plain,
! [SV245: $i,SV92: $i,SV273: $i] :
( ( ( ~ ( relation @ SV273 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV92 @ SV245 ) @ SV273 )
| ( in @ SV92 @ ( relation_field @ SV273 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1472,plain,
! [SV246: $i,SV92: $i,SV274: $i] :
( ( ( ~ ( relation @ SV274 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV92 @ SV246 ) @ SV274 )
| ( in @ SV246 @ ( relation_field @ SV274 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1473,plain,
! [SV247: $i,SV196: $i] :
( ( ( ~ ( subset @ SV196 @ SV247 ) )
= $true )
| ( ( ~ ( subset @ SV247 @ SV196 ) )
= $true )
| ( ( SV196 = SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1474,plain,
! [SV302: $i] :
( ( ! [SY687: $i] :
( ( SV302 != SY687 )
| ( subset @ SV302 @ SY687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1475,plain,
! [SV303: $i] :
( ( ! [SY688: $i] :
( ( SV303 != SY688 )
| ( subset @ SY688 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1476,plain,
! [SV197: $i,SV248: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV197 )
| ~ ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV248 ) )
= $false )
| ( ( disjoint @ SV197 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1477,plain,
! [SV249: $i,SV198: $i,SV304: $i] :
( ( ( ~ ( in @ SV304 @ SV198 )
| ~ ( in @ SV304 @ SV249 ) )
= $true )
| ( ( ~ ( disjoint @ SV198 @ SV249 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1478,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) ) ) )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1479,plain,
! [SV251: $i,SV93: $i,SV276: $i] :
( ( ( ( SV276
!= ( set_difference @ SV93 @ SV251 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV93 )
| ( in @ SY662 @ SV251 )
| ( in @ SY662 @ SV276 ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) )
| ~ ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1480,plain,
! [SV252: $i,SV199: $i] :
( ( ( element @ SV199 @ ( powerset @ SV252 ) )
= $false )
| ( ( subset @ SV199 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1481,plain,
! [SV253: $i,SV200: $i] :
( ( ( subset @ SV200 @ SV253 )
= $false )
| ( ( element @ SV200 @ ( powerset @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1482,plain,
! [SV254: $i,SV201: $i] :
( ( ( ( set_difference @ SV201 @ SV254 )
= empty_set )
= $false )
| ( ( subset @ SV201 @ SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1483,plain,
! [SV255: $i,SV202: $i] :
( ( ( subset @ SV202 @ SV255 )
= $false )
| ( ( ( set_difference @ SV202 @ SV255 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1484,plain,
! [SV94: $i,SV145: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) )
= $true )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1485,plain,
! [SV94: $i,SV145: $i] :
( ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
= $true )
| ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 )
= $true )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1486,plain,
! [SV305: $i] :
( ( ( SV305 = empty_set )
| ! [SY689: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SY689 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SY689 @ SV305 ) @ ( sK45_SY326 @ SY689 @ SV305 ) ) )
| ~ ( in @ ( sK44_C @ SY689 @ SV305 ) @ SY689 ) )
| ~ ( ! [SY690: $i] :
( ~ ( in @ SY690 @ SV305 )
| ( in @ ( sK44_C @ SY689 @ SV305 ) @ SY690 ) )
| ( in @ ( sK44_C @ SY689 @ SV305 ) @ SY689 ) ) )
| ( SY689
= ( set_meet @ SV305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1487,plain,
! [SV306: $i] :
( ( ( SV306 = empty_set )
| ! [SY691: $i] :
( ( SY691
!= ( set_meet @ SV306 ) )
| ~ ( ~ ! [SY692: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY692 @ SY691 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SY692 @ ( sK43_D @ SY692 @ SY691 @ SV306 ) ) )
| ( in @ SY692 @ SY691 ) )
| ~ ! [SY693: $i] :
( ~ ( in @ SY693 @ SY691 )
| ! [SY694: $i] :
( ~ ( in @ SY694 @ SV306 )
| ( in @ SY693 @ SY694 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1488,plain,
! [SV307: $i] :
( ( ( SV307 != empty_set )
| ! [SY695: $i] :
( ( SY695
!= ( set_meet @ SV307 ) )
| ( SY695 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1489,plain,
! [SV308: $i] :
( ( ( SV308 != empty_set )
| ! [SY696: $i] :
( ( SY696 != empty_set )
| ( SY696
= ( set_meet @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1490,plain,
! [SV256: $i,SV95: $i,SV277: $i] :
( ( ( ~ ( relation @ SV277 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV95 @ SV256 ) @ SV277 )
| ( in @ SV95 @ ( relation_dom @ SV277 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1491,plain,
! [SV257: $i,SV95: $i,SV278: $i] :
( ( ( ~ ( relation @ SV278 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV95 @ SV257 ) @ SV278 )
| ( in @ SV257 @ ( relation_rng @ SV278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1492,plain,
! [SV204: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV204 ) )
= $true )
| ( ( SV204 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1493,plain,
! [SV258: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV258 )
= $false )
| ( ( ! [SY641: $i] : ( subset @ ( cartesian_product2 @ SV96 @ SY641 ) @ ( cartesian_product2 @ SV258 @ SY641 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1494,plain,
! [SV259: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV259 )
= $false )
| ( ( ! [SY642: $i] : ( subset @ ( cartesian_product2 @ SY642 @ SV96 ) @ ( cartesian_product2 @ SY642 @ SV259 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1495,plain,
! [SV158: $i,SV7: $i] :
( ( ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SV158 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV7 @ SV158 ) )
= ( relation_dom @ SV7 ) )
= $true )
| ( ( relation @ SV158 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1496,plain,
! [SV159: $i,SV8: $i] :
( ( ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SV159 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV159 @ SV8 ) )
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV159 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1497,plain,
! [SV105: $i,SV29: $i,SV160: $i,SV146: $i] :
( ( ( subset @ SV146 @ SV160 )
= $false )
| ( ( subset @ SV29 @ SV105 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV29 @ SV146 ) @ ( cartesian_product2 @ SV105 @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1498,plain,
! [SV71: $i,SV138: $i,SV155: $i] :
( ( ( empty @ SV155 )
= $false )
| ( ( element @ SV138 @ ( powerset @ SV155 ) )
= $false )
| ( ( in @ SV71 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1499,plain,
! [SV210: $i,SV163: $i,SV279: $i] :
( ( ( in @ SV279 @ ( set_intersection2 @ SV163 @ SV210 ) )
= $false )
| ( ( ~ ( disjoint @ SV163 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1500,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) ) )
= $false )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1501,plain,
! [SV212: $i,SV74: $i,SV261: $i] :
( ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false )
| ( ( ~ ( ~ ! [SY643: $i] :
( ~ ( in @ SY643 @ SV74 )
| ~ ( in @ SY643 @ SV212 )
| ( in @ SY643 @ SV261 ) )
| ~ ~ ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1502,plain,
! [SV280: $i,SV141: $i,SV262: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV262 )
| ~ ( in @ SV141 @ SV280 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV262 @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1503,plain,
! [SV141: $i,SV75: $i] :
( ( ! [SY527: $i] :
( ! [SY528: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY527 @ SY528 ) )
| ( in @ SV75 @ SY527 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1504,plain,
! [SV141: $i,SV75: $i] :
( ( ! [SY529: $i,SY530: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SY529 @ SY530 ) )
| ( in @ SV141 @ SY530 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1505,plain,
! [SV76: $i,SV281: $i] :
( ( ( ~ ( relation @ SV281 ) )
= $true )
| ( ( ~ ( subset @ SV76 @ SV281 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SV281 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1506,plain,
! [SV76: $i,SV282: $i] :
( ( ( ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( subset @ SV76 @ SV282 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SV282 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1507,plain,
! [SV77: $i,SV166: $i] :
( ( ( ~ ! [SY547: $i] :
( ~ ( relation @ SY547 )
| ~ ( ~ ( ! [SY548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ SY548 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY548 @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) ) )
| ( SY547
= ( relation_composition @ SV77 @ SV166 ) ) ) )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1410]) ).
thf(1508,plain,
! [SV166: $i,SV77: $i] :
( ( ( ~ ! [SY549: $i] :
( ~ ( relation @ SY549 )
| ( SY549
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY550: $i,SY551: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY550 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY551 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY550 @ SY551 ) @ SY549 ) )
| ~ ! [SY553: $i,SY554: $i] :
( ~ ( in @ ( ordered_pair @ SY553 @ SY554 ) @ SY549 )
| ~ ( ~ ( in @ ( ordered_pair @ SY553 @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) @ SY554 ) @ SV166 ) ) ) ) ) )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1410]) ).
thf(1509,plain,
! [SV78: $i,SV283: $i] :
( ( ( ~ ( ~ ( ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY665 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SV283 @ SV78 ) @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) ) ) )
= $true )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1510,plain,
! [SV78: $i,SV284: $i] :
( ( ( ( SV284
!= ( relation_rng @ SV78 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY666: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY666 ) @ SV78 )
| ( in @ SY666 @ SV284 ) )
| ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV284 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY668 @ SV284 @ SV78 ) @ SY668 ) @ SV78 ) ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1511,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) ) )
| ~ ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV79 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV215 ) ) )
= $false )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1512,plain,
! [SV216: $i,SV79: $i,SV264: $i] :
( ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV264 )
| ( SY647 = SV79 )
| ( SY647 = SV216 ) )
| ~ ~ ( ~ ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) )
| ~ ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1513,plain,
! [SV167: $i,SV217: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ~ ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) ) )
= $false )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1514,plain,
! [SV167: $i,SV217: $i] :
( ( ( ~ ( ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) ) )
= $false )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1515,plain,
! [SV168: $i,SV218: $i] :
( ( ( ~ ! [SY608: $i] :
( ~ ( in @ SY608 @ SV218 )
| ( subset @ SY608 @ SV168 ) )
| ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV168 )
| ( in @ SY609 @ SV218 ) ) )
= $false )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1516,plain,
! [SV169: $i] :
( ( ( ! [SY559: $i,SY560: $i] :
( ( sK48_B @ SV169 )
!= ( ordered_pair @ SY559 @ SY560 ) ) )
= $true )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1517,plain,
! [SV169: $i] :
( ( ( in @ ( sK48_B @ SV169 ) @ SV169 )
= $true )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1518,plain,
! [SV170: $i,SV285: $i] :
( ( ( SV285
= ( ordered_pair @ ( sK46_C @ SV285 @ SV170 ) @ ( sK47_SY328 @ SV285 @ SV170 ) ) )
= $true )
| ( ( ~ ( in @ SV285 @ SV170 ) )
= $true )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1519,plain,
! [SV171: $i,SV219: $i] :
( ( ( in @ SV219 @ SV171 )
= $false )
| ( ( ( set_difference @ SV171 @ ( singleton @ SV219 ) )
= SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1520,plain,
! [SV221: $i,SV173: $i] :
( ( ( SV173 = empty_set )
= $true )
| ( ( SV173
= ( singleton @ SV221 ) )
= $true )
| ( ( subset @ SV173 @ ( singleton @ SV221 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1521,plain,
! [SV286: $i] :
( ( ( ( SV286 != empty_set ) )
= $true )
| ( ( ! [SY669: $i] : ( subset @ SV286 @ ( singleton @ SY669 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1522,plain,
! [SV310: $i,SV287: $i] :
( ( ( SV287
!= ( singleton @ SV310 ) )
| ( subset @ SV287 @ ( singleton @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1523,plain,
! [SV265: $i,SV224: $i,SV81: $i] :
( ( ( ~ ( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV81 )
| ~ ( in @ SY651 @ SV224 )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) ) )
= $false )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1524,plain,
! [SV225: $i,SV81: $i,SV266: $i] :
( ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ! [SY652: $i] :
( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SY615 @ SV81 )
| ~ ( in @ SY616 @ SV225 )
| ( SY652
!= ( ordered_pair @ SY615 @ SY616 ) ) )
| ( in @ SY652 @ SV266 ) )
| ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV266 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SY655
!= ( ordered_pair @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1525,plain,
! [SV288: $i,SV142: $i,SV267: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ SV267 )
| ~ ( in @ SV142 @ SV288 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV267 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1526,plain,
! [SV142: $i,SV82: $i] :
( ( ! [SY533: $i] :
( ! [SY534: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY533 @ SY534 ) )
| ( in @ SV82 @ SY533 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1527,plain,
! [SV142: $i,SV82: $i] :
( ( ! [SY535: $i,SY536: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SY535 @ SY536 ) )
| ( in @ SV142 @ SY536 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1528,plain,
! [SV289: $i] :
( ( ( empty @ SV289 )
= $true )
| ( ( ! [SY671: $i] :
( ~ ( element @ SY671 @ SV289 )
| ( in @ SY671 @ SV289 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1529,plain,
! [SV290: $i] :
( ( ( empty @ SV290 )
= $true )
| ( ( ! [SY672: $i] :
( ~ ( in @ SY672 @ SV290 )
| ( element @ SY672 @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1530,plain,
! [SV291: $i] :
( ( ( ~ ( empty @ SV291 ) )
= $true )
| ( ( ! [SY673: $i] :
( ~ ( element @ SY673 @ SV291 )
| ( empty @ SY673 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1531,plain,
! [SV292: $i] :
( ( ( ~ ( empty @ SV292 ) )
= $true )
| ( ( ! [SY674: $i] :
( ~ ( empty @ SY674 )
| ( element @ SY674 @ SV292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1532,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) )
| ~ ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) )
= $false )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1533,plain,
! [SV227: $i,SV83: $i,SV269: $i] :
( ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false )
| ( ( ~ ( ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV269 )
| ( in @ SY657 @ SV83 )
| ( in @ SY657 @ SV227 ) )
| ~ ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1534,plain,
! [SV178: $i,SV228: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV178 ) )
= $false )
| ( ( subset @ SV178 @ SV228 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1535,plain,
! [SV178: $i,SV228: $i] :
( ( ( ~ ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV228 ) )
= $false )
| ( ( subset @ SV178 @ SV228 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1536,plain,
! [SV229: $i,SV179: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ SV179 )
| ( in @ SV311 @ SV229 ) )
= $true )
| ( ( subset @ SV179 @ SV229 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1537,plain,
! [SV312: $i,SV270: $i,SV143: $i,SV84: $i] :
( ( ( ( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SV270 @ SV312 ) ) )
= $true )
| ( ( SV84 = SV270 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1538,plain,
! [SV293: $i,SV271: $i,SV143: $i,SV84: $i] :
( ( ( ( ( ordered_pair @ SV84 @ SV143 )
!= ( ordered_pair @ SV271 @ SV293 ) ) )
= $true )
| ( ( SV143 = SV293 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1539,plain,
! [SV85: $i,SV230: $i] :
( ( ( subset @ SV230 @ ( sK2_B @ SV85 ) )
= $false )
| ( ( are_equipotent @ SV230 @ ( sK2_B @ SV85 ) )
= $true )
| ( ( in @ SV230 @ ( sK2_B @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1540,plain,
! [SV85: $i,SV313: $i] :
( ( ~ ( ~ ! [SY697: $i] :
( ~ ( subset @ SY697 @ SV313 )
| ( in @ SY697 @ ( sK3_SY299 @ SV313 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SV313 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1541,plain,
! [SV85: $i] :
( ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1542,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( ! [SY624: $i] :
( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SY624 )
| ~ ( in @ SY624 @ SV184 ) )
| ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) ) )
= $false )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1543,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) )
| ~ ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 ) )
| ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) ) )
= $false )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1544,plain,
! [SV234: $i,SV185: $i] :
( ( ( ~ ! [SY625: $i] :
( ! [SY576: $i] :
( ~ ( in @ SY625 @ SY576 )
| ~ ( in @ SY576 @ SV185 ) )
| ( in @ SY625 @ SV234 ) )
| ~ ! [SY627: $i] :
( ~ ( in @ SY627 @ SV234 )
| ~ ( ~ ( in @ SY627 @ ( sK16_D @ SY627 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SY627 @ SV234 @ SV185 ) @ SV185 ) ) ) )
= $false )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1545,plain,
! [SV86: $i,SV294: $i] :
( ( ( ~ ( ~ ( ! [SY675: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SY675 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ ( sK41_SY325 @ SV294 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) ) ) )
= $true )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1546,plain,
! [SV86: $i,SV295: $i] :
( ( ( ( SV295
!= ( relation_dom @ SV86 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY676: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY676 @ SY472 ) @ SV86 )
| ( in @ SY676 @ SV295 ) )
| ~ ! [SY678: $i] :
( ~ ( in @ SY678 @ SV295 )
| ( in @ ( ordered_pair @ SY678 @ ( sK39_D @ SY678 @ SV295 @ SV86 ) ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1547,plain,
! [SV237: $i,SV188: $i] :
( ( ( subset @ SV188 @ SV237 )
= $false )
| ( ( SV188 = SV237 )
= $true )
| ( ( proper_subset @ SV188 @ SV237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1548,plain,
! [SV314: $i,SV296: $i] :
( ( ~ ( proper_subset @ SV296 @ SV314 )
| ( SV296 != SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1549,plain,
! [SV315: $i,SV297: $i] :
( ( ~ ( proper_subset @ SV297 @ SV315 )
| ( subset @ SV297 @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1550,plain,
! [SV87: $i,SV238: $i] :
( ( ( subset @ SV238 @ ( sK32_B @ SV87 ) )
= $false )
| ( ( are_equipotent @ SV238 @ ( sK32_B @ SV87 ) )
= $true )
| ( ( in @ SV238 @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1551,plain,
! [SV87: $i,SV316: $i] :
( ( ~ ( in @ SV316 @ ( sK32_B @ SV87 ) )
| ( in @ ( powerset @ SV316 ) @ ( sK32_B @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1552,plain,
! [SV87: $i] :
( ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) )
| ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1553,plain,
! [SV239: $i,SV191: $i] :
( ( ( SV191 = empty_set )
= $true )
| ( ( SV191
= ( singleton @ SV239 ) )
= $true )
| ( ( subset @ SV191 @ ( singleton @ SV239 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1554,plain,
! [SV298: $i] :
( ( ( ( SV298 != empty_set ) )
= $true )
| ( ( ! [SY681: $i] : ( subset @ SV298 @ ( singleton @ SY681 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1555,plain,
! [SV317: $i,SV299: $i] :
( ( ( SV299
!= ( singleton @ SV317 ) )
| ( subset @ SV299 @ ( singleton @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1556,plain,
! [SV242: $i,SV272: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV272 ) )
= $true )
| ( ( ~ ( in @ SV242 @ SV272 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV89 @ SV242 ) @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1557,plain,
! [SV318: $i,SV89: $i] :
( ( ! [SY698: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SV318 ) @ SY698 )
| ( in @ SV89 @ SY698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1558,plain,
! [SV319: $i,SV89: $i] :
( ( ! [SY699: $i] :
( ~ ( subset @ ( unordered_pair @ SV89 @ SV319 ) @ SY699 )
| ( in @ SV319 @ SY699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1559,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( relation @ SV300 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) ) )
| ( SV300
= ( relation_inverse @ SV90 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1560,plain,
! [SV90: $i,SV301: $i] :
( ( ( ~ ( relation @ SV301 ) )
= $true )
| ( ( ( SV301
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY683: $i,SY684: $i] :
( ~ ( in @ ( ordered_pair @ SY683 @ SY684 ) @ SV301 )
| ( in @ ( ordered_pair @ SY684 @ SY683 ) @ SV90 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY686 @ SY685 ) @ SV90 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV301 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1561,plain,
! [SV194: $i,SV243: $i] :
( ( ( ~ ( ( ( sK29_C @ SV243 @ SV194 )
!= SV194 )
| ~ ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) ) )
= $false )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1562,plain,
! [SV194: $i,SV243: $i] :
( ( ( ~ ( ( ( sK29_C @ SV243 @ SV194 )
= SV194 )
| ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) ) )
= $false )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1563,plain,
! [SV244: $i,SV195: $i] :
( ( ( ~ ! [SY629: $i] :
( ( SY629 != SV195 )
| ( in @ SY629 @ SV244 ) )
| ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ SV244 )
| ( SY630 = SV195 ) ) )
= $false )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1564,plain,
! [SV245: $i,SV92: $i,SV273: $i] :
( ( ( relation @ SV273 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV92 @ SV245 ) @ SV273 )
| ( in @ SV92 @ ( relation_field @ SV273 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1565,plain,
! [SV246: $i,SV92: $i,SV274: $i] :
( ( ( relation @ SV274 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV92 @ SV246 ) @ SV274 )
| ( in @ SV246 @ ( relation_field @ SV274 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1566,plain,
! [SV247: $i,SV196: $i] :
( ( ( subset @ SV196 @ SV247 )
= $false )
| ( ( ~ ( subset @ SV247 @ SV196 ) )
= $true )
| ( ( SV196 = SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1567,plain,
! [SV320: $i,SV302: $i] :
( ( ( SV302 != SV320 )
| ( subset @ SV302 @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1568,plain,
! [SV321: $i,SV303: $i] :
( ( ( SV303 != SV321 )
| ( subset @ SV321 @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1569,plain,
! [SV197: $i,SV248: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV197 ) )
= $false )
| ( ( disjoint @ SV197 @ SV248 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1476]) ).
