TSTP Solution File: SEU189+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU189+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 : n009.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 12:07:54 EDT 2022
% Result : Theorem 1.66s 1.97s
% Output : CNFRefutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 211
% Syntax : Number of formulae : 3971 (1894 unt; 80 typ; 0 def)
% Number of atoms : 29305 (10638 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 64533 (11290 ~;10571 |; 486 &;41903 @)
% ( 101 <=>; 182 =>; 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 : 11842 ( 0 ^11810 !; 32 ?;11842 :)
% 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_SY305,type,
sK11_SY305: $i > $i > $i > $i ).
thf(tp_sK12_SY309,type,
sK12_SY309: $i > $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY310,type,
sK14_SY310: $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_SY312,type,
sK18_SY312: $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_SY313,type,
sK22_SY313: $i > $i > $i > $i > $i ).
thf(tp_sK23_D,type,
sK23_D: $i > $i > $i > $i ).
thf(tp_sK24_SY316,type,
sK24_SY316: $i > $i > $i > $i ).
thf(tp_sK25_SY318,type,
sK25_SY318: $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_SY324,type,
sK38_SY324: $i > $i > $i ).
thf(tp_sK39_D,type,
sK39_D: $i > $i > $i > $i ).
thf(tp_sK3_SY300,type,
sK3_SY300: $i > $i > $i ).
thf(tp_sK40_C,type,
sK40_C: $i > $i > $i ).
thf(tp_sK41_SY326,type,
sK41_SY326: $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_SY327,type,
sK45_SY327: $i > $i > $i ).
thf(tp_sK46_C,type,
sK46_C: $i > $i > $i ).
thf(tp_sK47_SY329,type,
sK47_SY329: $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_SY332,type,
sK50_SY332: $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] :
( ( 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(112,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(113,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(114,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(115,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(118,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(119,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(122,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(123,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(125,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(126,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(127,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(128,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(130,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(131,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(132,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(133,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(134,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(135,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(136,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(137,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(138,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(139,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(140,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(141,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(142,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(143,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(145,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(146,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(147,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(148,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(149,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(150,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(151,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(152,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(153,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(154,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(155,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(156,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(158,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(159,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(160,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(161,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(162,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(163,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(164,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(165,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(166,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(168,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(169,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(170,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(171,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(172,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[171]) ).
thf(173,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[172]) ).
thf(174,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(175,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(176,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(177,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(178,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(179,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(185,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(186,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(187,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(188,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(191,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(192,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(195,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(196,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(197,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(198,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(199,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(200,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(201,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(202,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(203,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(204,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(205,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(206,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(207,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(208,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(209,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(210,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(212,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(213,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(214,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(216,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(217,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(218,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(219,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(220,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(221,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(224,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(225,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(226,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(227,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(228,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)],[118]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(233,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)],[132]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(235,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)],[135]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(237,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(238,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)],[140]) ).
thf(239,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)],[141]) ).
thf(240,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)],[142]) ).
thf(241,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(242,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)],[145]) ).
thf(243,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(244,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)],[151]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(246,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)],[153]) ).
thf(247,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(248,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)],[155]) ).
thf(249,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)],[156]) ).
thf(250,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)],[158]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(252,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)],[160]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(254,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)],[163]) ).
thf(255,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(260,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(261,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(262,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(263,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(264,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(265,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(266,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(267,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(268,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(269,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(270,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(271,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(272,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(274,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(276,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(278,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(279,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(280,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(281,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(282,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(283,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(284,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(285,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(286,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(287,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(288,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)],[122]) ).
thf(289,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)],[125]) ).
thf(290,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)],[127]) ).
thf(291,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)],[128]) ).
thf(292,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(293,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(295,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)],[138]) ).
thf(296,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(297,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)],[146]) ).
thf(298,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(299,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)],[148]) ).
thf(300,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(303,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(304,plain,
( ( ( relation @ sK1_A )
=> ( ( ( relation_dom @ sK1_A )
= empty_set )
<=> ( ( relation_rng @ sK1_A )
= empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(305,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[304]) ).
thf(306,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
<=> ( ( relation_rng @ sK1_A )
= empty_set ) )
= $false ),
inference(standard_cnf,[status(thm)],[304]) ).
thf(307,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
=> ( ( relation_rng @ sK1_A )
= empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[306]) ).
thf(308,plain,
( ( ( ( relation_rng @ sK1_A )
= empty_set )
=> ( ( relation_dom @ sK1_A )
= empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[306]) ).
thf(309,plain,
( ( ~ ( ( ( relation_dom @ sK1_A )
= empty_set )
=> ( ( relation_rng @ sK1_A )
= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[307]) ).
thf(310,plain,
( ( ~ ( ( ( relation_rng @ sK1_A )
= empty_set )
=> ( ( relation_dom @ sK1_A )
= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[308]) ).
thf(311,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
& ( ( relation_rng @ sK1_A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(312,plain,
( ( ( ( relation_rng @ sK1_A )
= empty_set )
& ( ( relation_dom @ sK1_A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[310]) ).
thf(313,plain,
( ( ! [A: $i] :
( ! [SY298: $i] :
( ~ ( subset @ SY298 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY298 @ ( sK2_B @ A ) )
| ( in @ SY298 @ ( sK2_B @ A ) ) )
& ! [SY299: $i] :
( ( ! [SY304: $i] :
( ~ ( subset @ SY304 @ SY299 )
| ( in @ SY304 @ ( sK3_SY300 @ SY299 @ A ) ) )
& ( in @ ( sK3_SY300 @ SY299 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY299 @ ( sK2_B @ A ) ) )
& ! [SY302: $i,SY303: $i] :
( ~ ( in @ SY302 @ ( sK2_B @ A ) )
| ~ ( subset @ SY303 @ SY302 )
| ( in @ SY303 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(314,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(316,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(317,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(318,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)],[179]) ).
thf(319,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)],[180]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(321,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(323,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(324,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(325,plain,
( ( ! [A: $i] :
( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK6_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(326,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(327,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(328,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(329,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(331,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[192]) ).
thf(332,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(333,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)],[198]) ).
thf(334,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY308: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ SY308 ) @ A )
| ~ ( in @ ( ordered_pair @ SY308 @ ( sK11_SY305 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY305 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK12_SY309 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_SY309 @ C @ B @ A ) @ ( sK11_SY305 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY305 @ 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)],[199]) ).
thf(335,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY310 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY310 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ 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)],[200]) ).
thf(336,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)],[202]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY311: $i] :
( ~ ( in @ ( sK17_C @ B @ A ) @ SY311 )
| ~ ( in @ SY311 @ A ) )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK17_C @ B @ A ) @ ( sK18_SY312 @ B @ A ) )
& ( in @ ( sK18_SY312 @ 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)],[203]) ).
thf(338,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)],[204]) ).
thf(339,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)],[205]) ).
thf(340,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY314: $i,SY315: $i] :
( ~ ( in @ SY314 @ A )
| ~ ( in @ SY315 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY314 @ SY315 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY316 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY318 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY316 @ C @ B @ A ) @ ( sK25_SY318 @ 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_SY313 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY313 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[206]) ).
thf(341,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)],[207]) ).
thf(342,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)],[208]) ).
thf(343,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)],[209]) ).
thf(344,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)],[210]) ).
thf(345,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)],[211]) ).
thf(346,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)],[212]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[215]) ).
thf(348,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[216]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[218]) ).
thf(350,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[219]) ).
thf(351,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)],[220]) ).
thf(352,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)],[221]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[223]) ).
thf(354,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)],[225]) ).
thf(355,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[226]) ).
thf(356,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[227]) ).
thf(357,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)],[228]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[230]) ).
thf(359,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[231]) ).
thf(360,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)],[233]) ).
thf(361,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)],[235]) ).
thf(362,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)],[236]) ).
thf(363,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)],[238]) ).
thf(364,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)],[239]) ).
thf(365,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)],[240]) ).
thf(366,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[241]) ).
thf(367,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)],[242]) ).
thf(368,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[243]) ).
thf(369,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)],[244]) ).
thf(370,plain,
( ( ! [A: $i] :
( ! [SY319: $i] :
( ~ ( subset @ SY319 @ ( sK32_B @ A ) )
| ( are_equipotent @ SY319 @ ( sK32_B @ A ) )
| ( in @ SY319 @ ( sK32_B @ A ) ) )
& ! [SY320: $i] :
( ~ ( in @ SY320 @ ( sK32_B @ A ) )
| ( in @ ( powerset @ SY320 ) @ ( sK32_B @ A ) ) )
& ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ ( sK32_B @ A ) )
| ~ ( subset @ SY322 @ SY321 )
| ( in @ SY322 @ ( sK32_B @ A ) ) )
& ( in @ A @ ( sK32_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(371,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(372,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)],[248]) ).
thf(373,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)],[249]) ).
thf(374,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)],[250]) ).
thf(375,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)],[251]) ).
thf(376,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)],[252]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(378,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)],[254]) ).
thf(379,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[255]) ).
thf(380,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)],[256]) ).
thf(381,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[257]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(383,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(384,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[260]) ).
thf(385,plain,
( ( ~ ( empty @ sK34_A )
& ( relation @ sK34_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(386,plain,
( ( ( empty @ sK35_A )
& ( relation @ sK35_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[266]) ).
thf(387,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(388,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(389,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[269]) ).
thf(390,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[270]) ).
thf(391,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[271]) ).
thf(392,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(393,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[275]) ).
thf(394,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(395,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)],[277]) ).
thf(396,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(397,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY323: $i] :
~ ( in @ ( ordered_pair @ SY323 @ ( sK37_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK37_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK38_SY324 @ 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)],[279]) ).
thf(398,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY325: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ SY325 ) @ A )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY326 @ 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)],[280]) ).
thf(399,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)],[281]) ).
thf(400,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK45_SY327 @ B @ A ) @ A )
& ~ ( in @ ( sK44_C @ B @ A ) @ ( sK45_SY327 @ B @ A ) ) )
| ~ ( in @ ( sK44_C @ B @ A ) @ B ) )
& ( ! [SY328: $i] :
( ~ ( in @ SY328 @ A )
| ( in @ ( sK44_C @ B @ A ) @ SY328 ) )
| ( 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)],[282]) ).
thf(401,plain,
( ( ! [A: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ( sK48_B @ A )
!= ( ordered_pair @ SY330 @ SY331 ) )
& ( in @ ( sK48_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK46_C @ B @ A ) @ ( sK47_SY329 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[283]) ).
thf(402,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[284]) ).
thf(403,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( A = empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(404,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK49_B @ A ) @ ( sK50_SY332 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(405,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)],[288]) ).
thf(406,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)],[289]) ).
thf(407,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)],[290]) ).
thf(408,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)],[291]) ).
thf(409,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[292]) ).
thf(410,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)],[293]) ).
thf(411,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)],[294]) ).
thf(412,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)],[295]) ).
thf(413,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)],[297]) ).
thf(414,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[298]) ).
thf(415,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)],[299]) ).
thf(416,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)],[301]) ).
thf(417,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)],[302]) ).
thf(418,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[303]) ).
thf(419,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(420,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)],[417]) ).
thf(421,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)],[416]) ).