thf(1570,plain,
! [SV197: $i,SV248: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV248 ) )
= $false )
| ( ( disjoint @ SV197 @ SV248 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1476]) ).
thf(1571,plain,
! [SV249: $i,SV198: $i,SV304: $i] :
( ( ( ~ ( in @ SV304 @ SV198 ) )
= $true )
| ( ( ~ ( in @ SV304 @ SV249 ) )
= $true )
| ( ( ~ ( disjoint @ SV198 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1572,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) ) )
= $false )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1573,plain,
! [SV251: $i,SV93: $i,SV276: $i] :
( ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false )
| ( ( ~ ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV93 )
| ( in @ SY662 @ SV251 )
| ( in @ SY662 @ SV276 ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) )
| ~ ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1574,plain,
! [SV94: $i,SV145: $i] :
( ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 ) )
= $true )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1575,plain,
! [SV305: $i] :
( ( ( SV305 = empty_set )
= $true )
| ( ( ! [SY689: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SY689 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SY689 @ SV305 ) @ ( sK45_SY326 @ SY689 @ SV305 ) ) )
| ~ ( in @ ( sK44_C @ SY689 @ SV305 ) @ SY689 ) )
| ~ ( ! [SY690: $i] :
( ~ ( in @ SY690 @ SV305 )
| ( in @ ( sK44_C @ SY689 @ SV305 ) @ SY690 ) )
| ( in @ ( sK44_C @ SY689 @ SV305 ) @ SY689 ) ) )
| ( SY689
= ( set_meet @ SV305 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1576,plain,
! [SV306: $i] :
( ( ( SV306 = empty_set )
= $true )
| ( ( ! [SY691: $i] :
( ( SY691
!= ( set_meet @ SV306 ) )
| ~ ( ~ ! [SY692: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY692 @ SY691 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SY692 @ ( sK43_D @ SY692 @ SY691 @ SV306 ) ) )
| ( in @ SY692 @ SY691 ) )
| ~ ! [SY693: $i] :
( ~ ( in @ SY693 @ SY691 )
| ! [SY694: $i] :
( ~ ( in @ SY694 @ SV306 )
| ( in @ SY693 @ SY694 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1577,plain,
! [SV307: $i] :
( ( ( ( SV307 != empty_set ) )
= $true )
| ( ( ! [SY695: $i] :
( ( SY695
!= ( set_meet @ SV307 ) )
| ( SY695 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1578,plain,
! [SV308: $i] :
( ( ( ( SV308 != empty_set ) )
= $true )
| ( ( ! [SY696: $i] :
( ( SY696 != empty_set )
| ( SY696
= ( set_meet @ SV308 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1579,plain,
! [SV256: $i,SV95: $i,SV277: $i] :
( ( ( relation @ SV277 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV95 @ SV256 ) @ SV277 )
| ( in @ SV95 @ ( relation_dom @ SV277 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1580,plain,
! [SV257: $i,SV95: $i,SV278: $i] :
( ( ( relation @ SV278 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV95 @ SV257 ) @ SV278 )
| ( in @ SV257 @ ( relation_rng @ SV278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1581,plain,
! [SV204: $i,SV309: $i] :
( ( ( in @ SV309 @ SV204 )
= $false )
| ( ( SV204 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1582,plain,
! [SV258: $i,SV322: $i,SV96: $i] :
( ( ( subset @ ( cartesian_product2 @ SV96 @ SV322 ) @ ( cartesian_product2 @ SV258 @ SV322 ) )
= $true )
| ( ( subset @ SV96 @ SV258 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1583,plain,
! [SV259: $i,SV96: $i,SV323: $i] :
( ( ( subset @ ( cartesian_product2 @ SV323 @ SV96 ) @ ( cartesian_product2 @ SV323 @ SV259 ) )
= $true )
| ( ( subset @ SV96 @ SV259 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1584,plain,
! [SV279: $i,SV210: $i,SV163: $i] :
( ( ( disjoint @ SV163 @ SV210 )
= $false )
| ( ( in @ SV279 @ ( set_intersection2 @ SV163 @ SV210 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1585,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) )
= $false )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1586,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) ) )
= $false )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1587,plain,
! [SV261: $i,SV212: $i,SV74: $i] :
( ( ( ~ ! [SY643: $i] :
( ~ ( in @ SY643 @ SV74 )
| ~ ( in @ SY643 @ SV212 )
| ( in @ SY643 @ SV261 ) )
| ~ ~ ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) ) )
= $false )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1588,plain,
! [SV280: $i,SV141: $i,SV262: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV262 ) )
= $true )
| ( ( ~ ( in @ SV141 @ SV280 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV262 @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1589,plain,
! [SV324: $i,SV141: $i,SV75: $i] :
( ( ! [SY700: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV324 @ SY700 ) )
| ( in @ SV75 @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1590,plain,
! [SV325: $i,SV141: $i,SV75: $i] :
( ( ! [SY701: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV325 @ SY701 ) )
| ( in @ SV141 @ SY701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1591,plain,
! [SV76: $i,SV281: $i] :
( ( ( relation @ SV281 )
= $false )
| ( ( ~ ( subset @ SV76 @ SV281 )
| ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SV281 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1592,plain,
! [SV76: $i,SV282: $i] :
( ( ( relation @ SV282 )
= $false )
| ( ( ~ ( subset @ SV76 @ SV282 )
| ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SV282 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1593,plain,
! [SV77: $i,SV166: $i] :
( ( ( ! [SY547: $i] :
( ~ ( relation @ SY547 )
| ~ ( ~ ( ! [SY548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ SY548 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY548 @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY547 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SY547 @ SV166 @ SV77 ) ) @ SY547 ) ) )
| ( SY547
= ( relation_composition @ SV77 @ SV166 ) ) ) )
= $true )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1594,plain,
! [SV166: $i,SV77: $i] :
( ( ( ! [SY549: $i] :
( ~ ( relation @ SY549 )
| ( SY549
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY550: $i,SY551: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY550 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY551 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY550 @ SY551 ) @ SY549 ) )
| ~ ! [SY553: $i,SY554: $i] :
( ~ ( in @ ( ordered_pair @ SY553 @ SY554 ) @ SY549 )
| ~ ( ~ ( in @ ( ordered_pair @ SY553 @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY554 @ SY553 @ SY549 @ SV166 @ SV77 ) @ SY554 ) @ SV166 ) ) ) ) ) )
= $true )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1595,plain,
! [SV78: $i,SV283: $i] :
( ( ( ~ ( ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY665 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SV283 @ SV78 ) @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) ) )
= $false )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1596,plain,
! [SV78: $i,SV284: $i] :
( ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( ~ ( ~ ! [SY666: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY666 ) @ SV78 )
| ( in @ SY666 @ SV284 ) )
| ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV284 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY668 @ SV284 @ SV78 ) @ SY668 ) @ SV78 ) ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1597,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) ) ) )
= $false )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1598,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV79 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV215 ) ) )
= $false )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1599,plain,
! [SV216: $i,SV79: $i,SV264: $i] :
( ( ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV264 )
| ( SY647 = SV79 )
| ( SY647 = SV216 ) )
| ~ ~ ( ~ ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) )
| ~ ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) ) )
= $false )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1600,plain,
! [SV167: $i,SV217: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ~ ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) )
= $true )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1601,plain,
! [SV167: $i,SV217: $i] :
( ( ( ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
| ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) )
= $true )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1602,plain,
! [SV168: $i,SV218: $i] :
( ( ( ~ ! [SY608: $i] :
( ~ ( in @ SY608 @ SV218 )
| ( subset @ SY608 @ SV168 ) ) )
= $false )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1515]) ).
thf(1603,plain,
! [SV218: $i,SV168: $i] :
( ( ( ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV168 )
| ( in @ SY609 @ SV218 ) ) )
= $false )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1515]) ).
thf(1604,plain,
! [SV326: $i,SV169: $i] :
( ( ( ! [SY702: $i] :
( ( sK48_B @ SV169 )
!= ( ordered_pair @ SV326 @ SY702 ) ) )
= $true )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1605,plain,
! [SV170: $i,SV285: $i] :
( ( ( in @ SV285 @ SV170 )
= $false )
| ( ( SV285
= ( ordered_pair @ ( sK46_C @ SV285 @ SV170 ) @ ( sK47_SY328 @ SV285 @ SV170 ) ) )
= $true )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1606,plain,
! [SV286: $i] :
( ( ( SV286 = empty_set )
= $false )
| ( ( ! [SY669: $i] : ( subset @ SV286 @ ( singleton @ SY669 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1607,plain,
! [SV310: $i,SV287: $i] :
( ( ( ( SV287
!= ( singleton @ SV310 ) ) )
= $true )
| ( ( subset @ SV287 @ ( singleton @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1608,plain,
! [SV265: $i,SV224: $i,SV81: $i] :
( ( ( ~ ( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV81 )
| ~ ( in @ SY651 @ SV224 )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) ) )
= $false )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1523]) ).
thf(1609,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) ) )
= $false )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1523]) ).
thf(1610,plain,
! [SV266: $i,SV225: $i,SV81: $i] :
( ( ( ~ ! [SY652: $i] :
( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SY615 @ SV81 )
| ~ ( in @ SY616 @ SV225 )
| ( SY652
!= ( ordered_pair @ SY615 @ SY616 ) ) )
| ( in @ SY652 @ SV266 ) )
| ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV266 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SY655
!= ( ordered_pair @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) ) ) ) ) )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1611,plain,
! [SV288: $i,SV142: $i,SV267: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ SV267 ) )
= $true )
| ( ( ~ ( in @ SV142 @ SV288 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV267 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1612,plain,
! [SV327: $i,SV142: $i,SV82: $i] :
( ( ! [SY703: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV327 @ SY703 ) )
| ( in @ SV82 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1613,plain,
! [SV328: $i,SV142: $i,SV82: $i] :
( ( ! [SY704: $i] :
( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV328 @ SY704 ) )
| ( in @ SV142 @ SY704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1614,plain,
! [SV289: $i,SV329: $i] :
( ( ( ~ ( element @ SV329 @ SV289 )
| ( in @ SV329 @ SV289 ) )
= $true )
| ( ( empty @ SV289 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1615,plain,
! [SV290: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV290 )
| ( element @ SV330 @ SV290 ) )
= $true )
| ( ( empty @ SV290 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1616,plain,
! [SV291: $i] :
( ( ( empty @ SV291 )
= $false )
| ( ( ! [SY673: $i] :
( ~ ( element @ SY673 @ SV291 )
| ( empty @ SY673 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1617,plain,
! [SV292: $i] :
( ( ( empty @ SV292 )
= $false )
| ( ( ! [SY674: $i] :
( ~ ( empty @ SY674 )
| ( element @ SY674 @ SV292 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1618,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) ) )
= $false )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1619,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) )
= $false )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1620,plain,
! [SV227: $i,SV83: $i,SV269: $i] :
( ( ( ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV269 )
| ( in @ SY657 @ SV83 )
| ( in @ SY657 @ SV227 ) )
| ~ ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) ) )
= $false )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1621,plain,
! [SV178: $i,SV228: $i] :
( ( ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV178 )
= $true )
| ( ( subset @ SV178 @ SV228 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1622,plain,
! [SV178: $i,SV228: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV228 ) )
= $true )
| ( ( subset @ SV178 @ SV228 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1623,plain,
! [SV229: $i,SV179: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ SV179 ) )
= $true )
| ( ( in @ SV311 @ SV229 )
= $true )
| ( ( subset @ SV179 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1624,plain,
! [SV312: $i,SV270: $i,SV143: $i,SV84: $i] :
( ( ( ( ordered_pair @ SV84 @ SV143 )
= ( ordered_pair @ SV270 @ SV312 ) )
= $false )
| ( ( SV84 = SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1625,plain,
! [SV293: $i,SV271: $i,SV143: $i,SV84: $i] :
( ( ( ( ordered_pair @ SV84 @ SV143 )
= ( ordered_pair @ SV271 @ SV293 ) )
= $false )
| ( ( SV143 = SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1626,plain,
! [SV85: $i,SV313: $i] :
( ( ( ~ ( ~ ! [SY697: $i] :
( ~ ( subset @ SY697 @ SV313 )
| ( in @ SY697 @ ( sK3_SY299 @ SV313 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SV313 @ SV85 ) @ ( sK2_B @ SV85 ) ) ) )
= $true )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1627,plain,
! [SV85: $i] :
( ( ~ ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1628,plain,
! [SV85: $i] :
( ( ~ ( in @ SV85 @ ( sK2_B @ SV85 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1629,plain,
! [SV184: $i,SV233: $i] :
( ( ( ! [SY624: $i] :
( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SY624 )
| ~ ( in @ SY624 @ SV184 ) )
| ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1630,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) )
| ~ ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 ) )
| ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1631,plain,
! [SV234: $i,SV185: $i] :
( ( ( ~ ! [SY625: $i] :
( ! [SY576: $i] :
( ~ ( in @ SY625 @ SY576 )
| ~ ( in @ SY576 @ SV185 ) )
| ( in @ SY625 @ SV234 ) ) )
= $false )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1632,plain,
! [SV185: $i,SV234: $i] :
( ( ( ~ ! [SY627: $i] :
( ~ ( in @ SY627 @ SV234 )
| ~ ( ~ ( in @ SY627 @ ( sK16_D @ SY627 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SY627 @ SV234 @ SV185 ) @ SV185 ) ) ) )
= $false )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1633,plain,
! [SV86: $i,SV294: $i] :
( ( ( ~ ( ! [SY675: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SY675 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ ( sK41_SY325 @ SV294 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) ) )
= $false )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1634,plain,
! [SV86: $i,SV295: $i] :
( ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( ~ ( ~ ! [SY676: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY676 @ SY472 ) @ SV86 )
| ( in @ SY676 @ SV295 ) )
| ~ ! [SY678: $i] :
( ~ ( in @ SY678 @ SV295 )
| ( in @ ( ordered_pair @ SY678 @ ( sK39_D @ SY678 @ SV295 @ SV86 ) ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1635,plain,
! [SV314: $i,SV296: $i] :
( ( ( ~ ( proper_subset @ SV296 @ SV314 ) )
= $true )
| ( ( ( SV296 != SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1636,plain,
! [SV315: $i,SV297: $i] :
( ( ( ~ ( proper_subset @ SV297 @ SV315 ) )
= $true )
| ( ( subset @ SV297 @ SV315 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1637,plain,
! [SV87: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ ( sK32_B @ SV87 ) ) )
= $true )
| ( ( in @ ( powerset @ SV316 ) @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1638,plain,
! [SV87: $i] :
( ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1639,plain,
! [SV87: $i] :
( ( ~ ( in @ SV87 @ ( sK32_B @ SV87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1640,plain,
! [SV298: $i] :
( ( ( SV298 = empty_set )
= $false )
| ( ( ! [SY681: $i] : ( subset @ SV298 @ ( singleton @ SY681 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1641,plain,
! [SV317: $i,SV299: $i] :
( ( ( ( SV299
!= ( singleton @ SV317 ) ) )
= $true )
| ( ( subset @ SV299 @ ( singleton @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1642,plain,
! [SV242: $i,SV272: $i,SV89: $i] :
( ( ( in @ SV89 @ SV272 )
= $false )
| ( ( ~ ( in @ SV242 @ SV272 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV89 @ SV242 ) @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1643,plain,
! [SV331: $i,SV318: $i,SV89: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV89 @ SV318 ) @ SV331 )
| ( in @ SV89 @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1644,plain,
! [SV332: $i,SV319: $i,SV89: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV89 @ SV319 ) @ SV332 )
| ( in @ SV319 @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1645,plain,
! [SV90: $i,SV300: $i] :
( ( ( relation @ SV300 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) ) )
| ( SV300
= ( relation_inverse @ SV90 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1646,plain,
! [SV90: $i,SV301: $i] :
( ( ( relation @ SV301 )
= $false )
| ( ( ( SV301
!= ( relation_inverse @ SV90 ) )
| ~ ( ~ ! [SY683: $i,SY684: $i] :
( ~ ( in @ ( ordered_pair @ SY683 @ SY684 ) @ SV301 )
| ( in @ ( ordered_pair @ SY684 @ SY683 ) @ SV90 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY686 @ SY685 ) @ SV90 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV301 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1647,plain,
! [SV194: $i,SV243: $i] :
( ( ( ( ( sK29_C @ SV243 @ SV194 )
!= SV194 )
| ~ ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) )
= $true )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1648,plain,
! [SV194: $i,SV243: $i] :
( ( ( ( ( sK29_C @ SV243 @ SV194 )
= SV194 )
| ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) )
= $true )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1649,plain,
! [SV244: $i,SV195: $i] :
( ( ( ~ ! [SY629: $i] :
( ( SY629 != SV195 )
| ( in @ SY629 @ SV244 ) ) )
= $false )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1650,plain,
! [SV195: $i,SV244: $i] :
( ( ( ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ SV244 )
| ( SY630 = SV195 ) ) )
= $false )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1651,plain,
! [SV273: $i,SV245: $i,SV92: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV92 @ SV245 ) @ SV273 ) )
= $true )
| ( ( in @ SV92 @ ( relation_field @ SV273 ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1652,plain,
! [SV274: $i,SV246: $i,SV92: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV92 @ SV246 ) @ SV274 ) )
= $true )
| ( ( in @ SV246 @ ( relation_field @ SV274 ) )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1653,plain,
! [SV196: $i,SV247: $i] :
( ( ( subset @ SV247 @ SV196 )
= $false )
| ( ( subset @ SV196 @ SV247 )
= $false )
| ( ( SV196 = SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1654,plain,
! [SV320: $i,SV302: $i] :
( ( ( ( SV302 != SV320 ) )
= $true )
| ( ( subset @ SV302 @ SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1655,plain,
! [SV321: $i,SV303: $i] :
( ( ( ( SV303 != SV321 ) )
= $true )
| ( ( subset @ SV321 @ SV303 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1656,plain,
! [SV197: $i,SV248: $i] :
( ( ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV197 )
= $true )
| ( ( disjoint @ SV197 @ SV248 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1657,plain,
! [SV197: $i,SV248: $i] :
( ( ( in @ ( sK31_C @ SV248 @ SV197 ) @ SV248 )
= $true )
| ( ( disjoint @ SV197 @ SV248 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1658,plain,
! [SV249: $i,SV198: $i,SV304: $i] :
( ( ( in @ SV304 @ SV198 )
= $false )
| ( ( ~ ( in @ SV304 @ SV249 ) )
= $true )
| ( ( ~ ( disjoint @ SV198 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1659,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) )
= $false )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1660,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) ) )
= $false )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1661,plain,
! [SV276: $i,SV251: $i,SV93: $i] :
( ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV93 )
| ( in @ SY662 @ SV251 )
| ( in @ SY662 @ SV276 ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) )
| ~ ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) ) )
= $false )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1662,plain,
! [SV94: $i,SV145: $i] :
( ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV145 )
= $false )
| ( ( in @ ( sK4_C @ SV145 @ SV94 ) @ SV94 )
= $false )
| ( ( SV94 = SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1663,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) )
| ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
| ~ ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV305 )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) ) )
| ( SV333
= ( set_meet @ SV305 ) ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1664,plain,
! [SV306: $i,SV334: $i] :
( ( ( ( SV334
!= ( set_meet @ SV306 ) )
| ~ ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV334 @ SV306 ) ) )
| ( in @ SY706 @ SV334 ) )
| ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV334 )
| ! [SY694: $i] :
( ~ ( in @ SY694 @ SV306 )
| ( in @ SY707 @ SY694 ) ) ) ) )
= $true )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1665,plain,
! [SV307: $i] :
( ( ( SV307 = empty_set )
= $false )
| ( ( ! [SY695: $i] :
( ( SY695
!= ( set_meet @ SV307 ) )
| ( SY695 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1666,plain,
! [SV308: $i] :
( ( ( SV308 = empty_set )
= $false )
| ( ( ! [SY696: $i] :
( ( SY696 != empty_set )
| ( SY696
= ( set_meet @ SV308 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1667,plain,
! [SV277: $i,SV256: $i,SV95: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV95 @ SV256 ) @ SV277 ) )
= $true )
| ( ( in @ SV95 @ ( relation_dom @ SV277 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1668,plain,
! [SV278: $i,SV257: $i,SV95: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV95 @ SV257 ) @ SV278 ) )
= $true )
| ( ( in @ SV257 @ ( relation_rng @ SV278 ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1580]) ).
thf(1669,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1670,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1671,plain,
! [SV261: $i,SV212: $i,SV74: $i] :
( ( ( ~ ! [SY643: $i] :
( ~ ( in @ SY643 @ SV74 )
| ~ ( in @ SY643 @ SV212 )
| ( in @ SY643 @ SV261 ) ) )
= $false )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1672,plain,
! [SV212: $i,SV74: $i,SV261: $i] :
( ( ( ~ ~ ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) ) )
= $false )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1673,plain,
! [SV280: $i,SV141: $i,SV262: $i,SV75: $i] :
( ( ( in @ SV75 @ SV262 )
= $false )
| ( ( ~ ( in @ SV141 @ SV280 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV262 @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1674,plain,
! [SV324: $i,SV141: $i,SV75: $i] :
( ( ( ! [SY700: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV324 @ SY700 ) ) )
= $true )
| ( ( in @ SV75 @ SV324 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1675,plain,
! [SV335: $i,SV325: $i,SV141: $i,SV75: $i] :
( ( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV325 @ SV335 ) )
| ( in @ SV141 @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1676,plain,
! [SV281: $i,SV76: $i] :
( ( ( ~ ( subset @ SV76 @ SV281 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SV281 ) )
= $true )
| ( ( relation @ SV281 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1677,plain,
! [SV282: $i,SV76: $i] :
( ( ( ~ ( subset @ SV76 @ SV282 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SV282 ) )
= $true )
| ( ( relation @ SV282 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1678,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( relation @ SV336 )
| ~ ( ~ ( ! [SY709: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SY709 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY709 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) ) )
| ( SV336
= ( relation_composition @ SV77 @ SV166 ) ) )
= $true )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1679,plain,
! [SV166: $i,SV77: $i,SV337: $i] :
( ( ( ~ ( relation @ SV337 )
| ( SV337
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY710: $i,SY711: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY710 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY711 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY710 @ SY711 ) @ SV337 ) )
| ~ ! [SY713: $i,SY714: $i] :
( ~ ( in @ ( ordered_pair @ SY713 @ SY714 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SY713 @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) @ SY714 ) @ SV166 ) ) ) ) )
= $true )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1680,plain,
! [SV78: $i,SV283: $i] :
( ( ( ~ ( ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY665 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) ) )
= $false )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1681,plain,
! [SV78: $i,SV283: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SV283 @ SV78 ) @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) ) )
= $false )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1682,plain,
! [SV284: $i,SV78: $i] :
( ( ( ~ ! [SY666: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY666 ) @ SV78 )
| ( in @ SY666 @ SV284 ) )
| ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV284 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY668 @ SV284 @ SV78 ) @ SY668 ) @ SV78 ) ) )
= $false )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1683,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) ) ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1597]) ).
thf(1684,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV79 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV215 ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1598]) ).
thf(1685,plain,
! [SV216: $i,SV79: $i,SV264: $i] :
( ( ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV264 )
| ( SY647 = SV79 )
| ( SY647 = SV216 ) ) )
= $false )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1686,plain,
! [SV216: $i,SV264: $i,SV79: $i] :
( ( ( ~ ~ ( ~ ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) )
| ~ ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) ) )
= $false )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1687,plain,
! [SV167: $i,SV217: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 ) )
= $true )
| ( ( ~ ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) )
= $true )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1688,plain,
! [SV167: $i,SV217: $i] :
( ( ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
= $true )
| ( ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 )
= $true )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1689,plain,
! [SV168: $i,SV218: $i] :
( ( ( ! [SY608: $i] :
( ~ ( in @ SY608 @ SV218 )
| ( subset @ SY608 @ SV168 ) ) )
= $true )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1690,plain,
! [SV218: $i,SV168: $i] :
( ( ( ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV168 )
| ( in @ SY609 @ SV218 ) ) )
= $true )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1691,plain,
! [SV338: $i,SV326: $i,SV169: $i] :
( ( ( ( ( sK48_B @ SV169 )
!= ( ordered_pair @ SV326 @ SV338 ) ) )
= $true )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1692,plain,
! [SV339: $i,SV286: $i] :
( ( ( subset @ SV286 @ ( singleton @ SV339 ) )
= $true )
| ( ( SV286 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1693,plain,
! [SV310: $i,SV287: $i] :
( ( ( SV287
= ( singleton @ SV310 ) )
= $false )
| ( ( subset @ SV287 @ ( singleton @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1694,plain,
! [SV265: $i,SV224: $i,SV81: $i] :
( ( ( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV81 )
| ~ ( in @ SY651 @ SV224 )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1695,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) ) )
| ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1696,plain,
! [SV266: $i,SV225: $i,SV81: $i] :
( ( ( ~ ! [SY652: $i] :
( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SY615 @ SV81 )
| ~ ( in @ SY616 @ SV225 )
| ( SY652
!= ( ordered_pair @ SY615 @ SY616 ) ) )
| ( in @ SY652 @ SV266 ) ) )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1697,plain,
! [SV81: $i,SV225: $i,SV266: $i] :
( ( ( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV266 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SY655
!= ( ordered_pair @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) ) ) ) ) )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1698,plain,
! [SV288: $i,SV142: $i,SV267: $i,SV82: $i] :
( ( ( in @ SV82 @ SV267 )
= $false )
| ( ( ~ ( in @ SV142 @ SV288 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV267 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1699,plain,
! [SV327: $i,SV142: $i,SV82: $i] :
( ( ( ! [SY703: $i] :
~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV327 @ SY703 ) ) )
= $true )
| ( ( in @ SV82 @ SV327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1700,plain,
! [SV340: $i,SV328: $i,SV142: $i,SV82: $i] :
( ( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV328 @ SV340 ) )
| ( in @ SV142 @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1701,plain,
! [SV289: $i,SV329: $i] :
( ( ( ~ ( element @ SV329 @ SV289 ) )
= $true )
| ( ( in @ SV329 @ SV289 )
= $true )
| ( ( empty @ SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1702,plain,
! [SV290: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV290 ) )
= $true )
| ( ( element @ SV330 @ SV290 )
= $true )
| ( ( empty @ SV290 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1703,plain,
! [SV291: $i,SV341: $i] :
( ( ( ~ ( element @ SV341 @ SV291 )