thf(422,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(423,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)],[415]) ).
thf(424,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(425,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)],[413]) ).
thf(426,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(427,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)],[412]) ).
thf(428,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)],[411]) ).
thf(429,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)],[410]) ).
thf(430,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(431,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(432,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(433,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)],[406]) ).
thf(434,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)],[405]) ).
thf(435,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK49_B @ A ) @ ( sK50_SY332 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(436,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(437,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( A = empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(438,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(439,plain,
( ( ! [A: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ( sK48_B @ A )
!= ( ordered_pair @ SY330 @ SY331 ) )
& ( in @ ( sK48_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK46_C @ B @ A ) @ ( sK47_SY329 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(440,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK45_SY327 @ B @ A ) @ A )
& ~ ( in @ ( sK44_C @ B @ A ) @ ( sK45_SY327 @ B @ A ) ) )
| ~ ( in @ ( sK44_C @ B @ A ) @ B ) )
& ( ! [SY328: $i] :
( ~ ( in @ SY328 @ A )
| ( in @ ( sK44_C @ B @ A ) @ SY328 ) )
| ( 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)],[400]) ).
thf(441,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)],[399]) ).
thf(442,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY325: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ SY325 ) @ A )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY326 @ 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)],[398]) ).
thf(443,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY323: $i] :
~ ( in @ ( ordered_pair @ SY323 @ ( sK37_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK37_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK38_SY324 @ 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)],[397]) ).
thf(444,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(445,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)],[395]) ).
thf(446,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(448,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(449,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(450,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(451,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(452,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(453,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(454,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(455,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(456,plain,
( ( ( empty @ sK35_A )
& ( relation @ sK35_A ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(457,plain,
( ( ~ ( empty @ sK34_A )
& ( relation @ sK34_A ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(458,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(459,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(460,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(461,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(462,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(463,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(466,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)],[380]) ).
thf(467,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(468,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)],[378]) ).
thf(469,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(470,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)],[376]) ).
thf(471,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)],[375]) ).
thf(472,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)],[374]) ).
thf(473,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)],[373]) ).
thf(474,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)],[372]) ).
thf(475,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(476,plain,
( ( ! [A: $i] :
( ! [SY319: $i] :
( ~ ( subset @ SY319 @ ( sK32_B @ A ) )
| ( are_equipotent @ SY319 @ ( sK32_B @ A ) )
| ( in @ SY319 @ ( sK32_B @ A ) ) )
& ! [SY320: $i] :
( ~ ( in @ SY320 @ ( sK32_B @ A ) )
| ( in @ ( powerset @ SY320 ) @ ( sK32_B @ A ) ) )
& ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ ( sK32_B @ A ) )
| ~ ( subset @ SY322 @ SY321 )
| ( in @ SY322 @ ( sK32_B @ A ) ) )
& ( in @ A @ ( sK32_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(477,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(478,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(479,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(481,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(482,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)],[365]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(484,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)],[363]) ).
thf(485,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(486,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)],[362]) ).
thf(487,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)],[361]) ).
thf(488,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(489,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)],[360]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(491,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(494,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)],[357]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(496,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(497,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)],[354]) ).
thf(498,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(500,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(501,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)],[352]) ).
thf(502,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(503,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(504,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(505,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(506,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(507,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(508,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(509,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(510,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)],[346]) ).
thf(511,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)],[345]) ).
thf(512,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)],[344]) ).
thf(513,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)],[343]) ).
thf(514,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)],[342]) ).
thf(515,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)],[341]) ).
thf(516,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY314: $i,SY315: $i] :
( ~ ( in @ SY314 @ A )
| ~ ( in @ SY315 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY314 @ SY315 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY316 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY318 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY316 @ C @ B @ A ) @ ( sK25_SY318 @ 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_SY313 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY313 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(517,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)],[339]) ).
thf(518,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)],[338]) ).
thf(519,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY311: $i] :
( ~ ( in @ ( sK17_C @ B @ A ) @ SY311 )
| ~ ( in @ SY311 @ A ) )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK17_C @ B @ A ) @ ( sK18_SY312 @ B @ A ) )
& ( in @ ( sK18_SY312 @ 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)],[337]) ).
thf(520,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)],[336]) ).
thf(521,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(522,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY310 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY310 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ 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)],[335]) ).
thf(523,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY308: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ SY308 ) @ A )
| ~ ( in @ ( ordered_pair @ SY308 @ ( sK11_SY305 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY305 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK12_SY309 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_SY309 @ C @ B @ A ) @ ( sK11_SY305 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY305 @ 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)],[334]) ).
thf(524,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)],[333]) ).
thf(525,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(526,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(527,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(528,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(529,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(530,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(532,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(533,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(534,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(535,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(536,plain,
( ( ! [A: $i] :
( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK6_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(537,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(538,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(542,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)],[319]) ).
thf(543,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)],[318]) ).
thf(544,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(545,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(546,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(547,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(548,plain,
( ( ! [A: $i] :
( ! [SY298: $i] :
( ~ ( subset @ SY298 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY298 @ ( sK2_B @ A ) )
| ( in @ SY298 @ ( sK2_B @ A ) ) )
& ! [SY299: $i] :
( ( ! [SY304: $i] :
( ~ ( subset @ SY304 @ SY299 )
| ( in @ SY304 @ ( sK3_SY300 @ SY299 @ A ) ) )
& ( in @ ( sK3_SY300 @ SY299 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY299 @ ( sK2_B @ A ) ) )
& ! [SY302: $i,SY303: $i] :
( ~ ( in @ SY302 @ ( sK2_B @ A ) )
| ~ ( subset @ SY303 @ SY302 )
| ( in @ SY303 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(549,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(550,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
& ( ( relation_rng @ sK1_A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(551,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)],[486]) ).
thf(552,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)],[510]) ).
thf(553,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)],[524]) ).
thf(554,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)],[494]) ).
thf(555,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)],[471]) ).
thf(556,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)],[472]) ).
thf(557,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)],[473]) ).
thf(558,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(559,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(560,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)],[501]) ).
thf(561,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)],[423]) ).
thf(562,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(563,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)],[542]) ).
thf(564,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)],[515]) ).
thf(565,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)],[489]) ).
thf(566,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)],[520]) ).
thf(567,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)],[428]) ).
thf(568,plain,
( ( ~ ( ~ ~ ( empty @ sK34_A )
| ~ ( relation @ sK34_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(569,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)],[517]) ).
thf(570,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)],[518]) ).
thf(571,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)],[420]) ).
thf(572,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)],[476]) ).
thf(573,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)],[470]) ).
thf(574,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)],[511]) ).
thf(575,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_SY312 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY312 @ 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)],[519]) ).
thf(576,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(577,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)],[429]) ).
thf(578,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_SY300 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK3_SY300 @ 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)],[548]) ).
thf(579,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)],[427]) ).
thf(580,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_SY316 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_SY318 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK24_SY316 @ SX2 @ SX1 @ SX0 ) @ ( sK25_SY318 @ 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_SY313 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY313 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(581,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_SY326 @ 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)],[442]) ).
thf(582,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK6_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK6_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(583,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)],[466]) ).
thf(584,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)],[445]) ).
thf(585,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_SY324 @ 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)],[443]) ).
thf(586,plain,
( ( ~ ( ~ ( empty @ sK35_A )
| ~ ( relation @ sK35_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(587,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[440]) ).
thf(588,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)],[514]) ).
thf(589,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)],[497]) ).
thf(590,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)],[513]) ).
thf(591,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_SY305 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY305 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY309 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY305 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY305 @ 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)],[523]) ).
thf(592,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(593,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)],[512]) ).
thf(594,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY310 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY310 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ 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)],[522]) ).
thf(595,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)],[421]) ).
thf(596,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)],[543]) ).
thf(597,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(598,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)],[487]) ).
thf(599,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)],[482]) ).
thf(600,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)],[441]) ).
thf(601,plain,
( ( ~ ( ( ( relation_dom @ sK1_A )
!= empty_set )
| ~ ( ( ( relation_rng @ sK1_A )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(602,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)],[484]) ).
thf(603,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)],[425]) ).