| ( empty @ SV341 ) )
= $true )
| ( ( empty @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1704,plain,
! [SV292: $i,SV342: $i] :
( ( ( ~ ( empty @ SV342 )
| ( element @ SV342 @ SV292 ) )
= $true )
| ( ( empty @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1705,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1706,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1707,plain,
! [SV227: $i,SV83: $i,SV269: $i] :
( ( ( ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV269 )
| ( in @ SY657 @ SV83 )
| ( in @ SY657 @ SV227 ) ) )
= $false )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1708,plain,
! [SV227: $i,SV269: $i,SV83: $i] :
( ( ( ~ ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) ) )
= $false )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1709,plain,
! [SV178: $i,SV228: $i] :
( ( ( in @ ( sK20_C @ SV228 @ SV178 ) @ SV228 )
= $false )
| ( ( subset @ SV178 @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1710,plain,
! [SV229: $i,SV179: $i,SV311: $i] :
( ( ( in @ SV311 @ SV179 )
= $false )
| ( ( in @ SV311 @ SV229 )
= $true )
| ( ( subset @ SV179 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1711,plain,
! [SV85: $i,SV313: $i] :
( ( ( ~ ! [SY697: $i] :
( ~ ( subset @ SY697 @ SV313 )
| ( in @ SY697 @ ( sK3_SY299 @ SV313 @ SV85 ) ) )
| ~ ( in @ ( sK3_SY299 @ SV313 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
= $false )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1712,plain,
! [SV85: $i] :
( ( ! [SY466: $i,SY467: $i] :
( ~ ( in @ SY466 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY467 @ SY466 )
| ( in @ SY467 @ ( sK2_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1713,plain,
! [SV85: $i] :
( ( in @ SV85 @ ( sK2_B @ SV85 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1714,plain,
! [SV184: $i,SV233: $i] :
( ( ( ! [SY624: $i] :
( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SY624 )
| ~ ( in @ SY624 @ SV184 ) ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1715,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) )
| ~ ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 ) ) )
= $true )
| ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1716,plain,
! [SV234: $i,SV185: $i] :
( ( ( ! [SY625: $i] :
( ! [SY576: $i] :
( ~ ( in @ SY625 @ SY576 )
| ~ ( in @ SY576 @ SV185 ) )
| ( in @ SY625 @ SV234 ) ) )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1717,plain,
! [SV185: $i,SV234: $i] :
( ( ( ! [SY627: $i] :
( ~ ( in @ SY627 @ SV234 )
| ~ ( ~ ( in @ SY627 @ ( sK16_D @ SY627 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SY627 @ SV234 @ SV185 ) @ SV185 ) ) ) )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1718,plain,
! [SV86: $i,SV294: $i] :
( ( ( ~ ( ! [SY675: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SY675 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) ) )
= $false )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1719,plain,
! [SV86: $i,SV294: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ ( sK41_SY325 @ SV294 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) ) )
= $false )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1720,plain,
! [SV295: $i,SV86: $i] :
( ( ( ~ ! [SY676: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY676 @ SY472 ) @ SV86 )
| ( in @ SY676 @ SV295 ) )
| ~ ! [SY678: $i] :
( ~ ( in @ SY678 @ SV295 )
| ( in @ ( ordered_pair @ SY678 @ ( sK39_D @ SY678 @ SV295 @ SV86 ) ) @ SV86 ) ) )
= $false )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1721,plain,
! [SV314: $i,SV296: $i] :
( ( ( proper_subset @ SV296 @ SV314 )
= $false )
| ( ( ( SV296 != SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1722,plain,
! [SV315: $i,SV297: $i] :
( ( ( proper_subset @ SV297 @ SV315 )
= $false )
| ( ( subset @ SV297 @ SV315 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1723,plain,
! [SV87: $i,SV316: $i] :
( ( ( in @ SV316 @ ( sK32_B @ SV87 ) )
= $false )
| ( ( in @ ( powerset @ SV316 ) @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1724,plain,
! [SV87: $i] :
( ( ! [SY476: $i,SY477: $i] :
( ~ ( in @ SY476 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY477 @ SY476 )
| ( in @ SY477 @ ( sK32_B @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1725,plain,
! [SV87: $i] :
( ( in @ SV87 @ ( sK32_B @ SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1726,plain,
! [SV343: $i,SV298: $i] :
( ( ( subset @ SV298 @ ( singleton @ SV343 ) )
= $true )
| ( ( SV298 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1727,plain,
! [SV317: $i,SV299: $i] :
( ( ( SV299
= ( singleton @ SV317 ) )
= $false )
| ( ( subset @ SV299 @ ( singleton @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1728,plain,
! [SV89: $i,SV272: $i,SV242: $i] :
( ( ( in @ SV242 @ SV272 )
= $false )
| ( ( in @ SV89 @ SV272 )
= $false )
| ( ( subset @ ( unordered_pair @ SV89 @ SV242 ) @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1729,plain,
! [SV331: $i,SV318: $i,SV89: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV89 @ SV318 ) @ SV331 ) )
= $true )
| ( ( in @ SV89 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1730,plain,
! [SV332: $i,SV319: $i,SV89: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV89 @ SV319 ) @ SV332 ) )
= $true )
| ( ( in @ SV319 @ SV332 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1731,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) ) ) )
= $true )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1732,plain,
! [SV90: $i,SV301: $i] :
( ( ( ( SV301
!= ( relation_inverse @ SV90 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY683: $i,SY684: $i] :
( ~ ( in @ ( ordered_pair @ SY683 @ SY684 ) @ SV301 )
| ( in @ ( ordered_pair @ SY684 @ SY683 ) @ SV90 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY686 @ SY685 ) @ SV90 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV301 ) ) ) )
= $true )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1733,plain,
! [SV194: $i,SV243: $i] :
( ( ( ( ( sK29_C @ SV243 @ SV194 )
!= SV194 ) )
= $true )
| ( ( ~ ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) )
= $true )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1734,plain,
! [SV194: $i,SV243: $i] :
( ( ( ( sK29_C @ SV243 @ SV194 )
= SV194 )
= $true )
| ( ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 )
= $true )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1735,plain,
! [SV244: $i,SV195: $i] :
( ( ( ! [SY629: $i] :
( ( SY629 != SV195 )
| ( in @ SY629 @ SV244 ) ) )
= $true )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1736,plain,
! [SV195: $i,SV244: $i] :
( ( ( ! [SY630: $i] :
( ~ ( in @ SY630 @ SV244 )
| ( SY630 = SV195 ) ) )
= $true )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1737,plain,
! [SV273: $i,SV245: $i,SV92: $i] :
( ( ( in @ ( ordered_pair @ SV92 @ SV245 ) @ SV273 )
= $false )
| ( ( in @ SV92 @ ( relation_field @ SV273 ) )
= $true )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1738,plain,
! [SV274: $i,SV246: $i,SV92: $i] :
( ( ( in @ ( ordered_pair @ SV92 @ SV246 ) @ SV274 )
= $false )
| ( ( in @ SV246 @ ( relation_field @ SV274 ) )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1739,plain,
! [SV320: $i,SV302: $i] :
( ( ( SV302 = SV320 )
= $false )
| ( ( subset @ SV302 @ SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1740,plain,
! [SV321: $i,SV303: $i] :
( ( ( SV303 = SV321 )
= $false )
| ( ( subset @ SV321 @ SV303 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1741,plain,
! [SV198: $i,SV249: $i,SV304: $i] :
( ( ( in @ SV304 @ SV249 )
= $false )
| ( ( in @ SV304 @ SV198 )
= $false )
| ( ( ~ ( disjoint @ SV198 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1742,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1743,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) ) )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1744,plain,
! [SV276: $i,SV251: $i,SV93: $i] :
( ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV93 )
| ( in @ SY662 @ SV251 )
| ( in @ SY662 @ SV276 ) ) )
= $false )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1745,plain,
! [SV251: $i,SV93: $i,SV276: $i] :
( ( ( ~ ~ ( ~ ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) )
| ~ ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) ) )
= $false )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1746,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) )
| ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
| ~ ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV305 )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) ) ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(1747,plain,
! [SV306: $i,SV334: $i] :
( ( ( ( SV334
!= ( set_meet @ SV306 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV334 @ SV306 ) ) )
| ( in @ SY706 @ SV334 ) )
| ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV334 )
| ! [SY694: $i] :
( ~ ( in @ SY694 @ SV306 )
| ( in @ SY707 @ SY694 ) ) ) ) )
= $true )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(1748,plain,
! [SV307: $i,SV344: $i] :
( ( ( ( SV344
!= ( set_meet @ SV307 ) )
| ( SV344 = empty_set ) )
= $true )
| ( ( SV307 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1749,plain,
! [SV308: $i,SV345: $i] :
( ( ( ( SV345 != empty_set )
| ( SV345
= ( set_meet @ SV308 ) ) )
= $true )
| ( ( SV308 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1750,plain,
! [SV277: $i,SV256: $i,SV95: $i] :
( ( ( in @ ( ordered_pair @ SV95 @ SV256 ) @ SV277 )
= $false )
| ( ( in @ SV95 @ ( relation_dom @ SV277 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1751,plain,
! [SV278: $i,SV257: $i,SV95: $i] :
( ( ( in @ ( ordered_pair @ SV95 @ SV257 ) @ SV278 )
= $false )
| ( ( in @ SV257 @ ( relation_rng @ SV278 ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1752,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1753,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
| ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) )
= $false )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1754,plain,
! [SV261: $i,SV212: $i,SV74: $i] :
( ( ( ! [SY643: $i] :
( ~ ( in @ SY643 @ SV74 )
| ~ ( in @ SY643 @ SV212 )
| ( in @ SY643 @ SV261 ) ) )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1755,plain,
! [SV212: $i,SV74: $i,SV261: $i] :
( ( ( ~ ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) ) )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1756,plain,
! [SV262: $i,SV75: $i,SV280: $i,SV141: $i] :
( ( ( in @ SV141 @ SV280 )
= $false )
| ( ( in @ SV75 @ SV262 )
= $false )
| ( ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV262 @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1757,plain,
! [SV346: $i,SV324: $i,SV141: $i,SV75: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV324 @ SV346 ) ) )
= $true )
| ( ( in @ SV75 @ SV324 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1758,plain,
! [SV335: $i,SV325: $i,SV141: $i,SV75: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV325 @ SV335 ) ) )
= $true )
| ( ( in @ SV141 @ SV335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1759,plain,
! [SV281: $i,SV76: $i] :
( ( ( subset @ SV76 @ SV281 )
= $false )
| ( ( subset @ ( relation_dom @ SV76 ) @ ( relation_dom @ SV281 ) )
= $true )
| ( ( relation @ SV281 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1760,plain,
! [SV282: $i,SV76: $i] :
( ( ( subset @ SV76 @ SV282 )
= $false )
| ( ( subset @ ( relation_rng @ SV76 ) @ ( relation_rng @ SV282 ) )
= $true )
| ( ( relation @ SV282 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1761,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( relation @ SV336 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY709: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SY709 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY709 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) ) )
| ( SV336
= ( relation_composition @ SV77 @ SV166 ) ) )
= $true )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1762,plain,
! [SV166: $i,SV77: $i,SV337: $i] :
( ( ( ~ ( relation @ SV337 ) )
= $true )
| ( ( ( SV337
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY710: $i,SY711: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY710 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY711 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY710 @ SY711 ) @ SV337 ) )
| ~ ! [SY713: $i,SY714: $i] :
( ~ ( in @ ( ordered_pair @ SY713 @ SY714 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SY713 @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) @ SY714 ) @ SV166 ) ) ) ) )
= $true )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1763,plain,
! [SV78: $i,SV283: $i] :
( ( ( ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY665 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ~ ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) )
= $true )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1764,plain,
! [SV78: $i,SV283: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SV283 @ SV78 ) @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
| ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) )
= $true )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1765,plain,
! [SV284: $i,SV78: $i] :
( ( ( ~ ! [SY666: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY666 ) @ SV78 )
| ( in @ SY666 @ SV284 ) ) )
= $false )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1766,plain,
! [SV78: $i,SV284: $i] :
( ( ( ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV284 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY668 @ SV284 @ SV78 ) @ SY668 ) @ SV78 ) ) )
= $false )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1767,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) ) )
= $false )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1768,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
= $true )
| ( ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV79 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV215 ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1769,plain,
! [SV216: $i,SV79: $i,SV264: $i] :
( ( ( ! [SY647: $i] :
( ~ ( in @ SY647 @ SV264 )
| ( SY647 = SV79 )
| ( SY647 = SV216 ) ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1685]) ).
thf(1770,plain,
! [SV216: $i,SV264: $i,SV79: $i] :
( ( ( ~ ( ~ ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) )
| ~ ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1771,plain,
! [SV167: $i,SV217: $i] :
( ( ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
= $false )
| ( ( ~ ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 ) )
= $true )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1772,plain,
! [SV168: $i,SV218: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ SV218 )
| ( subset @ SV347 @ SV168 ) )
= $true )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1773,plain,
! [SV218: $i,SV168: $i,SV348: $i] :
( ( ( ~ ( subset @ SV348 @ SV168 )
| ( in @ SV348 @ SV218 ) )
= $true )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(1774,plain,
! [SV338: $i,SV326: $i,SV169: $i] :
( ( ( ( sK48_B @ SV169 )
= ( ordered_pair @ SV326 @ SV338 ) )
= $false )
| ( ( relation @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1775,plain,
! [SV265: $i,SV224: $i,SV81: $i] :
( ( ( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV81 )
| ~ ( in @ SY651 @ SV224 )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SY650 @ SY651 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1776,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1777,plain,
! [SV266: $i,SV225: $i,SV81: $i] :
( ( ( ! [SY652: $i] :
( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SY615 @ SV81 )
| ~ ( in @ SY616 @ SV225 )
| ( SY652
!= ( ordered_pair @ SY615 @ SY616 ) ) )
| ( in @ SY652 @ SV266 ) ) )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(1778,plain,
! [SV81: $i,SV225: $i,SV266: $i] :
( ( ( ! [SY655: $i] :
( ~ ( in @ SY655 @ SV266 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SY655
!= ( ordered_pair @ ( sK21_E @ SY655 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SY655 @ SV266 @ SV225 @ SV81 ) ) ) ) ) )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1779,plain,
! [SV267: $i,SV82: $i,SV288: $i,SV142: $i] :
( ( ( in @ SV142 @ SV288 )
= $false )
| ( ( in @ SV82 @ SV267 )
= $false )
| ( ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV267 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1780,plain,
! [SV349: $i,SV327: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV327 @ SV349 ) ) )
= $true )
| ( ( in @ SV82 @ SV327 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1781,plain,
! [SV340: $i,SV328: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV328 @ SV340 ) ) )
= $true )
| ( ( in @ SV142 @ SV340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(1782,plain,
! [SV289: $i,SV329: $i] :
( ( ( element @ SV329 @ SV289 )
= $false )
| ( ( in @ SV329 @ SV289 )
= $true )
| ( ( empty @ SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1783,plain,
! [SV290: $i,SV330: $i] :
( ( ( in @ SV330 @ SV290 )
= $false )
| ( ( element @ SV330 @ SV290 )
= $true )
| ( ( empty @ SV290 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1784,plain,
! [SV291: $i,SV341: $i] :
( ( ( ~ ( element @ SV341 @ SV291 ) )
= $true )
| ( ( empty @ SV341 )
= $true )
| ( ( empty @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1785,plain,
! [SV292: $i,SV342: $i] :
( ( ( ~ ( empty @ SV342 ) )
= $true )
| ( ( element @ SV342 @ SV292 )
= $true )
| ( ( empty @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1786,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) )
= $false )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1787,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
= $true )
| ( ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 )
| ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1788,plain,
! [SV227: $i,SV83: $i,SV269: $i] :
( ( ( ! [SY657: $i] :
( ~ ( in @ SY657 @ SV269 )
| ( in @ SY657 @ SV83 )
| ( in @ SY657 @ SV227 ) ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1707]) ).
thf(1789,plain,
! [SV227: $i,SV269: $i,SV83: $i] :
( ( ( ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1790,plain,
! [SV85: $i,SV313: $i] :
( ( ( ~ ! [SY697: $i] :
( ~ ( subset @ SY697 @ SV313 )
| ( in @ SY697 @ ( sK3_SY299 @ SV313 @ SV85 ) ) ) )
= $false )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1791,plain,
! [SV85: $i,SV313: $i] :
( ( ( ~ ( in @ ( sK3_SY299 @ SV313 @ SV85 ) @ ( sK2_B @ SV85 ) ) )
= $false )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1792,plain,
! [SV85: $i,SV350: $i] :
( ( ! [SY715: $i] :
( ~ ( in @ SV350 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SY715 @ SV350 )
| ( in @ SY715 @ ( sK2_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1793,plain,
! [SV351: $i,SV184: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV351 )
| ~ ( in @ SV351 @ SV184 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1794,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) )
| ~ ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 ) )
= $false )
| ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1795,plain,
! [SV234: $i,SV185: $i,SV352: $i] :
( ( ( ! [SY716: $i] :
( ~ ( in @ SV352 @ SY716 )
| ~ ( in @ SY716 @ SV185 ) )
| ( in @ SV352 @ SV234 ) )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1796,plain,
! [SV185: $i,SV234: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ SV234 )
| ~ ( ~ ( in @ SV353 @ ( sK16_D @ SV353 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SV353 @ SV234 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(1797,plain,
! [SV86: $i,SV294: $i] :
( ( ( ! [SY675: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SY675 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1798,plain,
! [SV86: $i,SV294: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ ( sK41_SY325 @ SV294 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1799,plain,
! [SV295: $i,SV86: $i] :
( ( ( ~ ! [SY676: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY676 @ SY472 ) @ SV86 )
| ( in @ SY676 @ SV295 ) ) )
= $false )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1720]) ).
thf(1800,plain,
! [SV86: $i,SV295: $i] :
( ( ( ~ ! [SY678: $i] :
( ~ ( in @ SY678 @ SV295 )
| ( in @ ( ordered_pair @ SY678 @ ( sK39_D @ SY678 @ SV295 @ SV86 ) ) @ SV86 ) ) )
= $false )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1720]) ).