thf(604,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_SY329 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(605,plain,
! [SV1: $i] :
( ( ( ( singleton @ SV1 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(606,plain,
! [SV2: $i] :
( ( ~ ( relation @ SV2 )
| ( subset @ SV2 @ ( cartesian_product2 @ ( relation_dom @ SV2 ) @ ( relation_rng @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(607,plain,
! [SV3: $i] :
( ( subset @ empty_set @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(608,plain,
! [SV4: $i] :
( ( ~ ( subset @ SV4 @ empty_set )
| ( SV4 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(609,plain,
! [SV5: $i] :
( ( ~ ( relation @ SV5 )
| ! [SY333: $i] :
( ~ ( relation @ SY333 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SY333 ) ) @ ( relation_dom @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(610,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ! [SY334: $i] :
( ~ ( relation @ SY334 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SY334 ) ) @ ( relation_rng @ SY334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(611,plain,
! [SV7: $i] :
( ( ~ ( relation @ SV7 )
| ! [SY335: $i] :
( ~ ( relation @ SY335 )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SY335 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SY335 ) )
= ( relation_dom @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(612,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ! [SY336: $i] :
( ~ ( relation @ SY336 )
| ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SY336 ) )
| ( ( relation_rng @ ( relation_composition @ SY336 @ SV8 ) )
= ( relation_rng @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(613,plain,
! [SV9: $i] :
( ( ~ ( relation @ SV9 )
| ( in @ ( ordered_pair @ ( sK49_B @ SV9 ) @ ( sK50_SY332 @ SV9 ) ) @ SV9 )
| ( SV9 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(614,plain,
! [SV10: $i] :
( ( ~ ( empty @ SV10 )
| ( relation @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(615,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(616,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ( relation @ ( relation_inverse @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(617,plain,
! [SV13: $i] :
( ( ! [SY337: $i] :
( ~ ( relation @ SV13 )
| ~ ( relation @ SY337 )
| ( relation @ ( relation_composition @ SV13 @ SY337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(618,plain,
! [SV14: $i] :
( ( ! [SY338: $i] :
( ~ ( relation @ SV14 )
| ~ ( relation @ SY338 )
| ( relation @ ( set_union2 @ SV14 @ SY338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(619,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
| ~ ( relation @ SV15 )
| ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(620,plain,
! [SV16: $i] :
( ( ( empty @ SV16 )
| ~ ( relation @ SV16 )
| ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(621,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(622,plain,
! [SV18: $i] :
( ( ( set_union2 @ SV18 @ empty_set )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(623,plain,
! [SV19: $i] :
( ( ( set_intersection2 @ SV19 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(624,plain,
! [SV20: $i] :
( ( ( set_difference @ SV20 @ empty_set )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(625,plain,
! [SV21: $i] :
( ( ( set_difference @ empty_set @ SV21 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(626,plain,
! [SV22: $i] :
( ( ~ ( empty @ SV22 )
| ( SV22 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(627,plain,
! [SV23: $i] :
( ( ! [SY339: $i] :
( ~ ( in @ SV23 @ SY339 )
| ( ( set_union2 @ ( singleton @ SV23 ) @ SY339 )
= SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(628,plain,
! [SV24: $i] :
( ( ! [SY340: $i] :
( ~ ( disjoint @ ( singleton @ SV24 ) @ SY340 )
| ~ ( in @ SV24 @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(629,plain,
! [SV25: $i] :
( ( ! [SY341: $i] :
( ( in @ SV25 @ SY341 )
| ( disjoint @ ( singleton @ SV25 ) @ SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(630,plain,
! [SV26: $i] :
( ( ! [SY342: $i] :
( ~ ( element @ SY342 @ ( powerset @ SV26 ) )
| ! [SY343: $i] :
( ~ ( in @ SY343 @ SY342 )
| ( in @ SY343 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(631,plain,
! [SV27: $i] :
( ( ! [SY344: $i] :
( ~ ( subset @ SV27 @ SY344 )
| ! [SY345: $i] :
( ( in @ SY345 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SY344 @ ( singleton @ SY345 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(632,plain,
! [SV28: $i] :
( ( ! [SY346: $i] :
( ~ ( in @ SV28 @ SY346 )
| ( subset @ SV28 @ ( union @ SY346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(633,plain,
! [SV29: $i] :
( ( ! [SY347: $i,SY348: $i,SY349: $i] :
( ~ ( subset @ SV29 @ SY347 )
| ~ ( subset @ SY348 @ SY349 )
| ( subset @ ( cartesian_product2 @ SV29 @ SY348 ) @ ( cartesian_product2 @ SY347 @ SY349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(634,plain,
! [SV30: $i] :
( ( ! [SY350: $i] :
( ~ ( subset @ SV30 @ SY350 )
| ( ( set_union2 @ SV30 @ SY350 )
= SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(635,plain,
! [SV31: $i] :
( ( ! [SY351: $i] : ( subset @ ( set_intersection2 @ SV31 @ SY351 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(636,plain,
! [SV32: $i] :
( ( ! [SY352: $i,SY353: $i] :
( ~ ( subset @ SV32 @ SY352 )
| ~ ( subset @ SV32 @ SY353 )
| ( subset @ SV32 @ ( set_intersection2 @ SY352 @ SY353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(637,plain,
! [SV33: $i] :
( ( ! [SY354: $i,SY355: $i] :
( ~ ( subset @ SV33 @ SY354 )
| ~ ( subset @ SY354 @ SY355 )
| ( subset @ SV33 @ SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(638,plain,
! [SV34: $i] :
( ( ! [SY356: $i] :
( ~ ( subset @ SV34 @ SY356 )
| ! [SY357: $i] : ( subset @ ( set_intersection2 @ SV34 @ SY357 ) @ ( set_intersection2 @ SY356 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(639,plain,
! [SV35: $i] :
( ( ! [SY358: $i] :
( ~ ( subset @ SV35 @ SY358 )
| ( ( set_intersection2 @ SV35 @ SY358 )
= SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(640,plain,
! [SV36: $i] :
( ( ! [SY359: $i] :
( ~ ( subset @ SV36 @ SY359 )
| ! [SY360: $i] : ( subset @ ( set_difference @ SV36 @ SY360 ) @ ( set_difference @ SY359 @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(641,plain,
! [SV37: $i] :
( ( ! [SY361: $i] : ( subset @ ( set_difference @ SV37 @ SY361 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(642,plain,
! [SV38: $i] :
( ( ! [SY362: $i] :
( ( set_union2 @ SV38 @ ( set_difference @ SY362 @ SV38 ) )
= ( set_union2 @ SV38 @ SY362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(643,plain,
! [SV39: $i] :
( ( ! [SY363: $i] :
( ( set_difference @ ( set_union2 @ SV39 @ SY363 ) @ SY363 )
= ( set_difference @ SV39 @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(644,plain,
! [SV40: $i] :
( ( ! [SY364: $i] :
( ~ ( subset @ SV40 @ SY364 )
| ( SY364
= ( set_union2 @ SV40 @ ( set_difference @ SY364 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(645,plain,
! [SV41: $i] :
( ( ! [SY365: $i] :
( ~ ( in @ SV41 @ SY365 )
| ( ( set_union2 @ ( singleton @ SV41 ) @ SY365 )
= SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(646,plain,
! [SV42: $i] :
( ( ! [SY366: $i] :
( ( set_difference @ SV42 @ ( set_difference @ SV42 @ SY366 ) )
= ( set_intersection2 @ SV42 @ SY366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(647,plain,
! [SV43: $i] :
( ( ! [SY367: $i] :
( ~ ( proper_subset @ SY367 @ SV43 )
| ~ ( subset @ SV43 @ SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(648,plain,
! [SV44: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ~ ( disjoint @ SY368 @ SY369 )
| ~ ( subset @ SV44 @ SY368 )
| ( disjoint @ SV44 @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(649,plain,
! [SV45: $i] :
( ( ( unordered_pair @ SV45 @ SV45 )
= ( singleton @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(650,plain,
! [SV46: $i] :
( ( ! [SY370: $i] :
( ~ ( subset @ ( singleton @ SV46 ) @ ( singleton @ SY370 ) )
| ( SV46 = SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(651,plain,
! [SV47: $i] :
( ( ! [SY371: $i] : ( subset @ SV47 @ ( set_union2 @ SV47 @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(652,plain,
! [SV48: $i] :
( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SV48 @ SY372 )
| ~ ( subset @ SY373 @ SY372 )
| ( subset @ ( set_union2 @ SV48 @ SY373 ) @ SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(653,plain,
! [SV49: $i] :
( ( ! [SY374: $i] :
( ! [SY375: $i] :
( ( singleton @ SV49 )
!= ( unordered_pair @ SY374 @ SY375 ) )
| ( SV49 = SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(654,plain,
! [SV50: $i] :
( ( ! [SY376: $i] :
( ~ ( in @ SV50 @ SY376 )
| ( subset @ SV50 @ ( union @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(655,plain,
! [SV51: $i] :
( ( ( union @ ( powerset @ SV51 ) )
= SV51 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(656,plain,
! [SV52: $i] :
( ( ! [SY377: $i,SY378: $i] :
( ( ( singleton @ SV52 )
!= ( unordered_pair @ SY377 @ SY378 ) )
| ( SY377 = SY378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(657,plain,
! [SV53: $i] :
( ( ! [SY379: $i] :
( ~ ( in @ SV53 @ SY379 )
| ~ ( in @ SY379 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(658,plain,
! [SV54: $i] :
( ( ! [SY380: $i] :
( ( set_union2 @ SV54 @ SY380 )
= ( set_union2 @ SY380 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(659,plain,
! [SV55: $i] :
( ( ! [SY381: $i] :
( ( set_intersection2 @ SV55 @ SY381 )
= ( set_intersection2 @ SY381 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(660,plain,
! [SV56: $i] :
( ( ! [SY382: $i] :
( ( ordered_pair @ SV56 @ SY382 )
= ( unordered_pair @ ( unordered_pair @ SV56 @ SY382 ) @ ( singleton @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(661,plain,
! [SV57: $i] :
( ( ~ ( empty @ ( powerset @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(662,plain,
! [SV58: $i] :
( ( ! [SY383: $i] :
~ ( empty @ ( ordered_pair @ SV58 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(663,plain,
! [SV59: $i] :
( ( ~ ( empty @ ( singleton @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(664,plain,
! [SV60: $i] :
( ( ( empty @ SV60 )
| ! [SY384: $i] :
~ ( empty @ ( set_union2 @ SV60 @ SY384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(665,plain,
! [SV61: $i] :
( ( ! [SY385: $i] :
~ ( empty @ ( unordered_pair @ SV61 @ SY385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(666,plain,
! [SV62: $i] :
( ( ( empty @ SV62 )
| ! [SY386: $i] :
~ ( empty @ ( set_union2 @ SY386 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(667,plain,
! [SV63: $i] :
( ( ! [SY387: $i] :
( ( empty @ SV63 )
| ( empty @ SY387 )
| ~ ( empty @ ( cartesian_product2 @ SV63 @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(668,plain,
! [SV64: $i] :
( ( ( set_union2 @ SV64 @ SV64 )
= SV64 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(669,plain,
! [SV65: $i] :
( ( ( set_intersection2 @ SV65 @ SV65 )
= SV65 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(670,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(671,plain,
! [SV66: $i] :
( ( subset @ SV66 @ SV66 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(672,plain,
! [SV67: $i] :
( ( ! [SY388: $i] :
( ~ ( disjoint @ SV67 @ SY388 )
| ( disjoint @ SY388 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(673,plain,
! [SV68: $i] :
( ( ! [SY389: $i] :
( ~ ( in @ SV68 @ SY389 )
| ( element @ SV68 @ SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(674,plain,
! [SV69: $i] :
( ( ! [SY390: $i] :
( ~ ( element @ SV69 @ SY390 )
| ( empty @ SY390 )
| ( in @ SV69 @ SY390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(675,plain,
! [SV70: $i] :
( ( ! [SY391: $i,SY392: $i] :
( ~ ( element @ SY391 @ ( powerset @ SY392 ) )
| ~ ( in @ SV70 @ SY391 )
| ( element @ SV70 @ SY392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(676,plain,
! [SV71: $i] :
( ( ! [SY393: $i,SY394: $i] :
( ~ ( element @ SY393 @ ( powerset @ SY394 ) )
| ~ ( in @ SV71 @ SY393 )
| ~ ( empty @ SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(677,plain,
! [SV72: $i] :
( ( ! [SY395: $i] :
( ~ ( empty @ SY395 )
| ~ ( in @ SV72 @ SY395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(678,plain,
! [SV73: $i] :
( ( ! [SY396: $i] :
( ( SV73 = SY396 )
| ~ ( empty @ SV73 )
| ~ ( empty @ SY396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(679,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)],[551]) ).
thf(680,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)],[552]) ).
thf(681,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)],[553]) ).
thf(682,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)],[554]) ).
thf(683,plain,
! [SV74: $i] :
( ( ! [SY397: $i] :
( ~ ( ~ ( in @ ( sK33_C @ SY397 @ SV74 ) @ SV74 )
| ~ ~ ( in @ ( sK33_C @ SY397 @ SV74 ) @ SY397 ) )
| ( element @ SV74 @ ( powerset @ SY397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(684,plain,
! [SV75: $i] :
( ( ! [SY398: $i] :
~ ( ~ ! [SY399: $i,SY400: $i] :
( ~ ( in @ SV75 @ SY399 )
| ~ ( in @ SY398 @ SY400 )
| ( in @ ( ordered_pair @ SV75 @ SY398 ) @ ( cartesian_product2 @ SY399 @ SY400 ) ) )
| ~ ~ ( ~ ! [SY401: $i] :
( ! [SY402: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SY398 ) @ ( cartesian_product2 @ SY401 @ SY402 ) )
| ( in @ SV75 @ SY401 ) )
| ~ ! [SY403: $i,SY404: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SY398 ) @ ( cartesian_product2 @ SY403 @ SY404 ) )
| ( in @ SY398 @ SY404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(685,plain,
! [SV76: $i] :
( ( ~ ( ~ ! [SY405: $i] :
( ~ ( subset @ SV76 @ SY405 )
| ! [SY406: $i] : ( subset @ ( cartesian_product2 @ SV76 @ SY406 ) @ ( cartesian_product2 @ SY405 @ SY406 ) ) )
| ~ ! [SY407: $i] :
( ~ ( subset @ SV76 @ SY407 )
| ! [SY408: $i] : ( subset @ ( cartesian_product2 @ SY408 @ SV76 ) @ ( cartesian_product2 @ SY408 @ SY407 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(686,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(687,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(688,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)],[560]) ).
thf(689,plain,
! [SV77: $i] :
( ( ~ ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( in @ ( ordered_pair @ SV77 @ SY409 ) @ SY410 )
| ( in @ SV77 @ ( relation_dom @ SY410 ) ) )
| ~ ! [SY411: $i,SY412: $i] :
( ~ ( relation @ SY412 )
| ~ ( in @ ( ordered_pair @ SV77 @ SY411 ) @ SY412 )
| ( in @ SY411 @ ( relation_rng @ SY412 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(690,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(691,plain,
! [SV78: $i] :
( ( ! [SY413: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_C @ SY413 @ SV78 ) @ SV78 )
| ~ ( in @ ( sK4_C @ SY413 @ SV78 ) @ SY413 ) )
| ~ ( ( in @ ( sK4_C @ SY413 @ SV78 ) @ SV78 )
| ( in @ ( sK4_C @ SY413 @ SV78 ) @ SY413 ) ) )
| ( SV78 = SY413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(692,plain,
! [SV79: $i] :
( ( ~ ( ~ ! [SY414: $i,SY415: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY414 ) ) )
| ~ ( ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY414 ) ) )
| ( SY415
= ( set_union2 @ SV79 @ SY414 ) ) )
| ~ ! [SY416: $i,SY417: $i] :
( ( SY417
!= ( set_union2 @ SV79 @ SY416 ) )
| ~ ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SY417 )
| ( in @ SY418 @ SV79 )
| ( in @ SY418 @ SY416 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV79 )
| ( in @ SY419 @ SY417 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY416 )
| ( in @ SX3 @ SY417 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(693,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)],[565]) ).
thf(694,plain,
! [SV80: $i] :
( ( ~ ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY421 )
| ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY421 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) ) ) )
| ( SY422
= ( set_difference @ SV80 @ SY421 ) ) )
| ~ ! [SY423: $i,SY424: $i] :
( ( SY424
!= ( set_difference @ SV80 @ SY423 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV80 )
| ( in @ SY425 @ SY423 )
| ( in @ SY425 @ SY424 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY424 )
| ( in @ SY426 @ SV80 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY424 )
| ~ ( in @ SX3 @ SY423 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(695,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)],[567]) ).
thf(696,plain,
( ( ~ ~ ( empty @ sK34_A )
| ~ ( relation @ sK34_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(697,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)],[569]) ).
thf(698,plain,
! [SV81: $i] :
( ( ~ ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY428 )
| ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) )
| ~ ( ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY428 )
| ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) ) ) )
| ( SY429
= ( set_intersection2 @ SV81 @ SY428 ) ) )
| ~ ! [SY430: $i,SY431: $i] :
( ( SY431
!= ( set_intersection2 @ SV81 @ SY430 ) )
| ~ ( ~ ! [SY432: $i] :
( ~ ( in @ SY432 @ SV81 )
| ~ ( in @ SY432 @ SY430 )
| ( in @ SY432 @ SY431 ) )
| ~ ~ ( ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SY431 )
| ( in @ SY433 @ SV81 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY431 )
| ( in @ SX3 @ SY430 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(699,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)],[571]) ).
thf(700,plain,
! [SV82: $i] :
( ( ~ ( ~ ! [SY435: $i] :
( ~ ( subset @ SY435 @ ( sK32_B @ SV82 ) )
| ( are_equipotent @ SY435 @ ( sK32_B @ SV82 ) )
| ( in @ SY435 @ ( sK32_B @ SV82 ) ) )
| ~ ~ ( ~ ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK32_B @ SV82 ) )
| ( in @ ( powerset @ SY436 ) @ ( sK32_B @ SV82 ) ) )
| ~ ~ ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) )
| ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(701,plain,
! [SV83: $i] :
( ( ! [SY439: $i] :
~ ( ~ ! [SY440: $i,SY441: $i] :
( ~ ( in @ SV83 @ SY440 )
| ~ ( in @ SY439 @ SY441 )
| ( in @ ( ordered_pair @ SV83 @ SY439 ) @ ( cartesian_product2 @ SY440 @ SY441 ) ) )
| ~ ~ ( ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SY439 ) @ ( cartesian_product2 @ SY442 @ SY443 ) )
| ( in @ SV83 @ SY442 ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SY439 ) @ ( cartesian_product2 @ SY444 @ SY445 ) )
| ( in @ SY439 @ SY445 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(702,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)],[574]) ).
thf(703,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_SY312 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY312 @ 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)],[575]) ).
thf(704,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(705,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)],[577]) ).
thf(706,plain,
! [SV84: $i] :
( ( ~ ( ~ ! [SY446: $i] :
( ~ ( subset @ SY446 @ ( sK2_B @ SV84 ) )
| ( are_equipotent @ SY446 @ ( sK2_B @ SV84 ) )
| ( in @ SY446 @ ( sK2_B @ SV84 ) ) )
| ~ ~ ( ~ ! [SY447: $i] :
( ~ ( ~ ! [SY448: $i] :
( ~ ( subset @ SY448 @ SY447 )
| ( in @ SY448 @ ( sK3_SY300 @ SY447 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY447 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SY447 @ ( sK2_B @ SV84 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(707,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)],[579]) ).
thf(708,plain,
! [SV85: $i] :
( ( ~ ( ~ ! [SY451: $i,SY452: $i] :
( ~ ( ~ ( ! [SY453: $i,SY454: $i] :
( ~ ( in @ SY453 @ SV85 )
| ~ ( in @ SY454 @ SY451 )
| ( ( sK23_D @ SY452 @ SY451 @ SV85 )
!= ( ordered_pair @ SY453 @ SY454 ) ) )
| ~ ( in @ ( sK23_D @ SY452 @ SY451 @ SV85 ) @ SY452 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY452 @ SY451 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SY452 @ SY451 @ SV85 ) @ SY451 ) )
| ( ( sK23_D @ SY452 @ SY451 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SY452 @ SY451 @ SV85 ) @ ( sK25_SY318 @ SY452 @ SY451 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SY452 @ SY451 @ SV85 ) @ SY452 ) ) )
| ( SY452
= ( cartesian_product2 @ SV85 @ SY451 ) ) )
| ~ ! [SY455: $i,SY456: $i] :
( ( SY456
!= ( cartesian_product2 @ SV85 @ SY455 ) )
| ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i,SY459: $i] :
( ~ ( in @ SY458 @ SV85 )
| ~ ( in @ SY459 @ SY455 )
| ( SY457
!= ( ordered_pair @ SY458 @ SY459 ) ) )
| ( in @ SY457 @ SY456 ) )
| ~ ! [SY460: $i] :
( ~ ( in @ SY460 @ SY456 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY460 @ SY456 @ SY455 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY460 @ SY456 @ SY455 @ SV85 ) @ SY455 ) )
| ( SY460
!= ( ordered_pair @ ( sK21_E @ SY460 @ SY456 @ SY455 @ SV85 ) @ ( sK22_SY313 @ SY460 @ SY456 @ SY455 @ SV85 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(709,plain,
! [SV86: $i] :
( ( ~ ( relation @ SV86 )
| ~ ( ~ ! [SY461: $i] :
( ~ ( ~ ( ! [SY462: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ SY462 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ ( sK41_SY326 @ SY461 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) ) )
| ( SY461
= ( relation_dom @ SV86 ) ) )
| ~ ! [SY463: $i] :
( ( SY463
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY464: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY464 @ SY465 ) @ SV86 )
| ( in @ SY464 @ SY463 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SY463 )
| ( in @ ( ordered_pair @ SY466 @ ( sK39_D @ SY466 @ SY463 @ SV86 ) ) @ SV86 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(710,plain,
! [SV87: $i] :
( ( ~ ( ~ ( element @ ( sK6_B @ SV87 ) @ ( powerset @ SV87 ) )
| ~ ( empty @ ( sK6_B @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(711,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)],[583]) ).
thf(712,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)],[584]) ).
thf(713,plain,
! [SV88: $i] :
( ( ~ ( relation @ SV88 )
| ~ ( ~ ! [SY467: $i] :
( ~ ( ~ ( ! [SY468: $i] :
~ ( in @ ( ordered_pair @ SY468 @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY467 @ SV88 ) @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) ) )
| ( SY467
= ( relation_rng @ SV88 ) ) )
| ~ ! [SY469: $i] :
( ( SY469
!= ( relation_rng @ SV88 ) )
| ~ ( ~ ! [SY470: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY470 ) @ SV88 )
| ( in @ SY470 @ SY469 ) )
| ~ ! [SY472: $i] :
( ~ ( in @ SY472 @ SY469 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY472 @ SY469 @ SV88 ) @ SY472 ) @ SV88 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(714,plain,
( ( ~ ( empty @ sK35_A )
| ~ ( relation @ sK35_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(715,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[587]) ).
thf(716,plain,
! [SV89: $i] :
( ( ~ ( ~ ! [SY473: $i,SY474: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
!= SY473 ) ) )
| ~ ( ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
= SV89 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
= SY473 ) ) )
| ( SY474
= ( unordered_pair @ SV89 @ SY473 ) ) )
| ~ ! [SY475: $i,SY476: $i] :
( ( SY476
!= ( unordered_pair @ SV89 @ SY475 ) )
| ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY476 )
| ( SY477 = SV89 )
| ( SY477 = SY475 ) )
| ~ ~ ( ~ ! [SY478: $i] :
( ( SY478 != SV89 )
| ( in @ SY478 @ SY476 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY475 )
| ( in @ SX3 @ SY476 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(717,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)],[589]) ).
thf(718,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)],[590]) ).
thf(719,plain,
! [SV90: $i] :
( ( ~ ( relation @ SV90 )
| ! [SY480: $i] :
( ~ ( relation @ SY480 )
| ~ ( ~ ! [SY481: $i] :
( ~ ( relation @ SY481 )
| ~ ( ~ ( ! [SY482: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ SY482 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY482 @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY480 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY481 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK12_SY309 @ SY481 @ SY480 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY480 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY481 ) ) )
| ( SY481
= ( relation_composition @ SV90 @ SY480 ) ) )
| ~ ! [SY483: $i] :
( ~ ( relation @ SY483 )
| ( SY483
!= ( relation_composition @ SV90 @ SY480 ) )
| ~ ( ~ ! [SY484: $i,SY485: $i] :
( ! [SY486: $i] :
( ~ ( in @ ( ordered_pair @ SY484 @ SY486 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY486 @ SY485 ) @ SY480 ) )
| ( in @ ( ordered_pair @ SY484 @ SY485 ) @ SY483 ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ( in @ ( ordered_pair @ SY487 @ SY488 ) @ SY483 )
| ~ ( ~ ( in @ ( ordered_pair @ SY487 @ ( sK9_F @ SY488 @ SY487 @ SY483 @ SY480 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY488 @ SY487 @ SY483 @ SY480 @ SV90 ) @ SY488 ) @ SY480 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(720,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(721,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)],[593]) ).