thf(1801,plain,
! [SV314: $i,SV296: $i] :
( ( ( SV296 = SV314 )
= $false )
| ( ( proper_subset @ SV296 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1802,plain,
! [SV87: $i,SV354: $i] :
( ( ! [SY717: $i] :
( ~ ( in @ SV354 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SY717 @ SV354 )
| ( in @ SY717 @ ( sK32_B @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(1803,plain,
! [SV331: $i,SV318: $i,SV89: $i] :
( ( ( subset @ ( unordered_pair @ SV89 @ SV318 ) @ SV331 )
= $false )
| ( ( in @ SV89 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1804,plain,
! [SV332: $i,SV319: $i,SV89: $i] :
( ( ( subset @ ( unordered_pair @ SV89 @ SV319 ) @ SV332 )
= $false )
| ( ( in @ SV319 @ SV332 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1805,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) ) )
= $false )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1806,plain,
! [SV90: $i,SV301: $i] :
( ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( ~ ( ~ ! [SY683: $i,SY684: $i] :
( ~ ( in @ ( ordered_pair @ SY683 @ SY684 ) @ SV301 )
| ( in @ ( ordered_pair @ SY684 @ SY683 ) @ SV90 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY686 @ SY685 ) @ SV90 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV301 ) ) ) )
= $true )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1807,plain,
! [SV194: $i,SV243: $i] :
( ( ( ( sK29_C @ SV243 @ SV194 )
= SV194 )
= $false )
| ( ( ~ ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 ) )
= $true )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1808,plain,
! [SV244: $i,SV195: $i,SV355: $i] :
( ( ( ( SV355 != SV195 )
| ( in @ SV355 @ SV244 ) )
= $true )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(1809,plain,
! [SV195: $i,SV244: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ SV244 )
| ( SV356 = SV195 ) )
= $true )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(1810,plain,
! [SV304: $i,SV249: $i,SV198: $i] :
( ( ( disjoint @ SV198 @ SV249 )
= $false )
| ( ( in @ SV304 @ SV198 )
= $false )
| ( ( in @ SV304 @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1811,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(1812,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) )
= $false )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1813,plain,
! [SV276: $i,SV251: $i,SV93: $i] :
( ( ( ! [SY662: $i] :
( ~ ( in @ SY662 @ SV93 )
| ( in @ SY662 @ SV251 )
| ( in @ SY662 @ SV276 ) ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1814,plain,
! [SV251: $i,SV93: $i,SV276: $i] :
( ( ( ~ ( ~ ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) )
| ~ ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1815,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) )
| ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
| ~ ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV305 )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) ) )
= $false )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1816,plain,
! [SV306: $i,SV334: $i] :
( ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( ~ ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV334 @ SV306 ) ) )
| ( in @ SY706 @ SV334 ) )
| ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV334 )
| ! [SY694: $i] :
( ~ ( in @ SY694 @ SV306 )
| ( in @ SY707 @ SY694 ) ) ) ) )
= $true )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1817,plain,
! [SV307: $i,SV344: $i] :
( ( ( ( SV344
!= ( set_meet @ SV307 ) ) )
= $true )
| ( ( SV344 = empty_set )
= $true )
| ( ( SV307 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1818,plain,
! [SV308: $i,SV345: $i] :
( ( ( ( SV345 != empty_set ) )
= $true )
| ( ( SV345
= ( set_meet @ SV308 ) )
= $true )
| ( ( SV308 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(1819,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1820,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) )
= $false )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1753]) ).
thf(1821,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) ) )
= $false )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1753]) ).
thf(1822,plain,
! [SV261: $i,SV212: $i,SV74: $i,SV357: $i] :
( ( ( ~ ( in @ SV357 @ SV74 )
| ~ ( in @ SV357 @ SV212 )
| ( in @ SV357 @ SV261 ) )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1823,plain,
! [SV212: $i,SV74: $i,SV261: $i] :
( ( ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) )
= $false )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1824,plain,
! [SV346: $i,SV324: $i,SV141: $i,SV75: $i] :
( ( ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV324 @ SV346 ) )
= $false )
| ( ( in @ SV75 @ SV324 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1825,plain,
! [SV335: $i,SV325: $i,SV141: $i,SV75: $i] :
( ( ( in @ ( ordered_pair @ SV75 @ SV141 ) @ ( cartesian_product2 @ SV325 @ SV335 ) )
= $false )
| ( ( in @ SV141 @ SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1826,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( relation @ SV336 )
= $false )
| ( ( ~ ( ~ ( ! [SY709: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SY709 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY709 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) ) )
| ( SV336
= ( relation_composition @ SV77 @ SV166 ) ) )
= $true )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1827,plain,
! [SV166: $i,SV77: $i,SV337: $i] :
( ( ( relation @ SV337 )
= $false )
| ( ( ( SV337
!= ( relation_composition @ SV77 @ SV166 ) )
| ~ ( ~ ! [SY710: $i,SY711: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY710 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY711 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY710 @ SY711 ) @ SV337 ) )
| ~ ! [SY713: $i,SY714: $i] :
( ~ ( in @ ( ordered_pair @ SY713 @ SY714 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SY713 @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) @ SY714 ) @ SV166 ) ) ) ) )
= $true )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1828,plain,
! [SV78: $i,SV283: $i] :
( ( ( ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY665 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 ) )
= $true )
| ( ( ~ ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) )
= $true )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(1829,plain,
! [SV78: $i,SV283: $i] :
( ( ( in @ ( ordered_pair @ ( sK38_SY323 @ SV283 @ SV78 ) @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
= $true )
| ( ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 )
= $true )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(1830,plain,
! [SV284: $i,SV78: $i] :
( ( ( ! [SY666: $i] :
( ! [SY425: $i] :
~ ( in @ ( ordered_pair @ SY425 @ SY666 ) @ SV78 )
| ( in @ SY666 @ SV284 ) ) )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1831,plain,
! [SV78: $i,SV284: $i] :
( ( ( ! [SY668: $i] :
( ~ ( in @ SY668 @ SV284 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY668 @ SV284 @ SV78 ) @ SY668 ) @ SV78 ) ) )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1832,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) ) )
= $false )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1833,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) ) )
= $false )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1834,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV79 )
= $true )
| ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV215 )
= $true )
| ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1835,plain,
! [SV216: $i,SV79: $i,SV264: $i,SV358: $i] :
( ( ( ~ ( in @ SV358 @ SV264 )
| ( SV358 = SV79 )
| ( SV358 = SV216 ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(1836,plain,
! [SV216: $i,SV264: $i,SV79: $i] :
( ( ( ~ ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) )
| ~ ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) )
= $false )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1837,plain,
! [SV167: $i,SV217: $i] :
( ( ( subset @ ( sK28_C @ SV217 @ SV167 ) @ SV167 )
= $false )
| ( ( in @ ( sK28_C @ SV217 @ SV167 ) @ SV217 )
= $false )
| ( ( SV217
= ( powerset @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1838,plain,
! [SV168: $i,SV218: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ SV218 ) )
= $true )
| ( ( subset @ SV347 @ SV168 )
= $true )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1839,plain,
! [SV218: $i,SV168: $i,SV348: $i] :
( ( ( ~ ( subset @ SV348 @ SV168 ) )
= $true )
| ( ( in @ SV348 @ SV218 )
= $true )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1840,plain,
! [SV265: $i,SV224: $i,SV81: $i,SV359: $i] :
( ( ( ! [SY718: $i] :
( ~ ( in @ SV359 @ SV81 )
| ~ ( in @ SY718 @ SV224 )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SV359 @ SY718 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(1841,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1842,plain,
! [SV266: $i,SV360: $i,SV225: $i,SV81: $i] :
( ( ( ! [SY719: $i,SY720: $i] :
( ~ ( in @ SY719 @ SV81 )
| ~ ( in @ SY720 @ SV225 )
| ( SV360
!= ( ordered_pair @ SY719 @ SY720 ) ) )
| ( in @ SV360 @ SV266 ) )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(1843,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ SV266 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SV361
!= ( ordered_pair @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) ) ) ) )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(1844,plain,
! [SV349: $i,SV327: $i,SV142: $i,SV82: $i] :
( ( ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV327 @ SV349 ) )
= $false )
| ( ( in @ SV82 @ SV327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1845,plain,
! [SV340: $i,SV328: $i,SV142: $i,SV82: $i] :
( ( ( in @ ( ordered_pair @ SV82 @ SV142 ) @ ( cartesian_product2 @ SV328 @ SV340 ) )
= $false )
| ( ( in @ SV142 @ SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1846,plain,
! [SV291: $i,SV341: $i] :
( ( ( element @ SV341 @ SV291 )
= $false )
| ( ( empty @ SV341 )
= $true )
| ( ( empty @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1847,plain,
! [SV292: $i,SV342: $i] :
( ( ( empty @ SV342 )
= $false )
| ( ( element @ SV342 @ SV292 )
= $true )
| ( ( empty @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1848,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) ) )
= $false )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1786]) ).
thf(1849,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) ) )
= $false )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1786]) ).
thf(1850,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 )
= $true )
| ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 )
= $true )
| ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(1851,plain,
! [SV227: $i,SV83: $i,SV269: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV269 )
| ( in @ SV362 @ SV83 )
| ( in @ SV362 @ SV227 ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(1852,plain,
! [SV227: $i,SV269: $i,SV83: $i] :
( ( ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) )
= $false )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1853,plain,
! [SV85: $i,SV313: $i] :
( ( ( ! [SY697: $i] :
( ~ ( subset @ SY697 @ SV313 )
| ( in @ SY697 @ ( sK3_SY299 @ SV313 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1854,plain,
! [SV85: $i,SV313: $i] :
( ( ( in @ ( sK3_SY299 @ SV313 @ SV85 ) @ ( sK2_B @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1855,plain,
! [SV363: $i,SV85: $i,SV350: $i] :
( ( ~ ( in @ SV350 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SV363 @ SV350 )
| ( in @ SV363 @ ( sK2_B @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1856,plain,
! [SV351: $i,SV184: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV351 ) )
= $true )
| ( ( ~ ( in @ SV351 @ SV184 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1857,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) ) )
= $false )
| ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1794]) ).
thf(1858,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 ) )
= $false )
| ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1794]) ).
thf(1859,plain,
! [SV234: $i,SV185: $i,SV352: $i] :
( ( ( ! [SY716: $i] :
( ~ ( in @ SV352 @ SY716 )
| ~ ( in @ SY716 @ SV185 ) ) )
= $true )
| ( ( in @ SV352 @ SV234 )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(1860,plain,
! [SV185: $i,SV234: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ SV234 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV353 @ ( sK16_D @ SV353 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SV353 @ SV234 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1861,plain,
! [SV86: $i,SV294: $i] :
( ( ( ! [SY675: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SY675 ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(1862,plain,
! [SV86: $i,SV294: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ ( sK41_SY325 @ SV294 @ SV86 ) ) @ SV86 )
= $true )
| ( ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 )
= $true )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1863,plain,
! [SV295: $i,SV86: $i] :
( ( ( ! [SY676: $i] :
( ! [SY472: $i] :
~ ( in @ ( ordered_pair @ SY676 @ SY472 ) @ SV86 )
| ( in @ SY676 @ SV295 ) ) )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1864,plain,
! [SV86: $i,SV295: $i] :
( ( ( ! [SY678: $i] :
( ~ ( in @ SY678 @ SV295 )
| ( in @ ( ordered_pair @ SY678 @ ( sK39_D @ SY678 @ SV295 @ SV86 ) ) @ SV86 ) ) )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1865,plain,
! [SV364: $i,SV87: $i,SV354: $i] :
( ( ~ ( in @ SV354 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SV364 @ SV354 )
| ( in @ SV364 @ ( sK32_B @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(1866,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) ) )
= $false )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1805]) ).
thf(1867,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) ) )
= $false )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1805]) ).
thf(1868,plain,
! [SV90: $i,SV301: $i] :
( ( ( ~ ! [SY683: $i,SY684: $i] :
( ~ ( in @ ( ordered_pair @ SY683 @ SY684 ) @ SV301 )
| ( in @ ( ordered_pair @ SY684 @ SY683 ) @ SV90 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY686 @ SY685 ) @ SV90 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV301 ) ) )
= $false )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1869,plain,
! [SV194: $i,SV243: $i] :
( ( ( in @ ( sK29_C @ SV243 @ SV194 ) @ SV243 )
= $false )
| ( ( ( sK29_C @ SV243 @ SV194 )
= SV194 )
= $false )
| ( ( SV243
= ( singleton @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1870,plain,
! [SV244: $i,SV195: $i,SV355: $i] :
( ( ( ( SV355 != SV195 ) )
= $true )
| ( ( in @ SV355 @ SV244 )
= $true )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(1871,plain,
! [SV195: $i,SV244: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ SV244 ) )
= $true )
| ( ( SV356 = SV195 )
= $true )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1872,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 ) )
= $true )
| ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(1873,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) )
= $false )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1812]) ).
thf(1874,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) ) )
= $false )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1812]) ).
thf(1875,plain,
! [SV276: $i,SV251: $i,SV93: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV93 )
| ( in @ SV365 @ SV251 )
| ( in @ SV365 @ SV276 ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(1876,plain,
! [SV251: $i,SV93: $i,SV276: $i] :
( ( ( ~ ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) )
| ~ ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) )
= $false )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1877,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) )
| ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) ) )
= $false )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1815]) ).
thf(1878,plain,
! [SV333: $i,SV305: $i] :
( ( ( ~ ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV305 )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) ) )
= $false )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1815]) ).
thf(1879,plain,
! [SV306: $i,SV334: $i] :
( ( ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV334 @ SV306 ) ) )
| ( in @ SY706 @ SV334 ) )
| ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV334 )
| ! [SY694: $i] :
( ~ ( in @ SY694 @ SV306 )
| ( in @ SY707 @ SY694 ) ) ) )
= $false )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1880,plain,
! [SV307: $i,SV344: $i] :
( ( ( SV344
= ( set_meet @ SV307 ) )
= $false )
| ( ( SV344 = empty_set )
= $true )
| ( ( SV307 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1881,plain,
! [SV308: $i,SV345: $i] :
( ( ( SV345 = empty_set )
= $false )
| ( ( SV345
= ( set_meet @ SV308 ) )
= $true )
| ( ( SV308 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(1882,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1883,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1884,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
| ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1885,plain,
! [SV261: $i,SV212: $i,SV74: $i,SV357: $i] :
( ( ( ~ ( in @ SV357 @ SV74 )
| ~ ( in @ SV357 @ SV212 ) )
= $true )
| ( ( in @ SV357 @ SV261 )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(1886,plain,
! [SV212: $i,SV74: $i,SV261: $i] :
( ( ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) ) )
= $false )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1887,plain,
! [SV74: $i,SV212: $i,SV261: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) )
= $false )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1888,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( ~ ( ! [SY709: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SY709 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY709 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) ) ) )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(1889,plain,
! [SV166: $i,SV77: $i,SV337: $i] :
( ( ( ( SV337
!= ( relation_composition @ SV77 @ SV166 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY710: $i,SY711: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY710 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY711 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY710 @ SY711 ) @ SV337 ) )
| ~ ! [SY713: $i,SY714: $i] :
( ~ ( in @ ( ordered_pair @ SY713 @ SY714 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SY713 @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) @ SY714 ) @ SV166 ) ) ) ) )
= $true )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(1890,plain,
! [SV78: $i,SV283: $i,SV366: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV366 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 ) )
= $true )
| ( ( ~ ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) )
= $true )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(1891,plain,
! [SV284: $i,SV78: $i,SV367: $i] :
( ( ( ! [SY721: $i] :
~ ( in @ ( ordered_pair @ SY721 @ SV367 ) @ SV78 )
| ( in @ SV367 @ SV284 ) )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(1892,plain,
! [SV78: $i,SV284: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV284 )
| ( in @ ( ordered_pair @ ( sK36_D @ SV368 @ SV284 @ SV78 ) @ SV368 ) @ SV78 ) )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(1893,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1832]) ).
thf(1894,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
| ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1833]) ).
thf(1895,plain,
! [SV216: $i,SV79: $i,SV264: $i,SV358: $i] :
( ( ( ~ ( in @ SV358 @ SV264 ) )
= $true )
| ( ( ( SV358 = SV79 )
| ( SV358 = SV216 ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1896,plain,
! [SV216: $i,SV264: $i,SV79: $i] :
( ( ( ~ ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) ) )
= $false )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1897,plain,
! [SV79: $i,SV264: $i,SV216: $i] :
( ( ( ~ ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) )
= $false )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1898,plain,
! [SV168: $i,SV218: $i,SV347: $i] :
( ( ( in @ SV347 @ SV218 )
= $false )
| ( ( subset @ SV347 @ SV168 )
= $true )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1899,plain,
! [SV218: $i,SV168: $i,SV348: $i] :
( ( ( subset @ SV348 @ SV168 )
= $false )
| ( ( in @ SV348 @ SV218 )
= $true )
| ( ( SV218
= ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1900,plain,
! [SV265: $i,SV224: $i,SV369: $i,SV81: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV81 )
| ~ ( in @ SV369 @ SV224 )
| ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SV359 @ SV369 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(1901,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1902,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1903,plain,
! [SV266: $i,SV360: $i,SV225: $i,SV81: $i] :
( ( ( ! [SY719: $i,SY720: $i] :
( ~ ( in @ SY719 @ SV81 )
| ~ ( in @ SY720 @ SV225 )
| ( SV360
!= ( ordered_pair @ SY719 @ SY720 ) ) ) )
= $true )
| ( ( in @ SV360 @ SV266 )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(1904,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ SV266 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SV361
!= ( ordered_pair @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) ) ) ) )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(1905,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1906,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
| ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1907,plain,
! [SV227: $i,SV83: $i,SV269: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV269 ) )
= $true )
| ( ( ( in @ SV362 @ SV83 )
| ( in @ SV362 @ SV227 ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(1908,plain,
! [SV227: $i,SV269: $i,SV83: $i] :
( ( ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) ) )
= $false )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(1909,plain,
! [SV83: $i,SV269: $i,SV227: $i] :
( ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) )
= $false )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(1910,plain,
! [SV85: $i,SV313: $i,SV370: $i] :
( ( ( ~ ( subset @ SV370 @ SV313 )
| ( in @ SV370 @ ( sK3_SY299 @ SV313 @ SV85 ) ) )
= $true )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(1911,plain,
! [SV85: $i,SV313: $i] :
( ( ( in @ SV313 @ ( sK2_B @ SV85 ) )
= $false )
| ( ( in @ ( sK3_SY299 @ SV313 @ SV85 ) @ ( sK2_B @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1912,plain,
! [SV363: $i,SV85: $i,SV350: $i] :
( ( ( ~ ( in @ SV350 @ ( sK2_B @ SV85 ) )
| ~ ( subset @ SV363 @ SV350 ) )
= $true )
| ( ( in @ SV363 @ ( sK2_B @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(1913,plain,
! [SV351: $i,SV184: $i,SV233: $i] :
( ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV351 )
= $false )
| ( ( ~ ( in @ SV351 @ SV184 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1914,plain,
! [SV184: $i,SV233: $i] :
( ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ ( sK18_SY311 @ SV233 @ SV184 ) )
= $true )
| ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(1915,plain,
! [SV184: $i,SV233: $i] :
( ( ( in @ ( sK18_SY311 @ SV233 @ SV184 ) @ SV184 )
= $true )
| ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(1916,plain,
! [SV234: $i,SV185: $i,SV371: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ SV371 )
| ~ ( in @ SV371 @ SV185 ) )
= $true )
| ( ( in @ SV352 @ SV234 )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(1917,plain,
! [SV185: $i,SV234: $i,SV353: $i] :
( ( ( in @ SV353 @ SV234 )
= $false )
| ( ( ~ ( ~ ( in @ SV353 @ ( sK16_D @ SV353 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SV353 @ SV234 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1918,plain,
! [SV372: $i,SV86: $i,SV294: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SV372 ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(1919,plain,
! [SV295: $i,SV86: $i,SV373: $i] :
( ( ( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SV373 @ SY722 ) @ SV86 )
| ( in @ SV373 @ SV295 ) )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1920,plain,
! [SV86: $i,SV295: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ SV295 )
| ( in @ ( ordered_pair @ SV374 @ ( sK39_D @ SV374 @ SV295 @ SV86 ) ) @ SV86 ) )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(1921,plain,
! [SV364: $i,SV87: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ ( sK32_B @ SV87 ) )
| ~ ( subset @ SV364 @ SV354 ) )
= $true )
| ( ( in @ SV364 @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1922,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
= $true )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(1923,plain,
! [SV90: $i,SV300: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
| ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
= $true )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1867]) ).
thf(1924,plain,
! [SV90: $i,SV301: $i] :
( ( ( ~ ! [SY683: $i,SY684: $i] :
( ~ ( in @ ( ordered_pair @ SY683 @ SY684 ) @ SV301 )
| ( in @ ( ordered_pair @ SY684 @ SY683 ) @ SV90 ) ) )
= $false )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(1925,plain,
! [SV301: $i,SV90: $i] :
( ( ( ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY686 @ SY685 ) @ SV90 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV301 ) ) )
= $false )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(1926,plain,
! [SV244: $i,SV195: $i,SV355: $i] :
( ( ( SV355 = SV195 )
= $false )
| ( ( in @ SV355 @ SV244 )
= $true )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1927,plain,
! [SV195: $i,SV244: $i,SV356: $i] :
( ( ( in @ SV356 @ SV244 )
= $false )
| ( ( SV356 = SV195 )
= $true )
| ( ( SV244
= ( singleton @ SV195 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1928,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
= $false )
| ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1929,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1873]) ).
thf(1930,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
| ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 ) )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1874]) ).
thf(1931,plain,
! [SV276: $i,SV251: $i,SV93: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV93 )
| ( in @ SV365 @ SV251 ) )
= $true )
| ( ( in @ SV365 @ SV276 )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(1932,plain,
! [SV251: $i,SV93: $i,SV276: $i] :
( ( ( ~ ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) ) )
= $false )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1933,plain,
! [SV93: $i,SV251: $i,SV276: $i] :
( ( ( ~ ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) )
= $false )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1934,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) )
| ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1935,plain,
! [SV333: $i,SV305: $i] :
( ( ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV305 )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1936,plain,
! [SV306: $i,SV334: $i] :
( ( ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV334 @ SV306 ) ) )
| ( in @ SY706 @ SV334 ) ) )
= $false )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1937,plain,
! [SV306: $i,SV334: $i] :
( ( ( ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV334 )
| ! [SY694: $i] :
( ~ ( in @ SY694 @ SV306 )
| ( in @ SY707 @ SY694 ) ) ) )
= $false )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1938,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
= $false )
| ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1939,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
= $true )
| ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(1940,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
= $true )
| ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 )
= $true )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(1941,plain,
! [SV261: $i,SV212: $i,SV74: $i,SV357: $i] :
( ( ( ~ ( in @ SV357 @ SV74 ) )
= $true )
| ( ( ~ ( in @ SV357 @ SV212 ) )
= $true )
| ( ( in @ SV357 @ SV261 )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(1942,plain,
! [SV212: $i,SV74: $i,SV261: $i] :
( ( ( ! [SY644: $i] :
( ~ ( in @ SY644 @ SV261 )
| ( in @ SY644 @ SV74 ) ) )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1943,plain,
! [SV74: $i,SV212: $i,SV261: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ SV261 )
| ( in @ SY645 @ SV212 ) ) )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1887]) ).
thf(1944,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( ! [SY709: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SY709 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY709 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) ) )
= $false )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1945,plain,
! [SV166: $i,SV77: $i,SV337: $i] :
( ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( ~ ( ~ ! [SY710: $i,SY711: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY710 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY711 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY710 @ SY711 ) @ SV337 ) )
| ~ ! [SY713: $i,SY714: $i] :
( ~ ( in @ ( ordered_pair @ SY713 @ SY714 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SY713 @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) @ SY714 ) @ SV166 ) ) ) ) )
= $true )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1946,plain,
! [SV78: $i,SV283: $i,SV366: $i] :
( ( ( in @ ( ordered_pair @ SV366 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
= $false )
| ( ( ~ ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 ) )
= $true )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(1947,plain,
! [SV284: $i,SV78: $i,SV367: $i] :
( ( ( ! [SY721: $i] :
~ ( in @ ( ordered_pair @ SY721 @ SV367 ) @ SV78 ) )
= $true )
| ( ( in @ SV367 @ SV284 )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(1948,plain,
! [SV78: $i,SV284: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV284 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK36_D @ SV368 @ SV284 @ SV78 ) @ SV368 ) @ SV78 )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(1949,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 ) )
= $true )
| ( ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(1950,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 ) )
= $true )
| ( ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(1951,plain,
! [SV216: $i,SV79: $i,SV264: $i,SV358: $i] :
( ( ( in @ SV358 @ SV264 )
= $false )
| ( ( ( SV358 = SV79 )
| ( SV358 = SV216 ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1952,plain,
! [SV216: $i,SV264: $i,SV79: $i] :
( ( ( ! [SY648: $i] :
( ( SY648 != SV79 )
| ( in @ SY648 @ SV264 ) ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(1953,plain,
! [SV79: $i,SV264: $i,SV216: $i] :
( ( ( ! [SY649: $i] :
( ( SY649 != SV216 )
| ( in @ SY649 @ SV264 ) ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(1954,plain,
! [SV265: $i,SV224: $i,SV369: $i,SV81: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV81 )
| ~ ( in @ SV369 @ SV224 ) )
= $true )
| ( ( ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SV359 @ SV369 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(1955,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(1956,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ( sK23_D @ SV265 @ SV224 @ SV81 )
= ( ordered_pair @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1957,plain,
! [SV266: $i,SV360: $i,SV225: $i,SV81: $i,SV375: $i] :
( ( ( ! [SY723: $i] :
( ~ ( in @ SV375 @ SV81 )
| ~ ( in @ SY723 @ SV225 )
| ( SV360
!= ( ordered_pair @ SV375 @ SY723 ) ) ) )
= $true )
| ( ( in @ SV360 @ SV266 )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(1958,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( in @ SV361 @ SV266 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SV361
!= ( ordered_pair @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) ) ) ) )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1959,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(1960,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(1961,plain,
! [SV227: $i,SV83: $i,SV269: $i,SV362: $i] :
( ( ( in @ SV362 @ SV269 )
= $false )
| ( ( ( in @ SV362 @ SV83 )
| ( in @ SV362 @ SV227 ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(1962,plain,
! [SV227: $i,SV269: $i,SV83: $i] :
( ( ( ! [SY658: $i] :
( ~ ( in @ SY658 @ SV83 )
| ( in @ SY658 @ SV269 ) ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(1963,plain,
! [SV83: $i,SV269: $i,SV227: $i] :
( ( ( ! [SY659: $i] :
( ~ ( in @ SY659 @ SV227 )
| ( in @ SY659 @ SV269 ) ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1909]) ).
thf(1964,plain,
! [SV85: $i,SV313: $i,SV370: $i] :
( ( ( ~ ( subset @ SV370 @ SV313 ) )
= $true )
| ( ( in @ SV370 @ ( sK3_SY299 @ SV313 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(1965,plain,
! [SV363: $i,SV85: $i,SV350: $i] :
( ( ( ~ ( in @ SV350 @ ( sK2_B @ SV85 ) ) )
= $true )
| ( ( ~ ( subset @ SV363 @ SV350 ) )
= $true )
| ( ( in @ SV363 @ ( sK2_B @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(1966,plain,
! [SV233: $i,SV184: $i,SV351: $i] :
( ( ( in @ SV351 @ SV184 )
= $false )
| ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV351 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 ) )
= $true )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1967,plain,
! [SV234: $i,SV185: $i,SV371: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ SV371 ) )
= $true )
| ( ( ~ ( in @ SV371 @ SV185 ) )
= $true )
| ( ( in @ SV352 @ SV234 )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(1968,plain,
! [SV185: $i,SV234: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ ( sK16_D @ SV353 @ SV234 @ SV185 ) )
| ~ ( in @ ( sK16_D @ SV353 @ SV234 @ SV185 ) @ SV185 ) )
= $false )
| ( ( in @ SV353 @ SV234 )
= $false )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1969,plain,
! [SV372: $i,SV86: $i,SV294: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SV372 ) @ SV86 )
= $false )
| ( ( ~ ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(1970,plain,
! [SV295: $i,SV86: $i,SV373: $i] :
( ( ( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SV373 @ SY722 ) @ SV86 ) )
= $true )
| ( ( in @ SV373 @ SV295 )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1919]) ).
thf(1971,plain,
! [SV86: $i,SV295: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ SV295 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV374 @ ( sK39_D @ SV374 @ SV295 @ SV86 ) ) @ SV86 )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(1972,plain,
! [SV364: $i,SV87: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ ( sK32_B @ SV87 ) ) )
= $true )
| ( ( ~ ( subset @ SV364 @ SV354 ) )
= $true )
| ( ( in @ SV364 @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1921]) ).
thf(1973,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
= $true )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(1974,plain,
! [SV90: $i,SV300: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 )
= $true )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(1975,plain,
! [SV90: $i,SV301: $i] :
( ( ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ ( ordered_pair @ SY683 @ SY684 ) @ SV301 )
| ( in @ ( ordered_pair @ SY684 @ SY683 ) @ SV90 ) ) )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(1976,plain,
! [SV301: $i,SV90: $i] :
( ( ( ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY686 @ SY685 ) @ SV90 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV301 ) ) )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1977,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 )
= $false )
| ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
= $true )
| ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
= $false )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(1978,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV93 )
= $true )
| ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(1979,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 ) )
= $true )
| ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(1980,plain,
! [SV276: $i,SV251: $i,SV93: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV93 ) )
= $true )
| ( ( in @ SV365 @ SV251 )
= $true )
| ( ( in @ SV365 @ SV276 )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(1981,plain,
! [SV251: $i,SV93: $i,SV276: $i] :
( ( ( ! [SY663: $i] :
( ~ ( in @ SY663 @ SV276 )
| ( in @ SY663 @ SV93 ) ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(1982,plain,
! [SV93: $i,SV251: $i,SV276: $i] :
( ( ( ! [SY664: $i] :
( ~ ( in @ SY664 @ SV276 )
| ~ ( in @ SY664 @ SV251 ) ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1933]) ).
thf(1983,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(1984,plain,
! [SV333: $i,SV305: $i] :
( ( ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV305 )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SY705 ) ) )
= $true )
| ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(1985,plain,
! [SV306: $i,SV334: $i] :
( ( ( ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV334 @ SV306 ) ) )
| ( in @ SY706 @ SV334 ) ) )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(1986,plain,
! [SV306: $i,SV334: $i] :
( ( ( ! [SY707: $i] :
( ~ ( in @ SY707 @ SV334 )
| ! [SY694: $i] :
( ~ ( in @ SY694 @ SV306 )
| ( in @ SY707 @ SY694 ) ) ) )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(1987,plain,
! [SV74: $i,SV211: $i,SV260: $i] :
( ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV260 )
= $false )
| ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV74 )
= $false )
| ( ( in @ ( sK19_D @ SV260 @ SV211 @ SV74 ) @ SV211 )
= $false )
| ( ( SV260
= ( set_intersection2 @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(1988,plain,
! [SV261: $i,SV212: $i,SV74: $i,SV357: $i] :
( ( ( in @ SV357 @ SV74 )
= $false )
| ( ( ~ ( in @ SV357 @ SV212 ) )
= $true )
| ( ( in @ SV357 @ SV261 )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1989,plain,
! [SV212: $i,SV74: $i,SV261: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ SV261 )
| ( in @ SV376 @ SV74 ) )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(1990,plain,
! [SV74: $i,SV212: $i,SV261: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV261 )
| ( in @ SV377 @ SV212 ) )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(1991,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( ! [SY709: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SY709 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY709 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) ) )
= $false )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1944]) ).
thf(1992,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) ) )
= $false )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1944]) ).