thf(722,plain,
! [SV91: $i] :
( ( ~ ( relation @ SV91 )
| ~ ( ~ ! [SY489: $i] :
( ~ ( relation @ SY489 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) ) )
| ( SY489
= ( relation_inverse @ SV91 ) ) )
| ~ ! [SY490: $i] :
( ~ ( relation @ SY490 )
| ( SY490
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ ( ordered_pair @ SY491 @ SY492 ) @ SY490 )
| ( in @ ( ordered_pair @ SY492 @ SY491 ) @ SV91 ) )
| ~ ! [SY493: $i,SY494: $i] :
( ~ ( in @ ( ordered_pair @ SY494 @ SY493 ) @ SV91 )
| ( in @ ( ordered_pair @ SY493 @ SY494 ) @ SY490 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(723,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)],[595]) ).
thf(724,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)],[596]) ).
thf(725,plain,
! [SV92: $i] :
( ( ( empty @ SV92 )
| ~ ( ~ ( element @ ( sK8_B @ SV92 ) @ ( powerset @ SV92 ) )
| ~ ~ ( empty @ ( sK8_B @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(726,plain,
! [SV93: $i] :
( ( ~ ( ~ ! [SY495: $i,SY496: $i] :
( ~ ( in @ SV93 @ SY496 )
| ~ ( in @ SY495 @ SY496 )
| ( subset @ ( unordered_pair @ SV93 @ SY495 ) @ SY496 ) )
| ~ ~ ( ~ ! [SY497: $i,SY498: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY497 ) @ SY498 )
| ( in @ SV93 @ SY498 ) )
| ~ ! [SY499: $i,SY500: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY499 ) @ SY500 )
| ( in @ SY499 @ SY500 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(727,plain,
! [SV94: $i] :
( ( ~ ( ~ ! [SY501: $i,SY502: $i] :
( ~ ( relation @ SY502 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY501 ) @ SY502 )
| ( in @ SV94 @ ( relation_field @ SY502 ) ) )
| ~ ! [SY503: $i,SY504: $i] :
( ~ ( relation @ SY504 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY503 ) @ SY504 )
| ( in @ SY503 @ ( relation_field @ SY504 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(728,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)],[600]) ).
thf(729,plain,
( ( ( ( relation_dom @ sK1_A )
!= empty_set )
| ~ ( ( ( relation_rng @ sK1_A )
!= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(730,plain,
! [SV95: $i] :
( ( ! [SY505: $i] :
~ ( ~ ! [SY506: $i] :
( ! [SY507: $i] :
( ( ordered_pair @ SV95 @ SY505 )
!= ( ordered_pair @ SY506 @ SY507 ) )
| ( SV95 = SY506 ) )
| ~ ! [SY508: $i,SY509: $i] :
( ( ( ordered_pair @ SV95 @ SY505 )
!= ( ordered_pair @ SY508 @ SY509 ) )
| ( SY505 = SY509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(731,plain,
! [SV96: $i] :
( ( ~ ( relation @ SV96 )
| ~ ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV96 @ SY510 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SY510 ) ) )
| ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV96 @ SY511 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SY511 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(732,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_SY329 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(733,plain,
! [SV1: $i] :
( ( ( singleton @ SV1 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(734,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( subset @ SV2 @ ( cartesian_product2 @ ( relation_dom @ SV2 ) @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(735,plain,
! [SV4: $i] :
( ( ( ~ ( subset @ SV4 @ empty_set ) )
= $true )
| ( ( SV4 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(736,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ! [SY333: $i] :
( ~ ( relation @ SY333 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SY333 ) ) @ ( relation_dom @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(737,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ! [SY334: $i] :
( ~ ( relation @ SY334 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SY334 ) ) @ ( relation_rng @ SY334 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(738,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY335: $i] :
( ~ ( relation @ SY335 )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SY335 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SY335 ) )
= ( relation_dom @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(739,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ! [SY336: $i] :
( ~ ( relation @ SY336 )
| ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SY336 ) )
| ( ( relation_rng @ ( relation_composition @ SY336 @ SV8 ) )
= ( relation_rng @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(740,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK49_B @ SV9 ) @ ( sK50_SY332 @ SV9 ) ) @ SV9 )
| ( SV9 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(741,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $true )
| ( ( relation @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(742,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(743,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(744,plain,
! [SV97: $i,SV13: $i] :
( ( ~ ( relation @ SV13 )
| ~ ( relation @ SV97 )
| ( relation @ ( relation_composition @ SV13 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(745,plain,
! [SV98: $i,SV14: $i] :
( ( ~ ( relation @ SV14 )
| ~ ( relation @ SV98 )
| ( relation @ ( set_union2 @ SV14 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(746,plain,
! [SV15: $i] :
( ( ( ( empty @ SV15 )
| ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(747,plain,
! [SV16: $i] :
( ( ( ( empty @ SV16 )
| ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(748,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(749,plain,
! [SV22: $i] :
( ( ( ~ ( empty @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(750,plain,
! [SV99: $i,SV23: $i] :
( ( ~ ( in @ SV23 @ SV99 )
| ( ( set_union2 @ ( singleton @ SV23 ) @ SV99 )
= SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(751,plain,
! [SV100: $i,SV24: $i] :
( ( ~ ( disjoint @ ( singleton @ SV24 ) @ SV100 )
| ~ ( in @ SV24 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(752,plain,
! [SV101: $i,SV25: $i] :
( ( ( in @ SV25 @ SV101 )
| ( disjoint @ ( singleton @ SV25 ) @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(753,plain,
! [SV26: $i,SV102: $i] :
( ( ~ ( element @ SV102 @ ( powerset @ SV26 ) )
| ! [SY512: $i] :
( ~ ( in @ SY512 @ SV102 )
| ( in @ SY512 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(754,plain,
! [SV103: $i,SV27: $i] :
( ( ~ ( subset @ SV27 @ SV103 )
| ! [SY513: $i] :
( ( in @ SY513 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SY513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(755,plain,
! [SV104: $i,SV28: $i] :
( ( ~ ( in @ SV28 @ SV104 )
| ( subset @ SV28 @ ( union @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(756,plain,
! [SV105: $i,SV29: $i] :
( ( ! [SY514: $i,SY515: $i] :
( ~ ( subset @ SV29 @ SV105 )
| ~ ( subset @ SY514 @ SY515 )
| ( subset @ ( cartesian_product2 @ SV29 @ SY514 ) @ ( cartesian_product2 @ SV105 @ SY515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(757,plain,
! [SV106: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV106 )
| ( ( set_union2 @ SV30 @ SV106 )
= SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(758,plain,
! [SV107: $i,SV31: $i] :
( ( subset @ ( set_intersection2 @ SV31 @ SV107 ) @ SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(759,plain,
! [SV108: $i,SV32: $i] :
( ( ! [SY516: $i] :
( ~ ( subset @ SV32 @ SV108 )
| ~ ( subset @ SV32 @ SY516 )
| ( subset @ SV32 @ ( set_intersection2 @ SV108 @ SY516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(760,plain,
! [SV109: $i,SV33: $i] :
( ( ! [SY517: $i] :
( ~ ( subset @ SV33 @ SV109 )
| ~ ( subset @ SV109 @ SY517 )
| ( subset @ SV33 @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(761,plain,
! [SV110: $i,SV34: $i] :
( ( ~ ( subset @ SV34 @ SV110 )
| ! [SY518: $i] : ( subset @ ( set_intersection2 @ SV34 @ SY518 ) @ ( set_intersection2 @ SV110 @ SY518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(762,plain,
! [SV111: $i,SV35: $i] :
( ( ~ ( subset @ SV35 @ SV111 )
| ( ( set_intersection2 @ SV35 @ SV111 )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(763,plain,
! [SV112: $i,SV36: $i] :
( ( ~ ( subset @ SV36 @ SV112 )
| ! [SY519: $i] : ( subset @ ( set_difference @ SV36 @ SY519 ) @ ( set_difference @ SV112 @ SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(764,plain,
! [SV113: $i,SV37: $i] :
( ( subset @ ( set_difference @ SV37 @ SV113 ) @ SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(765,plain,
! [SV114: $i,SV38: $i] :
( ( ( set_union2 @ SV38 @ ( set_difference @ SV114 @ SV38 ) )
= ( set_union2 @ SV38 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(766,plain,
! [SV115: $i,SV39: $i] :
( ( ( set_difference @ ( set_union2 @ SV39 @ SV115 ) @ SV115 )
= ( set_difference @ SV39 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(767,plain,
! [SV116: $i,SV40: $i] :
( ( ~ ( subset @ SV40 @ SV116 )
| ( SV116
= ( set_union2 @ SV40 @ ( set_difference @ SV116 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(768,plain,
! [SV117: $i,SV41: $i] :
( ( ~ ( in @ SV41 @ SV117 )
| ( ( set_union2 @ ( singleton @ SV41 ) @ SV117 )
= SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(769,plain,
! [SV118: $i,SV42: $i] :
( ( ( set_difference @ SV42 @ ( set_difference @ SV42 @ SV118 ) )
= ( set_intersection2 @ SV42 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(770,plain,
! [SV43: $i,SV119: $i] :
( ( ~ ( proper_subset @ SV119 @ SV43 )
| ~ ( subset @ SV43 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(771,plain,
! [SV44: $i,SV120: $i] :
( ( ! [SY520: $i] :
( ~ ( disjoint @ SV120 @ SY520 )
| ~ ( subset @ SV44 @ SV120 )
| ( disjoint @ SV44 @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(772,plain,
! [SV121: $i,SV46: $i] :
( ( ~ ( subset @ ( singleton @ SV46 ) @ ( singleton @ SV121 ) )
| ( SV46 = SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(773,plain,
! [SV122: $i,SV47: $i] :
( ( subset @ SV47 @ ( set_union2 @ SV47 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(774,plain,
! [SV123: $i,SV48: $i] :
( ( ! [SY521: $i] :
( ~ ( subset @ SV48 @ SV123 )
| ~ ( subset @ SY521 @ SV123 )
| ( subset @ ( set_union2 @ SV48 @ SY521 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(775,plain,
! [SV124: $i,SV49: $i] :
( ( ! [SY522: $i] :
( ( singleton @ SV49 )
!= ( unordered_pair @ SV124 @ SY522 ) )
| ( SV49 = SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(776,plain,
! [SV125: $i,SV50: $i] :
( ( ~ ( in @ SV50 @ SV125 )
| ( subset @ SV50 @ ( union @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(777,plain,
! [SV126: $i,SV52: $i] :
( ( ! [SY523: $i] :
( ( ( singleton @ SV52 )
!= ( unordered_pair @ SV126 @ SY523 ) )
| ( SV126 = SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(778,plain,
! [SV127: $i,SV53: $i] :
( ( ~ ( in @ SV53 @ SV127 )
| ~ ( in @ SV127 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(779,plain,
! [SV128: $i,SV54: $i] :
( ( ( set_union2 @ SV54 @ SV128 )
= ( set_union2 @ SV128 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(780,plain,
! [SV129: $i,SV55: $i] :
( ( ( set_intersection2 @ SV55 @ SV129 )
= ( set_intersection2 @ SV129 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(781,plain,
! [SV130: $i,SV56: $i] :
( ( ( ordered_pair @ SV56 @ SV130 )
= ( unordered_pair @ ( unordered_pair @ SV56 @ SV130 ) @ ( singleton @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(782,plain,
! [SV57: $i] :
( ( empty @ ( powerset @ SV57 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(783,plain,
! [SV131: $i,SV58: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV58 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(784,plain,
! [SV59: $i] :
( ( empty @ ( singleton @ SV59 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(785,plain,
! [SV60: $i] :
( ( ( empty @ SV60 )
= $true )
| ( ( ! [SY384: $i] :
~ ( empty @ ( set_union2 @ SV60 @ SY384 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(786,plain,
! [SV132: $i,SV61: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV61 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(787,plain,
! [SV62: $i] :
( ( ( empty @ SV62 )
= $true )
| ( ( ! [SY386: $i] :
~ ( empty @ ( set_union2 @ SY386 @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(788,plain,
! [SV133: $i,SV63: $i] :
( ( ( empty @ SV63 )
| ( empty @ SV133 )
| ~ ( empty @ ( cartesian_product2 @ SV63 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(789,plain,
! [SV134: $i,SV67: $i] :
( ( ~ ( disjoint @ SV67 @ SV134 )
| ( disjoint @ SV134 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(790,plain,
! [SV135: $i,SV68: $i] :
( ( ~ ( in @ SV68 @ SV135 )
| ( element @ SV68 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(791,plain,
! [SV136: $i,SV69: $i] :
( ( ~ ( element @ SV69 @ SV136 )
| ( empty @ SV136 )
| ( in @ SV69 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(792,plain,
! [SV70: $i,SV137: $i] :
( ( ! [SY524: $i] :
( ~ ( element @ SV137 @ ( powerset @ SY524 ) )
| ~ ( in @ SV70 @ SV137 )
| ( element @ SV70 @ SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(793,plain,
! [SV71: $i,SV138: $i] :
( ( ! [SY525: $i] :
( ~ ( element @ SV138 @ ( powerset @ SY525 ) )
| ~ ( in @ SV71 @ SV138 )
| ~ ( empty @ SY525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(794,plain,
! [SV72: $i,SV139: $i] :
( ( ~ ( empty @ SV139 )
| ~ ( in @ SV72 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(795,plain,
! [SV140: $i,SV73: $i] :
( ( ( SV73 = SV140 )
| ~ ( empty @ SV73 )
| ~ ( empty @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(796,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(797,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(798,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(799,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)],[680]) ).