thf(1993,plain,
! [SV337: $i,SV166: $i,SV77: $i] :
( ( ( ~ ! [SY710: $i,SY711: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY710 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY711 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY710 @ SY711 ) @ SV337 ) )
| ~ ! [SY713: $i,SY714: $i] :
( ~ ( in @ ( ordered_pair @ SY713 @ SY714 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SY713 @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) @ SY714 ) @ SV166 ) ) ) )
= $false )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(1994,plain,
! [SV366: $i,SV78: $i,SV283: $i] :
( ( ( in @ ( sK37_C @ SV283 @ SV78 ) @ SV283 )
= $false )
| ( ( in @ ( ordered_pair @ SV366 @ ( sK37_C @ SV283 @ SV78 ) ) @ SV78 )
= $false )
| ( ( SV283
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(1995,plain,
! [SV284: $i,SV78: $i,SV367: $i,SV378: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV378 @ SV367 ) @ SV78 ) )
= $true )
| ( ( in @ SV367 @ SV284 )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(1996,plain,
! [SV78: $i,SV284: $i,SV368: $i] :
( ( ( in @ SV368 @ SV284 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK36_D @ SV368 @ SV284 @ SV78 ) @ SV368 ) @ SV78 )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(1997,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
= $false )
| ( ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV79 ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(1998,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
= $false )
| ( ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
!= SV215 ) )
= $true )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(1999,plain,
! [SV264: $i,SV216: $i,SV79: $i,SV358: $i] :
( ( ( SV358 = SV79 )
= $true )
| ( ( SV358 = SV216 )
= $true )
| ( ( in @ SV358 @ SV264 )
= $false )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2000,plain,
! [SV216: $i,SV264: $i,SV79: $i,SV379: $i] :
( ( ( ( SV379 != SV79 )
| ( in @ SV379 @ SV264 ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2001,plain,
! [SV79: $i,SV264: $i,SV216: $i,SV380: $i] :
( ( ( ( SV380 != SV216 )
| ( in @ SV380 @ SV264 ) )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2002,plain,
! [SV265: $i,SV224: $i,SV369: $i,SV81: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV81 ) )
= $true )
| ( ( ~ ( in @ SV369 @ SV224 ) )
= $true )
| ( ( ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SV359 @ SV369 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2003,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
= $false )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2004,plain,
! [SV266: $i,SV360: $i,SV225: $i,SV381: $i,SV81: $i,SV375: $i] :
( ( ( ~ ( in @ SV375 @ SV81 )
| ~ ( in @ SV381 @ SV225 )
| ( SV360
!= ( ordered_pair @ SV375 @ SV381 ) ) )
= $true )
| ( ( in @ SV360 @ SV266 )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2005,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
| ( SV361
!= ( ordered_pair @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) ) ) )
= $false )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2006,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2007,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 ) )
= $true )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2008,plain,
! [SV269: $i,SV227: $i,SV83: $i,SV362: $i] :
( ( ( in @ SV362 @ SV83 )
= $true )
| ( ( in @ SV362 @ SV227 )
= $true )
| ( ( in @ SV362 @ SV269 )
= $false )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2009,plain,
! [SV227: $i,SV269: $i,SV83: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ SV83 )
| ( in @ SV382 @ SV269 ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2010,plain,
! [SV83: $i,SV269: $i,SV227: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ SV227 )
| ( in @ SV383 @ SV269 ) )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2011,plain,
! [SV85: $i,SV313: $i,SV370: $i] :
( ( ( subset @ SV370 @ SV313 )
= $false )
| ( ( in @ SV370 @ ( sK3_SY299 @ SV313 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV313 @ ( sK2_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2012,plain,
! [SV363: $i,SV85: $i,SV350: $i] :
( ( ( in @ SV350 @ ( sK2_B @ SV85 ) )
= $false )
| ( ( ~ ( subset @ SV363 @ SV350 ) )
= $true )
| ( ( in @ SV363 @ ( sK2_B @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2013,plain,
! [SV351: $i,SV184: $i,SV233: $i] :
( ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV233 )
= $false )
| ( ( in @ ( sK17_C @ SV233 @ SV184 ) @ SV351 )
= $false )
| ( ( in @ SV351 @ SV184 )
= $false )
| ( ( SV233
= ( union @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2014,plain,
! [SV234: $i,SV185: $i,SV371: $i,SV352: $i] :
( ( ( in @ SV352 @ SV371 )
= $false )
| ( ( ~ ( in @ SV371 @ SV185 ) )
= $true )
| ( ( in @ SV352 @ SV234 )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2015,plain,
! [SV185: $i,SV234: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ ( sK16_D @ SV353 @ SV234 @ SV185 ) ) )
= $false )
| ( ( in @ SV353 @ SV234 )
= $false )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1968]) ).
thf(2016,plain,
! [SV185: $i,SV234: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK16_D @ SV353 @ SV234 @ SV185 ) @ SV185 ) )
= $false )
| ( ( in @ SV353 @ SV234 )
= $false )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1968]) ).
thf(2017,plain,
! [SV372: $i,SV86: $i,SV294: $i] :
( ( ( in @ ( sK40_C @ SV294 @ SV86 ) @ SV294 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK40_C @ SV294 @ SV86 ) @ SV372 ) @ SV86 )
= $false )
| ( ( SV294
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2018,plain,
! [SV295: $i,SV86: $i,SV384: $i,SV373: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV384 ) @ SV86 ) )
= $true )
| ( ( in @ SV373 @ SV295 )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2019,plain,
! [SV86: $i,SV295: $i,SV374: $i] :
( ( ( in @ SV374 @ SV295 )
= $false )
| ( ( in @ ( ordered_pair @ SV374 @ ( sK39_D @ SV374 @ SV295 @ SV86 ) ) @ SV86 )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1971]) ).
thf(2020,plain,
! [SV364: $i,SV87: $i,SV354: $i] :
( ( ( in @ SV354 @ ( sK32_B @ SV87 ) )
= $false )
| ( ( ~ ( subset @ SV364 @ SV354 ) )
= $true )
| ( ( in @ SV364 @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2021,plain,
! [SV90: $i,SV300: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 ) )
= $true )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2022,plain,
! [SV90: $i,SV301: $i,SV385: $i] :
( ( ( ! [SY724: $i] :
( ~ ( in @ ( ordered_pair @ SV385 @ SY724 ) @ SV301 )
| ( in @ ( ordered_pair @ SY724 @ SV385 ) @ SV90 ) ) )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2023,plain,
! [SV301: $i,SV90: $i,SV386: $i] :
( ( ( ! [SY725: $i] :
( ~ ( in @ ( ordered_pair @ SY725 @ SV386 ) @ SV90 )
| ( in @ ( ordered_pair @ SV386 @ SY725 ) @ SV301 ) ) )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2024,plain,
! [SV93: $i,SV250: $i,SV275: $i] :
( ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV250 )
= $false )
| ( ( in @ ( sK15_D @ SV275 @ SV250 @ SV93 ) @ SV275 )
= $true )
| ( ( SV275
= ( set_difference @ SV93 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2025,plain,
! [SV276: $i,SV251: $i,SV93: $i,SV365: $i] :
( ( ( in @ SV365 @ SV93 )
= $false )
| ( ( in @ SV365 @ SV251 )
= $true )
| ( ( in @ SV365 @ SV276 )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2026,plain,
! [SV251: $i,SV93: $i,SV276: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV276 )
| ( in @ SV387 @ SV93 ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2027,plain,
! [SV93: $i,SV251: $i,SV276: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV276 )
| ~ ( in @ SV388 @ SV251 ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2028,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
| ~ ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2029,plain,
! [SV333: $i,SV305: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV305 )
| ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV389 ) )
= $true )
| ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2030,plain,
! [SV306: $i,SV334: $i,SV390: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_D @ SV390 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SV390 @ ( sK43_D @ SV390 @ SV334 @ SV306 ) ) )
| ( in @ SV390 @ SV334 ) )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2031,plain,
! [SV306: $i,SV334: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ SV334 )
| ! [SY726: $i] :
( ~ ( in @ SY726 @ SV306 )
| ( in @ SV391 @ SY726 ) ) )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2032,plain,
! [SV261: $i,SV74: $i,SV212: $i,SV357: $i] :
( ( ( in @ SV357 @ SV212 )
= $false )
| ( ( in @ SV357 @ SV74 )
= $false )
| ( ( in @ SV357 @ SV261 )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2033,plain,
! [SV212: $i,SV74: $i,SV261: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ SV261 ) )
= $true )
| ( ( in @ SV376 @ SV74 )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2034,plain,
! [SV74: $i,SV212: $i,SV261: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV261 ) )
= $true )
| ( ( in @ SV377 @ SV212 )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2035,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ! [SY709: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SY709 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY709 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2036,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2037,plain,
! [SV337: $i,SV166: $i,SV77: $i] :
( ( ( ~ ! [SY710: $i,SY711: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY710 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY711 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY710 @ SY711 ) @ SV337 ) ) )
= $false )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2038,plain,
! [SV77: $i,SV166: $i,SV337: $i] :
( ( ( ~ ! [SY713: $i,SY714: $i] :
( ~ ( in @ ( ordered_pair @ SY713 @ SY714 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SY713 @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) @ SY714 ) @ SV166 ) ) ) )
= $false )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2039,plain,
! [SV284: $i,SV78: $i,SV367: $i,SV378: $i] :
( ( ( in @ ( ordered_pair @ SV378 @ SV367 ) @ SV78 )
= $false )
| ( ( in @ SV367 @ SV284 )
= $true )
| ( ( SV284
= ( relation_rng @ SV78 ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2040,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV79 )
= $false )
| ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
= $false )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2041,plain,
! [SV79: $i,SV215: $i,SV263: $i] :
( ( ( ( sK27_D @ SV263 @ SV215 @ SV79 )
= SV215 )
= $false )
| ( ( in @ ( sK27_D @ SV263 @ SV215 @ SV79 ) @ SV263 )
= $false )
| ( ( SV263
= ( unordered_pair @ SV79 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2042,plain,
! [SV216: $i,SV264: $i,SV79: $i,SV379: $i] :
( ( ( ( SV379 != SV79 ) )
= $true )
| ( ( in @ SV379 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2000]) ).
thf(2043,plain,
! [SV79: $i,SV264: $i,SV216: $i,SV380: $i] :
( ( ( ( SV380 != SV216 ) )
= $true )
| ( ( in @ SV380 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2044,plain,
! [SV265: $i,SV224: $i,SV369: $i,SV81: $i,SV359: $i] :
( ( ( in @ SV359 @ SV81 )
= $false )
| ( ( ~ ( in @ SV369 @ SV224 ) )
= $true )
| ( ( ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SV359 @ SV369 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2045,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 ) )
= $false )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2003]) ).
thf(2046,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 ) )
= $false )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2003]) ).
thf(2047,plain,
! [SV266: $i,SV360: $i,SV225: $i,SV381: $i,SV81: $i,SV375: $i] :
( ( ( ~ ( in @ SV375 @ SV81 )
| ~ ( in @ SV381 @ SV225 ) )
= $true )
| ( ( ( SV360
!= ( ordered_pair @ SV375 @ SV381 ) ) )
= $true )
| ( ( in @ SV360 @ SV266 )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2004]) ).
thf(2048,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 ) ) )
= $false )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2005]) ).
thf(2049,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ( SV361
!= ( ordered_pair @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) ) ) )
= $false )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2005]) ).
thf(2050,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV83 )
= $false )
| ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
= $false )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2051,plain,
! [SV83: $i,SV226: $i,SV268: $i] :
( ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV226 )
= $false )
| ( ( in @ ( sK26_D @ SV268 @ SV226 @ SV83 ) @ SV268 )
= $false )
| ( ( SV268
= ( set_union2 @ SV83 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2052,plain,
! [SV227: $i,SV269: $i,SV83: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ SV83 ) )
= $true )
| ( ( in @ SV382 @ SV269 )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2053,plain,
! [SV83: $i,SV269: $i,SV227: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ SV227 ) )
= $true )
| ( ( in @ SV383 @ SV269 )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2054,plain,
! [SV370: $i,SV85: $i,SV313: $i] :
( ( ( in @ SV313 @ ( sK2_B @ SV85 ) )
= $false )
| ( ( in @ SV370 @ ( sK3_SY299 @ SV313 @ SV85 ) )
= $true )
| ( ( subset @ SV370 @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2055,plain,
! [SV85: $i,SV350: $i,SV363: $i] :
( ( ( subset @ SV363 @ SV350 )
= $false )
| ( ( in @ SV350 @ ( sK2_B @ SV85 ) )
= $false )
| ( ( in @ SV363 @ ( sK2_B @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2056,plain,
! [SV234: $i,SV352: $i,SV185: $i,SV371: $i] :
( ( ( in @ SV371 @ SV185 )
= $false )
| ( ( in @ SV352 @ SV371 )
= $false )
| ( ( in @ SV352 @ SV234 )
= $true )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2057,plain,
! [SV185: $i,SV234: $i,SV353: $i] :
( ( ( in @ SV353 @ ( sK16_D @ SV353 @ SV234 @ SV185 ) )
= $true )
| ( ( in @ SV353 @ SV234 )
= $false )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2058,plain,
! [SV185: $i,SV234: $i,SV353: $i] :
( ( ( in @ ( sK16_D @ SV353 @ SV234 @ SV185 ) @ SV185 )
= $true )
| ( ( in @ SV353 @ SV234 )
= $false )
| ( ( SV234
= ( union @ SV185 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2016]) ).
thf(2059,plain,
! [SV295: $i,SV86: $i,SV384: $i,SV373: $i] :
( ( ( in @ ( ordered_pair @ SV373 @ SV384 ) @ SV86 )
= $false )
| ( ( in @ SV373 @ SV295 )
= $true )
| ( ( SV295
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2060,plain,
! [SV87: $i,SV354: $i,SV364: $i] :
( ( ( subset @ SV364 @ SV354 )
= $false )
| ( ( in @ SV354 @ ( sK32_B @ SV87 ) )
= $false )
| ( ( in @ SV364 @ ( sK32_B @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2061,plain,
! [SV90: $i,SV300: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY309 @ SV300 @ SV90 ) @ ( sK13_C @ SV300 @ SV90 ) ) @ SV90 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_C @ SV300 @ SV90 ) @ ( sK14_SY309 @ SV300 @ SV90 ) ) @ SV300 )
= $false )
| ( ( SV300
= ( relation_inverse @ SV90 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2062,plain,
! [SV90: $i,SV301: $i,SV392: $i,SV385: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV385 @ SV392 ) @ SV301 )
| ( in @ ( ordered_pair @ SV392 @ SV385 ) @ SV90 ) )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2063,plain,
! [SV301: $i,SV90: $i,SV386: $i,SV393: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV393 @ SV386 ) @ SV90 )
| ( in @ ( ordered_pair @ SV386 @ SV393 ) @ SV301 ) )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2064,plain,
! [SV251: $i,SV93: $i,SV276: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV276 ) )
= $true )
| ( ( in @ SV387 @ SV93 )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2065,plain,
! [SV93: $i,SV251: $i,SV276: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV276 ) )
= $true )
| ( ( ~ ( in @ SV388 @ SV251 ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2066,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2028]) ).
thf(2067,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2028]) ).
thf(2068,plain,
! [SV333: $i,SV305: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV305 ) )
= $true )
| ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV389 )
= $true )
| ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2069,plain,
! [SV306: $i,SV334: $i,SV390: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_D @ SV390 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SV390 @ ( sK43_D @ SV390 @ SV334 @ SV306 ) ) ) )
= $true )
| ( ( in @ SV390 @ SV334 )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2070,plain,
! [SV306: $i,SV334: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ SV334 ) )
= $true )
| ( ( ! [SY726: $i] :
( ~ ( in @ SY726 @ SV306 )
| ( in @ SV391 @ SY726 ) ) )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2071,plain,
! [SV212: $i,SV74: $i,SV261: $i,SV376: $i] :
( ( ( in @ SV376 @ SV261 )
= $false )
| ( ( in @ SV376 @ SV74 )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2072,plain,
! [SV74: $i,SV212: $i,SV261: $i,SV377: $i] :
( ( ( in @ SV377 @ SV261 )
= $false )
| ( ( in @ SV377 @ SV212 )
= $true )
| ( ( SV261
= ( set_intersection2 @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2073,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ! [SY709: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SY709 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY709 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2074,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2075,plain,
! [SV337: $i,SV166: $i,SV77: $i] :
( ( ( ! [SY710: $i,SY711: $i] :
( ! [SY552: $i] :
( ~ ( in @ ( ordered_pair @ SY710 @ SY552 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY552 @ SY711 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SY710 @ SY711 ) @ SV337 ) ) )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2037]) ).
thf(2076,plain,
! [SV77: $i,SV166: $i,SV337: $i] :
( ( ( ! [SY713: $i,SY714: $i] :
( ~ ( in @ ( ordered_pair @ SY713 @ SY714 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SY713 @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY714 @ SY713 @ SV337 @ SV166 @ SV77 ) @ SY714 ) @ SV166 ) ) ) )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2077,plain,
! [SV216: $i,SV264: $i,SV79: $i,SV379: $i] :
( ( ( SV379 = SV79 )
= $false )
| ( ( in @ SV379 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2078,plain,
! [SV79: $i,SV264: $i,SV216: $i,SV380: $i] :
( ( ( SV380 = SV216 )
= $false )
| ( ( in @ SV380 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_pair @ SV79 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2079,plain,
! [SV265: $i,SV81: $i,SV359: $i,SV224: $i,SV369: $i] :
( ( ( in @ SV369 @ SV224 )
= $false )
| ( ( in @ SV359 @ SV81 )
= $false )
| ( ( ( ( sK23_D @ SV265 @ SV224 @ SV81 )
!= ( ordered_pair @ SV359 @ SV369 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2080,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( in @ ( sK24_SY315 @ SV265 @ SV224 @ SV81 ) @ SV81 )
= $true )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2045]) ).
thf(2081,plain,
! [SV81: $i,SV224: $i,SV265: $i] :
( ( ( in @ ( sK25_SY317 @ SV265 @ SV224 @ SV81 ) @ SV224 )
= $true )
| ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2046]) ).
thf(2082,plain,
! [SV266: $i,SV360: $i,SV225: $i,SV381: $i,SV81: $i,SV375: $i] :
( ( ( ~ ( in @ SV375 @ SV81 ) )
= $true )
| ( ( ~ ( in @ SV381 @ SV225 ) )
= $true )
| ( ( ( SV360
!= ( ordered_pair @ SV375 @ SV381 ) ) )
= $true )
| ( ( in @ SV360 @ SV266 )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2083,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 ) ) )
= $true )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2084,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( SV361
= ( ordered_pair @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) ) )
= $true )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2085,plain,
! [SV227: $i,SV269: $i,SV83: $i,SV382: $i] :
( ( ( in @ SV382 @ SV83 )
= $false )
| ( ( in @ SV382 @ SV269 )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2086,plain,
! [SV83: $i,SV269: $i,SV227: $i,SV383: $i] :
( ( ( in @ SV383 @ SV227 )
= $false )
| ( ( in @ SV383 @ SV269 )
= $true )
| ( ( SV269
= ( set_union2 @ SV83 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2087,plain,
! [SV90: $i,SV301: $i,SV392: $i,SV385: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV385 @ SV392 ) @ SV301 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV392 @ SV385 ) @ SV90 )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2088,plain,
! [SV301: $i,SV90: $i,SV386: $i,SV393: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV393 @ SV386 ) @ SV90 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV386 @ SV393 ) @ SV301 )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2089,plain,
! [SV251: $i,SV93: $i,SV276: $i,SV387: $i] :
( ( ( in @ SV387 @ SV276 )
= $false )
| ( ( in @ SV387 @ SV93 )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2090,plain,
! [SV93: $i,SV251: $i,SV276: $i,SV388: $i] :
( ( ( in @ SV388 @ SV276 )
= $false )
| ( ( ~ ( in @ SV388 @ SV251 ) )
= $true )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2091,plain,
! [SV305: $i,SV333: $i] :
( ( ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2092,plain,
! [SV305: $i,SV333: $i] :
( ( ( ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2093,plain,
! [SV333: $i,SV305: $i,SV389: $i] :
( ( ( in @ SV389 @ SV305 )
= $false )
| ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV389 )
= $true )
| ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2094,plain,
! [SV306: $i,SV334: $i,SV390: $i] :
( ( ( ~ ( in @ ( sK43_D @ SV390 @ SV334 @ SV306 ) @ SV306 )
| ~ ~ ( in @ SV390 @ ( sK43_D @ SV390 @ SV334 @ SV306 ) ) )
= $false )
| ( ( in @ SV390 @ SV334 )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2095,plain,
! [SV306: $i,SV334: $i,SV391: $i] :
( ( ( in @ SV391 @ SV334 )
= $false )
| ( ( ! [SY726: $i] :
( ~ ( in @ SY726 @ SV306 )
| ( in @ SV391 @ SY726 ) ) )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2096,plain,
! [SV394: $i,SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SV394 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SV394 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2097,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2098,plain,
! [SV337: $i,SV166: $i,SV77: $i,SV395: $i] :
( ( ( ! [SY727: $i] :
( ! [SY728: $i] :
( ~ ( in @ ( ordered_pair @ SV395 @ SY728 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY728 @ SY727 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SV395 @ SY727 ) @ SV337 ) ) )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2099,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV396: $i] :
( ( ( ! [SY729: $i] :
( ~ ( in @ ( ordered_pair @ SV396 @ SY729 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK9_F @ SY729 @ SV396 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY729 @ SV396 @ SV337 @ SV166 @ SV77 ) @ SY729 ) @ SV166 ) ) ) )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2100,plain,
! [SV369: $i,SV359: $i,SV81: $i,SV224: $i,SV265: $i] :
( ( ( ( sK23_D @ SV265 @ SV224 @ SV81 )
= ( ordered_pair @ SV359 @ SV369 ) )
= $false )
| ( ( in @ SV359 @ SV81 )
= $false )
| ( ( in @ SV369 @ SV224 )
= $false )
| ( ( ~ ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 ) )
= $true )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2101,plain,
! [SV266: $i,SV360: $i,SV225: $i,SV381: $i,SV81: $i,SV375: $i] :
( ( ( in @ SV375 @ SV81 )
= $false )
| ( ( ~ ( in @ SV381 @ SV225 ) )
= $true )
| ( ( ( SV360
!= ( ordered_pair @ SV375 @ SV381 ) ) )
= $true )
| ( ( in @ SV360 @ SV266 )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2102,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
= $false )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2103,plain,
! [SV90: $i,SV301: $i,SV392: $i,SV385: $i] :
( ( ( in @ ( ordered_pair @ SV385 @ SV392 ) @ SV301 )
= $false )
| ( ( in @ ( ordered_pair @ SV392 @ SV385 ) @ SV90 )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2104,plain,
! [SV301: $i,SV90: $i,SV386: $i,SV393: $i] :
( ( ( in @ ( ordered_pair @ SV393 @ SV386 ) @ SV90 )
= $false )
| ( ( in @ ( ordered_pair @ SV386 @ SV393 ) @ SV301 )
= $true )
| ( ( SV301
= ( relation_inverse @ SV90 ) )
= $false )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2105,plain,
! [SV93: $i,SV276: $i,SV251: $i,SV388: $i] :
( ( ( in @ SV388 @ SV251 )
= $false )
| ( ( in @ SV388 @ SV276 )
= $false )
| ( ( SV276
= ( set_difference @ SV93 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2106,plain,
! [SV305: $i,SV333: $i] :
( ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 )
= $false )
| ( ( in @ ( sK45_SY326 @ SV333 @ SV305 ) @ SV305 )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2107,plain,
! [SV305: $i,SV333: $i] :
( ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 ) )
= $true )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2108,plain,
! [SV306: $i,SV334: $i,SV390: $i] :
( ( ( ~ ( in @ ( sK43_D @ SV390 @ SV334 @ SV306 ) @ SV306 ) )
= $false )
| ( ( in @ SV390 @ SV334 )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2109,plain,
! [SV306: $i,SV334: $i,SV390: $i] :
( ( ( ~ ~ ( in @ SV390 @ ( sK43_D @ SV390 @ SV334 @ SV306 ) ) )
= $false )
| ( ( in @ SV390 @ SV334 )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2110,plain,
! [SV334: $i,SV391: $i,SV306: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV306 )
| ( in @ SV391 @ SV397 ) )
= $true )
| ( ( in @ SV391 @ SV334 )
= $false )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2111,plain,
! [SV394: $i,SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SV394 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV394 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2112,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2097]) ).
thf(2113,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2097]) ).
thf(2114,plain,
! [SV337: $i,SV166: $i,SV398: $i,SV77: $i,SV395: $i] :
( ( ( ! [SY730: $i] :
( ~ ( in @ ( ordered_pair @ SV395 @ SY730 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY730 @ SV398 ) @ SV166 ) )
| ( in @ ( ordered_pair @ SV395 @ SV398 ) @ SV337 ) )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2115,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV399: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV396 @ SV399 ) @ SV337 )
| ~ ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) @ SV399 ) @ SV166 ) ) )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2116,plain,
! [SV359: $i,SV369: $i,SV81: $i,SV224: $i,SV265: $i] :
( ( ( in @ ( sK23_D @ SV265 @ SV224 @ SV81 ) @ SV265 )
= $false )
| ( ( in @ SV369 @ SV224 )
= $false )
| ( ( in @ SV359 @ SV81 )
= $false )
| ( ( ( sK23_D @ SV265 @ SV224 @ SV81 )
= ( ordered_pair @ SV359 @ SV369 ) )
= $false )
| ( ( SV265
= ( cartesian_product2 @ SV81 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2117,plain,
! [SV266: $i,SV360: $i,SV81: $i,SV375: $i,SV225: $i,SV381: $i] :
( ( ( in @ SV381 @ SV225 )
= $false )
| ( ( in @ SV375 @ SV81 )
= $false )
| ( ( ( SV360
!= ( ordered_pair @ SV375 @ SV381 ) ) )
= $true )
| ( ( in @ SV360 @ SV266 )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2118,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 ) )
= $false )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2102]) ).
thf(2119,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( ~ ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 ) )
= $false )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2102]) ).
thf(2120,plain,
! [SV305: $i,SV333: $i] :
( ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ SV333 )
= $false )
| ( ( in @ ( sK44_C @ SV333 @ SV305 ) @ ( sK45_SY326 @ SV333 @ SV305 ) )
= $false )
| ( ( SV333
= ( set_meet @ SV305 ) )
= $true )
| ( ( SV305 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2121,plain,
! [SV306: $i,SV334: $i,SV390: $i] :
( ( ( in @ ( sK43_D @ SV390 @ SV334 @ SV306 ) @ SV306 )
= $true )
| ( ( in @ SV390 @ SV334 )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2122,plain,
! [SV306: $i,SV334: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( sK43_D @ SV390 @ SV334 @ SV306 ) ) )
= $true )
| ( ( in @ SV390 @ SV334 )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2109]) ).
thf(2123,plain,
! [SV334: $i,SV391: $i,SV306: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV306 ) )
= $true )
| ( ( in @ SV391 @ SV397 )
= $true )
| ( ( in @ SV391 @ SV334 )
= $false )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2124,plain,
! [SV394: $i,SV77: $i,SV166: $i,SV336: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SV394 ) @ SV77 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV394 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2125,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) ) @ SV77 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2126,plain,
! [SV77: $i,SV166: $i,SV336: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY308 @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2127,plain,
! [SV337: $i,SV166: $i,SV398: $i,SV77: $i,SV395: $i] :
( ( ( ! [SY730: $i] :
( ~ ( in @ ( ordered_pair @ SV395 @ SY730 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY730 @ SV398 ) @ SV166 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV395 @ SV398 ) @ SV337 )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2128,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV399: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV396 @ SV399 ) @ SV337 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) @ SV399 ) @ SV166 ) ) )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2129,plain,
! [SV266: $i,SV225: $i,SV81: $i,SV381: $i,SV375: $i,SV360: $i] :
( ( ( SV360
= ( ordered_pair @ SV375 @ SV381 ) )
= $false )
| ( ( in @ SV375 @ SV81 )
= $false )
| ( ( in @ SV381 @ SV225 )
= $false )
| ( ( in @ SV360 @ SV266 )
= $true )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2130,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( in @ ( sK21_E @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV81 )
= $true )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2118]) ).
thf(2131,plain,
! [SV81: $i,SV225: $i,SV266: $i,SV361: $i] :
( ( ( in @ ( sK22_SY312 @ SV361 @ SV266 @ SV225 @ SV81 ) @ SV225 )
= $true )
| ( ( in @ SV361 @ SV266 )
= $false )
| ( ( SV266
= ( cartesian_product2 @ SV81 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2119]) ).
thf(2132,plain,
! [SV306: $i,SV334: $i,SV390: $i] :
( ( ( in @ SV390 @ ( sK43_D @ SV390 @ SV334 @ SV306 ) )
= $false )
| ( ( in @ SV390 @ SV334 )
= $true )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2133,plain,
! [SV334: $i,SV391: $i,SV306: $i,SV397: $i] :
( ( ( in @ SV397 @ SV306 )
= $false )
| ( ( in @ SV391 @ SV397 )
= $true )
| ( ( in @ SV391 @ SV334 )
= $false )
| ( ( SV334
= ( set_meet @ SV306 ) )
= $false )
| ( ( SV306 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2134,plain,
! [SV77: $i,SV166: $i,SV336: $i,SV394: $i] :
( ( ( in @ ( ordered_pair @ SV394 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SV394 ) @ SV77 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 ) )
= $true )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2135,plain,
! [SV337: $i,SV166: $i,SV398: $i,SV77: $i,SV400: $i,SV395: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV395 @ SV400 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SV400 @ SV398 ) @ SV166 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV395 @ SV398 ) @ SV337 )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2136,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV399: $i,SV396: $i] :
( ( ( in @ ( ordered_pair @ SV396 @ SV399 ) @ SV337 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) @ SV399 ) @ SV166 ) ) )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2137,plain,
! [SV394: $i,SV77: $i,SV166: $i,SV336: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV336 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV336 @ SV166 @ SV77 ) @ SV394 ) @ SV77 )
= $false )
| ( ( in @ ( ordered_pair @ SV394 @ ( sK11_SY304 @ SV336 @ SV166 @ SV77 ) ) @ SV166 )
= $false )
| ( ( SV336
= ( relation_composition @ SV77 @ SV166 ) )
= $true )
| ( ( relation @ SV336 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2138,plain,
! [SV337: $i,SV166: $i,SV398: $i,SV77: $i,SV400: $i,SV395: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV395 @ SV400 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV400 @ SV398 ) @ SV166 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV395 @ SV398 ) @ SV337 )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2139,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV399: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) @ SV399 ) @ SV166 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV396 @ SV399 ) @ SV337 )
= $false )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2140,plain,
! [SV337: $i,SV166: $i,SV398: $i,SV77: $i,SV400: $i,SV395: $i] :
( ( ( in @ ( ordered_pair @ SV395 @ SV400 ) @ SV77 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV400 @ SV398 ) @ SV166 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV395 @ SV398 ) @ SV337 )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2141,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV399: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV396 @ SV399 ) @ SV337 )
= $false )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2142,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV396: $i,SV399: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) @ SV399 ) @ SV166 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV396 @ SV399 ) @ SV337 )
= $false )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2143,plain,
! [SV337: $i,SV77: $i,SV395: $i,SV166: $i,SV398: $i,SV400: $i] :
( ( ( in @ ( ordered_pair @ SV400 @ SV398 ) @ SV166 )
= $false )
| ( ( in @ ( ordered_pair @ SV395 @ SV400 ) @ SV77 )
= $false )
| ( ( in @ ( ordered_pair @ SV395 @ SV398 ) @ SV337 )
= $true )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2144,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV399: $i,SV396: $i] :
( ( ( in @ ( ordered_pair @ SV396 @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) ) @ SV77 )
= $true )
| ( ( in @ ( ordered_pair @ SV396 @ SV399 ) @ SV337 )
= $false )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2145,plain,
! [SV77: $i,SV166: $i,SV337: $i,SV396: $i,SV399: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_F @ SV399 @ SV396 @ SV337 @ SV166 @ SV77 ) @ SV399 ) @ SV166 )
= $true )
| ( ( in @ ( ordered_pair @ SV396 @ SV399 ) @ SV337 )
= $false )
| ( ( SV337
= ( relation_composition @ SV77 @ SV166 ) )
= $false )
| ( ( relation @ SV337 )
= $false )
| ( ( relation @ SV166 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2142]) ).
thf(2146,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[415,2145,2144,2143,2137,2133,2132,2131,2130,2129,2126,2125,2121,2120,2116,2106,2105,2104,2103,2093,2089,2086,2085,2084,2081,2080,2078,2077,2072,2071,2061,2060,2059,2058,2057,2056,2055,2054,2051,2050,2041,2040,2039,2032,2025,2024,2019,2017,2013,2008,1999,1996,1994,1987,1978,1977,1974,1956,1940,1939,1927,1926,1915,1914,1911,1899,1898,1881,1880,1869,1862,1850,1847,1846,1845,1844,1837,1834,1829,1825,1824,1810,1804,1803,1801,1783,1782,1779,1774,1760,1759,1756,1751,1750,1740,1739,1738,1737,1734,1728,1727,1726,1725,1723,1722,1713,1710,1709,1693,1692,1688,1662,1657,1656,1653,1625,1624,1621,1605,1584,1583,1582,1581,1553,1550,1547,1539,1520,1519,1517,1498,1497,1496,1495,1485,1483,1482,1481,1480,1470,1462,1461,1451,1450,1445,1444,1425,1424,1407,1406,1398,1397,1396,1395,1394,1392,1364,1351,1350,1349,1331,1330,1323,1322,1308,1288,1287,1279,1277,1276,1273,1272,1268,1232,1169,1166,1165,1164,1163,1162,1159,1158,1157,1151,1150,1149,1101,1075,1074,1047,1046,1044,1043,1040,1037,1034,1033,1031,1027,1025,1021,1016,975,974,971,970,967,932,931,909,907,886,883,882,877,876,875,869,868,775,773,772,771,770,764,760,757,756,755,749,724,671,670,662,661,660,659,646,640,616,615,614,613,598,542,527,440]) ).
thf(2147,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU188+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 23:14:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.41 ....
% 0.20/0.47
% 0.20/0.47 No.of.Axioms: 169
% 0.20/0.47
% 0.20/0.47 Length.of.Defs: 0
% 0.20/0.47
% 0.20/0.47 Contains.Choice.Funs: false
% 0.35/0.52 ..........
% 0.37/0.56 (rf:2,axioms:129,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:171,loop_count:0,foatp_calls:0,translation:fof_full).................................................................................................................................................................
% 1.10/1.54
% 1.10/1.54 ********************************
% 1.10/1.54 * All subproblems solved! *
% 1.10/1.54 ********************************
% 1.10/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:131,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2146,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.60/2.85
% 2.60/2.85 %**** Beginning of derivation protocol ****
% 2.60/2.85 % SZS output start CNFRefutation
% See solution above
% 2.60/2.86
% 2.60/2.86 %**** End of derivation protocol ****
% 2.60/2.86 %**** no. of clauses in derivation: 2107 ****
% 2.60/2.86 %**** clause counter: 2146 ****
% 2.60/2.86
% 2.60/2.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:131,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2146,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------