thf(800,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(801,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)],[681]) ).
thf(802,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(803,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(804,plain,
! [SV74: $i,SV141: $i] :
( ( ~ ( ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV74 )
| ~ ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV141 ) )
| ( element @ SV74 @ ( powerset @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(805,plain,
! [SV142: $i,SV75: $i] :
( ( ~ ( ~ ! [SY526: $i,SY527: $i] :
( ~ ( in @ SV75 @ SY526 )
| ~ ( in @ SV142 @ SY527 )
| ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY526 @ SY527 ) ) )
| ~ ~ ( ~ ! [SY528: $i] :
( ! [SY529: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY528 @ SY529 ) )
| ( in @ SV75 @ SY528 ) )
| ~ ! [SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY530 @ SY531 ) )
| ( in @ SV142 @ SY531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(806,plain,
! [SV76: $i] :
( ( ~ ! [SY405: $i] :
( ~ ( subset @ SV76 @ SY405 )
| ! [SY406: $i] : ( subset @ ( cartesian_product2 @ SV76 @ SY406 ) @ ( cartesian_product2 @ SY405 @ SY406 ) ) )
| ~ ! [SY407: $i] :
( ~ ( subset @ SV76 @ SY407 )
| ! [SY408: $i] : ( subset @ ( cartesian_product2 @ SY408 @ SV76 ) @ ( cartesian_product2 @ SY408 @ SY407 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(807,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(808,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(809,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(810,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(811,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(812,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(813,plain,
! [SV77: $i] :
( ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( in @ ( ordered_pair @ SV77 @ SY409 ) @ SY410 )
| ( in @ SV77 @ ( relation_dom @ SY410 ) ) )
| ~ ! [SY411: $i,SY412: $i] :
( ~ ( relation @ SY412 )
| ~ ( in @ ( ordered_pair @ SV77 @ SY411 ) @ SY412 )
| ( in @ SY411 @ ( relation_rng @ SY412 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(814,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(815,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(816,plain,
! [SV78: $i,SV143: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) )
| ~ ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) ) )
| ( SV78 = SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(817,plain,
! [SV79: $i] :
( ( ~ ! [SY414: $i,SY415: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY414 ) ) )
| ~ ( ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY414 ) ) )
| ( SY415
= ( set_union2 @ SV79 @ SY414 ) ) )
| ~ ! [SY416: $i,SY417: $i] :
( ( SY417
!= ( set_union2 @ SV79 @ SY416 ) )
| ~ ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SY417 )
| ( in @ SY418 @ SV79 )
| ( in @ SY418 @ SY416 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV79 )
| ( in @ SY419 @ SY417 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY416 )
| ( in @ SX3 @ SY417 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(818,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)],[693]) ).
thf(819,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(820,plain,
! [SV80: $i] :
( ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY421 )
| ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY421 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) ) ) )
| ( SY422
= ( set_difference @ SV80 @ SY421 ) ) )
| ~ ! [SY423: $i,SY424: $i] :
( ( SY424
!= ( set_difference @ SV80 @ SY423 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV80 )
| ( in @ SY425 @ SY423 )
| ( in @ SY425 @ SY424 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY424 )
| ( in @ SY426 @ SV80 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY424 )
| ~ ( in @ SX3 @ SY423 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(821,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(822,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(823,plain,
( ( ~ ~ ( empty @ sK34_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(824,plain,
( ( ~ ( relation @ sK34_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(825,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)],[697]) ).
thf(826,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(827,plain,
! [SV81: $i] :
( ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY428 )
| ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) )
| ~ ( ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY428 )
| ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) ) ) )
| ( SY429
= ( set_intersection2 @ SV81 @ SY428 ) ) )
| ~ ! [SY430: $i,SY431: $i] :
( ( SY431
!= ( set_intersection2 @ SV81 @ SY430 ) )
| ~ ( ~ ! [SY432: $i] :
( ~ ( in @ SY432 @ SV81 )
| ~ ( in @ SY432 @ SY430 )
| ( in @ SY432 @ SY431 ) )
| ~ ~ ( ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SY431 )
| ( in @ SY433 @ SV81 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY431 )
| ( in @ SX3 @ SY430 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(828,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(829,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(830,plain,
! [SV82: $i] :
( ( ~ ! [SY435: $i] :
( ~ ( subset @ SY435 @ ( sK32_B @ SV82 ) )
| ( are_equipotent @ SY435 @ ( sK32_B @ SV82 ) )
| ( in @ SY435 @ ( sK32_B @ SV82 ) ) )
| ~ ~ ( ~ ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK32_B @ SV82 ) )
| ( in @ ( powerset @ SY436 ) @ ( sK32_B @ SV82 ) ) )
| ~ ~ ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) )
| ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(831,plain,
! [SV144: $i,SV83: $i] :
( ( ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SV83 @ SY532 )
| ~ ( in @ SV144 @ SY533 )
| ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY532 @ SY533 ) ) )
| ~ ~ ( ~ ! [SY534: $i] :
( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY534 @ SY535 ) )
| ( in @ SV83 @ SY534 ) )
| ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY536 @ SY537 ) )
| ( in @ SV144 @ SY537 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(832,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)],[702]) ).
thf(833,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)],[702]) ).
thf(834,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_SY312 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY312 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(835,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)],[703]) ).
thf(836,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(837,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(838,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(839,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)],[705]) ).
thf(840,plain,
! [SV84: $i] :
( ( ~ ! [SY446: $i] :
( ~ ( subset @ SY446 @ ( sK2_B @ SV84 ) )
| ( are_equipotent @ SY446 @ ( sK2_B @ SV84 ) )
| ( in @ SY446 @ ( sK2_B @ SV84 ) ) )
| ~ ~ ( ~ ! [SY447: $i] :
( ~ ( ~ ! [SY448: $i] :
( ~ ( subset @ SY448 @ SY447 )
| ( in @ SY448 @ ( sK3_SY300 @ SY447 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY447 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SY447 @ ( sK2_B @ SV84 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(841,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(842,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(843,plain,
! [SV85: $i] :
( ( ~ ! [SY451: $i,SY452: $i] :
( ~ ( ~ ( ! [SY453: $i,SY454: $i] :
( ~ ( in @ SY453 @ SV85 )
| ~ ( in @ SY454 @ SY451 )
| ( ( sK23_D @ SY452 @ SY451 @ SV85 )
!= ( ordered_pair @ SY453 @ SY454 ) ) )
| ~ ( in @ ( sK23_D @ SY452 @ SY451 @ SV85 ) @ SY452 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY452 @ SY451 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SY452 @ SY451 @ SV85 ) @ SY451 ) )
| ( ( sK23_D @ SY452 @ SY451 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SY452 @ SY451 @ SV85 ) @ ( sK25_SY318 @ SY452 @ SY451 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SY452 @ SY451 @ SV85 ) @ SY452 ) ) )
| ( SY452
= ( cartesian_product2 @ SV85 @ SY451 ) ) )
| ~ ! [SY455: $i,SY456: $i] :
( ( SY456
!= ( cartesian_product2 @ SV85 @ SY455 ) )
| ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i,SY459: $i] :
( ~ ( in @ SY458 @ SV85 )
| ~ ( in @ SY459 @ SY455 )
| ( SY457
!= ( ordered_pair @ SY458 @ SY459 ) ) )
| ( in @ SY457 @ SY456 ) )
| ~ ! [SY460: $i] :
( ~ ( in @ SY460 @ SY456 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY460 @ SY456 @ SY455 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY460 @ SY456 @ SY455 @ SV85 ) @ SY455 ) )
| ( SY460
!= ( ordered_pair @ ( sK21_E @ SY460 @ SY456 @ SY455 @ SV85 ) @ ( sK22_SY313 @ SY460 @ SY456 @ SY455 @ SV85 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(844,plain,
! [SV86: $i] :
( ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY461: $i] :
( ~ ( ~ ( ! [SY462: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ SY462 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ ( sK41_SY326 @ SY461 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) ) )
| ( SY461
= ( relation_dom @ SV86 ) ) )
| ~ ! [SY463: $i] :
( ( SY463
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY464: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY464 @ SY465 ) @ SV86 )
| ( in @ SY464 @ SY463 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SY463 )
| ( in @ ( ordered_pair @ SY466 @ ( sK39_D @ SY466 @ SY463 @ SV86 ) ) @ SV86 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(845,plain,
! [SV87: $i] :
( ( ~ ( element @ ( sK6_B @ SV87 ) @ ( powerset @ SV87 ) )
| ~ ( empty @ ( sK6_B @ SV87 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(846,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(847,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(848,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(849,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(850,plain,
! [SV88: $i] :
( ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( ~ ( ~ ! [SY467: $i] :
( ~ ( ~ ( ! [SY468: $i] :
~ ( in @ ( ordered_pair @ SY468 @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY467 @ SV88 ) @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) ) )
| ( SY467
= ( relation_rng @ SV88 ) ) )
| ~ ! [SY469: $i] :
( ( SY469
!= ( relation_rng @ SV88 ) )
| ~ ( ~ ! [SY470: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY470 ) @ SV88 )
| ( in @ SY470 @ SY469 ) )
| ~ ! [SY472: $i] :
( ~ ( in @ SY472 @ SY469 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY472 @ SY469 @ SV88 ) @ SY472 ) @ SV88 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(851,plain,
( ( ~ ( empty @ sK35_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(852,plain,
( ( ~ ( relation @ sK35_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(853,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[715]) ).
thf(854,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)],[715]) ).
thf(855,plain,
! [SV89: $i] :
( ( ~ ! [SY473: $i,SY474: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
!= SY473 ) ) )
| ~ ( ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
= SV89 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
= SY473 ) ) )
| ( SY474
= ( unordered_pair @ SV89 @ SY473 ) ) )
| ~ ! [SY475: $i,SY476: $i] :
( ( SY476
!= ( unordered_pair @ SV89 @ SY475 ) )
| ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY476 )
| ( SY477 = SV89 )
| ( SY477 = SY475 ) )
| ~ ~ ( ~ ! [SY478: $i] :
( ( SY478 != SV89 )
| ( in @ SY478 @ SY476 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY475 )
| ( in @ SX3 @ SY476 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(856,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(857,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(858,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)],[718]) ).
thf(859,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)],[718]) ).
thf(860,plain,
! [SV90: $i] :
( ( ( ~ ( relation @ SV90 ) )
= $true )
| ( ( ! [SY480: $i] :
( ~ ( relation @ SY480 )
| ~ ( ~ ! [SY481: $i] :
( ~ ( relation @ SY481 )
| ~ ( ~ ( ! [SY482: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ SY482 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY482 @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY480 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY481 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK12_SY309 @ SY481 @ SY480 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY480 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY481 ) ) )
| ( SY481
= ( relation_composition @ SV90 @ SY480 ) ) )
| ~ ! [SY483: $i] :
( ~ ( relation @ SY483 )
| ( SY483
!= ( relation_composition @ SV90 @ SY480 ) )
| ~ ( ~ ! [SY484: $i,SY485: $i] :
( ! [SY486: $i] :
( ~ ( in @ ( ordered_pair @ SY484 @ SY486 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY486 @ SY485 ) @ SY480 ) )
| ( in @ ( ordered_pair @ SY484 @ SY485 ) @ SY483 ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ( in @ ( ordered_pair @ SY487 @ SY488 ) @ SY483 )
| ~ ( ~ ( in @ ( ordered_pair @ SY487 @ ( sK9_F @ SY488 @ SY487 @ SY483 @ SY480 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY488 @ SY487 @ SY483 @ SY480 @ SV90 ) @ SY488 ) @ SY480 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(861,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(862,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(863,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)],[721]) ).
thf(864,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)],[721]) ).
thf(865,plain,
! [SV91: $i] :
( ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( ~ ( ~ ! [SY489: $i] :
( ~ ( relation @ SY489 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) ) )
| ( SY489
= ( relation_inverse @ SV91 ) ) )
| ~ ! [SY490: $i] :
( ~ ( relation @ SY490 )
| ( SY490
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ ( ordered_pair @ SY491 @ SY492 ) @ SY490 )
| ( in @ ( ordered_pair @ SY492 @ SY491 ) @ SV91 ) )
| ~ ! [SY493: $i,SY494: $i] :
( ~ ( in @ ( ordered_pair @ SY494 @ SY493 ) @ SV91 )
| ( in @ ( ordered_pair @ SY493 @ SY494 ) @ SY490 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(866,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(867,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)],[723]) ).
thf(868,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(869,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(870,plain,
! [SV92: $i] :
( ( ( empty @ SV92 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_B @ SV92 ) @ ( powerset @ SV92 ) )
| ~ ~ ( empty @ ( sK8_B @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(871,plain,
! [SV93: $i] :
( ( ~ ! [SY495: $i,SY496: $i] :
( ~ ( in @ SV93 @ SY496 )
| ~ ( in @ SY495 @ SY496 )
| ( subset @ ( unordered_pair @ SV93 @ SY495 ) @ SY496 ) )
| ~ ~ ( ~ ! [SY497: $i,SY498: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY497 ) @ SY498 )
| ( in @ SV93 @ SY498 ) )
| ~ ! [SY499: $i,SY500: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY499 ) @ SY500 )
| ( in @ SY499 @ SY500 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(872,plain,
! [SV94: $i] :
( ( ~ ! [SY501: $i,SY502: $i] :
( ~ ( relation @ SY502 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY501 ) @ SY502 )
| ( in @ SV94 @ ( relation_field @ SY502 ) ) )
| ~ ! [SY503: $i,SY504: $i] :
( ~ ( relation @ SY504 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY503 ) @ SY504 )
| ( in @ SY503 @ ( relation_field @ SY504 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(873,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(874,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(875,plain,
( ( ( ( relation_dom @ sK1_A )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(876,plain,
( ( ~ ( ( ( relation_rng @ sK1_A )
!= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(877,plain,
! [SV145: $i,SV95: $i] :
( ( ~ ( ~ ! [SY538: $i] :
( ! [SY539: $i] :
( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SY538 @ SY539 ) )
| ( SV95 = SY538 ) )
| ~ ! [SY540: $i,SY541: $i] :
( ( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SY540 @ SY541 ) )
| ( SV145 = SY541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(878,plain,
! [SV96: $i] :
( ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ~ ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV96 @ SY510 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SY510 ) ) )
| ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV96 @ SY511 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SY511 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(879,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)],[732]) ).
thf(880,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK46_C @ SX1 @ SX0 ) @ ( sK47_SY329 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(881,plain,
! [SV2: $i] :
( ( ( relation @ SV2 )
= $false )
| ( ( subset @ SV2 @ ( cartesian_product2 @ ( relation_dom @ SV2 ) @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(882,plain,
! [SV4: $i] :
( ( ( subset @ SV4 @ empty_set )
= $false )
| ( ( SV4 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(883,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ! [SY333: $i] :
( ~ ( relation @ SY333 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV5 @ SY333 ) ) @ ( relation_dom @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(884,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ! [SY334: $i] :
( ~ ( relation @ SY334 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV6 @ SY334 ) ) @ ( relation_rng @ SY334 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(885,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ! [SY335: $i] :
( ~ ( relation @ SY335 )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_dom @ SY335 ) )
| ( ( relation_dom @ ( relation_composition @ SV7 @ SY335 ) )
= ( relation_dom @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(886,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ! [SY336: $i] :
( ~ ( relation @ SY336 )
| ~ ( subset @ ( relation_dom @ SV8 ) @ ( relation_rng @ SY336 ) )
| ( ( relation_rng @ ( relation_composition @ SY336 @ SV8 ) )
= ( relation_rng @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(887,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK49_B @ SV9 ) @ ( sK50_SY332 @ SV9 ) ) @ SV9 )
| ( SV9 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(888,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $false )
| ( ( relation @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(889,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(890,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( relation @ ( relation_inverse @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(891,plain,
! [SV97: $i,SV13: $i] :
( ( ( ~ ( relation @ SV13 )
| ~ ( relation @ SV97 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV13 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(892,plain,
! [SV98: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 )
| ~ ( relation @ SV98 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV14 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(893,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $true )
| ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(894,plain,
! [SV16: $i] :
( ( ( empty @ SV16 )
= $true )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(895,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(896,plain,
! [SV22: $i] :
( ( ( empty @ SV22 )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(897,plain,
! [SV99: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV99 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV23 ) @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(898,plain,
! [SV100: $i,SV24: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV24 ) @ SV100 ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(899,plain,
! [SV101: $i,SV25: $i] :
( ( ( in @ SV25 @ SV101 )
= $true )
| ( ( disjoint @ ( singleton @ SV25 ) @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(900,plain,
! [SV26: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( ! [SY512: $i] :
( ~ ( in @ SY512 @ SV102 )
| ( in @ SY512 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(901,plain,
! [SV103: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV103 ) )
= $true )
| ( ( ! [SY513: $i] :
( ( in @ SY513 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SY513 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(902,plain,
! [SV104: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV104 ) )
= $true )
| ( ( subset @ SV28 @ ( union @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(903,plain,
! [SV146: $i,SV105: $i,SV29: $i] :
( ( ! [SY542: $i] :
( ~ ( subset @ SV29 @ SV105 )
| ~ ( subset @ SV146 @ SY542 )
| ( subset @ ( cartesian_product2 @ SV29 @ SV146 ) @ ( cartesian_product2 @ SV105 @ SY542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(904,plain,
! [SV106: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV106 ) )
= $true )
| ( ( ( set_union2 @ SV30 @ SV106 )
= SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(905,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)],[759]) ).
thf(906,plain,
! [SV148: $i,SV109: $i,SV33: $i] :
( ( ~ ( subset @ SV33 @ SV109 )
| ~ ( subset @ SV109 @ SV148 )
| ( subset @ SV33 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(907,plain,
! [SV110: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV110 ) )
= $true )
| ( ( ! [SY518: $i] : ( subset @ ( set_intersection2 @ SV34 @ SY518 ) @ ( set_intersection2 @ SV110 @ SY518 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(908,plain,
! [SV111: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV111 ) )
= $true )
| ( ( ( set_intersection2 @ SV35 @ SV111 )
= SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(909,plain,
! [SV112: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV112 ) )
= $true )
| ( ( ! [SY519: $i] : ( subset @ ( set_difference @ SV36 @ SY519 ) @ ( set_difference @ SV112 @ SY519 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(910,plain,
! [SV116: $i,SV40: $i] :
( ( ( ~ ( subset @ SV40 @ SV116 ) )
= $true )
| ( ( SV116
= ( set_union2 @ SV40 @ ( set_difference @ SV116 @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(911,plain,
! [SV117: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV117 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV41 ) @ SV117 )
= SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(912,plain,
! [SV43: $i,SV119: $i] :
( ( ( ~ ( proper_subset @ SV119 @ SV43 ) )
= $true )
| ( ( ~ ( subset @ SV43 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(913,plain,
! [SV44: $i,SV149: $i,SV120: $i] :
( ( ~ ( disjoint @ SV120 @ SV149 )
| ~ ( subset @ SV44 @ SV120 )
| ( disjoint @ SV44 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(914,plain,
! [SV121: $i,SV46: $i] :
( ( ( ~ ( subset @ ( singleton @ SV46 ) @ ( singleton @ SV121 ) ) )
= $true )
| ( ( SV46 = SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(915,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)],[774]) ).
thf(916,plain,
! [SV124: $i,SV49: $i] :
( ( ( ! [SY522: $i] :
( ( singleton @ SV49 )
!= ( unordered_pair @ SV124 @ SY522 ) ) )
= $true )
| ( ( SV49 = SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(917,plain,
! [SV125: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ SV125 ) )
= $true )
| ( ( subset @ SV50 @ ( union @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(918,plain,
! [SV151: $i,SV126: $i,SV52: $i] :
( ( ( ( singleton @ SV52 )
!= ( unordered_pair @ SV126 @ SV151 ) )
| ( SV126 = SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(919,plain,
! [SV127: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV127 ) )
= $true )
| ( ( ~ ( in @ SV127 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(920,plain,
! [SV131: $i,SV58: $i] :
( ( empty @ ( ordered_pair @ SV58 @ SV131 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(921,plain,
! [SV152: $i,SV60: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV60 @ SV152 ) ) )
= $true )
| ( ( empty @ SV60 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(922,plain,
! [SV132: $i,SV61: $i] :
( ( empty @ ( unordered_pair @ SV61 @ SV132 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(923,plain,
! [SV62: $i,SV153: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV153 @ SV62 ) ) )
= $true )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(924,plain,
! [SV133: $i,SV63: $i] :
( ( ( ( empty @ SV63 )
| ( empty @ SV133 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV63 @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(925,plain,
! [SV134: $i,SV67: $i] :
( ( ( ~ ( disjoint @ SV67 @ SV134 ) )
= $true )
| ( ( disjoint @ SV134 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(926,plain,
! [SV135: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ SV135 ) )
= $true )
| ( ( element @ SV68 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(927,plain,
! [SV136: $i,SV69: $i] :
( ( ( ~ ( element @ SV69 @ SV136 ) )
= $true )
| ( ( ( empty @ SV136 )
| ( in @ SV69 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(928,plain,
! [SV70: $i,SV154: $i,SV137: $i] :
( ( ~ ( element @ SV137 @ ( powerset @ SV154 ) )
| ~ ( in @ SV70 @ SV137 )
| ( element @ SV70 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(929,plain,
! [SV71: $i,SV155: $i,SV138: $i] :
( ( ~ ( element @ SV138 @ ( powerset @ SV155 ) )
| ~ ( in @ SV71 @ SV138 )
| ~ ( empty @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(930,plain,
! [SV72: $i,SV139: $i] :
( ( ( ~ ( empty @ SV139 ) )
= $true )
| ( ( ~ ( in @ SV72 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(931,plain,
! [SV140: $i,SV73: $i] :
( ( ( ( SV73 = SV140 )
| ~ ( empty @ SV73 ) )
= $true )
| ( ( ~ ( empty @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(932,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(933,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(934,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(935,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)],[799]) ).
thf(936,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(937,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)],[801]) ).
thf(938,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(939,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(940,plain,
! [SV74: $i,SV141: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV74 )
| ~ ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV141 ) ) )
= $true )
| ( ( element @ SV74 @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(941,plain,
! [SV142: $i,SV75: $i] :
( ( ~ ! [SY526: $i,SY527: $i] :
( ~ ( in @ SV75 @ SY526 )
| ~ ( in @ SV142 @ SY527 )
| ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY526 @ SY527 ) ) )
| ~ ~ ( ~ ! [SY528: $i] :
( ! [SY529: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY528 @ SY529 ) )
| ( in @ SV75 @ SY528 ) )
| ~ ! [SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY530 @ SY531 ) )
| ( in @ SV142 @ SY531 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(942,plain,
! [SV76: $i] :
( ( ~ ! [SY405: $i] :
( ~ ( subset @ SV76 @ SY405 )
| ! [SY406: $i] : ( subset @ ( cartesian_product2 @ SV76 @ SY406 ) @ ( cartesian_product2 @ SY405 @ SY406 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[806]) ).
thf(943,plain,
! [SV76: $i] :
( ( ~ ! [SY407: $i] :
( ~ ( subset @ SV76 @ SY407 )
| ! [SY408: $i] : ( subset @ ( cartesian_product2 @ SY408 @ SV76 ) @ ( cartesian_product2 @ SY408 @ SY407 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[806]) ).
thf(944,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(945,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(946,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(947,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(948,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(949,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(950,plain,
! [SV77: $i] :
( ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( in @ ( ordered_pair @ SV77 @ SY409 ) @ SY410 )
| ( in @ SV77 @ ( relation_dom @ SY410 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[813]) ).
thf(951,plain,
! [SV77: $i] :
( ( ~ ! [SY411: $i,SY412: $i] :
( ~ ( relation @ SY412 )
| ~ ( in @ ( ordered_pair @ SV77 @ SY411 ) @ SY412 )
| ( in @ SY411 @ ( relation_rng @ SY412 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[813]) ).
thf(952,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(953,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(954,plain,
! [SV78: $i,SV143: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) )
| ~ ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) ) ) )
= $true )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(955,plain,
! [SV79: $i] :
( ( ~ ! [SY414: $i,SY415: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY414 ) ) )
| ~ ( ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY414 ) ) )
| ( SY415
= ( set_union2 @ SV79 @ SY414 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(956,plain,
! [SV79: $i] :
( ( ~ ! [SY416: $i,SY417: $i] :
( ( SY417
!= ( set_union2 @ SV79 @ SY416 ) )
| ~ ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SY417 )
| ( in @ SY418 @ SV79 )
| ( in @ SY418 @ SY416 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV79 )
| ( in @ SY419 @ SY417 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY416 )
| ( in @ SX3 @ SY417 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(957,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)],[818]) ).
thf(958,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(959,plain,
! [SV80: $i] :
( ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY421 )
| ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY421 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) ) ) )
| ( SY422
= ( set_difference @ SV80 @ SY421 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(960,plain,
! [SV80: $i] :
( ( ~ ! [SY423: $i,SY424: $i] :
( ( SY424
!= ( set_difference @ SV80 @ SY423 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV80 )
| ( in @ SY425 @ SY423 )
| ( in @ SY425 @ SY424 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY424 )
| ( in @ SY426 @ SV80 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY424 )
| ~ ( in @ SX3 @ SY423 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(961,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(962,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(963,plain,
( ( ~ ( empty @ sK34_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(964,plain,
( ( relation @ sK34_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(965,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)],[825]) ).
thf(966,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(967,plain,
! [SV81: $i] :
( ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY428 )
| ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) )
| ~ ( ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY428 )
| ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) ) ) )
| ( SY429
= ( set_intersection2 @ SV81 @ SY428 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(968,plain,
! [SV81: $i] :
( ( ~ ! [SY430: $i,SY431: $i] :
( ( SY431
!= ( set_intersection2 @ SV81 @ SY430 ) )
| ~ ( ~ ! [SY432: $i] :
( ~ ( in @ SY432 @ SV81 )
| ~ ( in @ SY432 @ SY430 )
| ( in @ SY432 @ SY431 ) )
| ~ ~ ( ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SY431 )
| ( in @ SY433 @ SV81 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY431 )
| ( in @ SX3 @ SY430 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(969,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(970,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(971,plain,
! [SV82: $i] :
( ( ~ ! [SY435: $i] :
( ~ ( subset @ SY435 @ ( sK32_B @ SV82 ) )
| ( are_equipotent @ SY435 @ ( sK32_B @ SV82 ) )
| ( in @ SY435 @ ( sK32_B @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(972,plain,
! [SV82: $i] :
( ( ~ ~ ( ~ ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK32_B @ SV82 ) )
| ( in @ ( powerset @ SY436 ) @ ( sK32_B @ SV82 ) ) )
| ~ ~ ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) )
| ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(973,plain,
! [SV144: $i,SV83: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SV83 @ SY532 )
| ~ ( in @ SV144 @ SY533 )
| ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY532 @ SY533 ) ) )
| ~ ~ ( ~ ! [SY534: $i] :
( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY534 @ SY535 ) )
| ( in @ SV83 @ SY534 ) )
| ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY536 @ SY537 ) )
| ( in @ SV144 @ SY537 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(974,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)],[832]) ).
thf(975,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)],[833]) ).
thf(976,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_SY312 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY312 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(977,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)],[835]) ).
thf(978,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(979,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(980,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(981,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)],[839]) ).
thf(982,plain,
! [SV84: $i] :
( ( ~ ! [SY446: $i] :
( ~ ( subset @ SY446 @ ( sK2_B @ SV84 ) )
| ( are_equipotent @ SY446 @ ( sK2_B @ SV84 ) )
| ( in @ SY446 @ ( sK2_B @ SV84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(983,plain,
! [SV84: $i] :
( ( ~ ~ ( ~ ! [SY447: $i] :
( ~ ( ~ ! [SY448: $i] :
( ~ ( subset @ SY448 @ SY447 )
| ( in @ SY448 @ ( sK3_SY300 @ SY447 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY447 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SY447 @ ( sK2_B @ SV84 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(984,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(985,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(986,plain,
! [SV85: $i] :
( ( ~ ! [SY451: $i,SY452: $i] :
( ~ ( ~ ( ! [SY453: $i,SY454: $i] :
( ~ ( in @ SY453 @ SV85 )
| ~ ( in @ SY454 @ SY451 )
| ( ( sK23_D @ SY452 @ SY451 @ SV85 )
!= ( ordered_pair @ SY453 @ SY454 ) ) )
| ~ ( in @ ( sK23_D @ SY452 @ SY451 @ SV85 ) @ SY452 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY452 @ SY451 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SY452 @ SY451 @ SV85 ) @ SY451 ) )
| ( ( sK23_D @ SY452 @ SY451 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SY452 @ SY451 @ SV85 ) @ ( sK25_SY318 @ SY452 @ SY451 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SY452 @ SY451 @ SV85 ) @ SY452 ) ) )
| ( SY452
= ( cartesian_product2 @ SV85 @ SY451 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(987,plain,
! [SV85: $i] :
( ( ~ ! [SY455: $i,SY456: $i] :
( ( SY456
!= ( cartesian_product2 @ SV85 @ SY455 ) )
| ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i,SY459: $i] :
( ~ ( in @ SY458 @ SV85 )
| ~ ( in @ SY459 @ SY455 )
| ( SY457
!= ( ordered_pair @ SY458 @ SY459 ) ) )
| ( in @ SY457 @ SY456 ) )
| ~ ! [SY460: $i] :
( ~ ( in @ SY460 @ SY456 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY460 @ SY456 @ SY455 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY460 @ SY456 @ SY455 @ SV85 ) @ SY455 ) )
| ( SY460
!= ( ordered_pair @ ( sK21_E @ SY460 @ SY456 @ SY455 @ SV85 ) @ ( sK22_SY313 @ SY460 @ SY456 @ SY455 @ SV85 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(988,plain,
! [SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( ~ ( ~ ! [SY461: $i] :
( ~ ( ~ ( ! [SY462: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ SY462 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ ( sK41_SY326 @ SY461 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) ) )
| ( SY461
= ( relation_dom @ SV86 ) ) )
| ~ ! [SY463: $i] :
( ( SY463
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY464: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY464 @ SY465 ) @ SV86 )
| ( in @ SY464 @ SY463 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SY463 )
| ( in @ ( ordered_pair @ SY466 @ ( sK39_D @ SY466 @ SY463 @ SV86 ) ) @ SV86 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(989,plain,
! [SV87: $i] :
( ( ~ ( element @ ( sK6_B @ SV87 ) @ ( powerset @ SV87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(990,plain,
! [SV87: $i] :
( ( ~ ( empty @ ( sK6_B @ SV87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(991,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(992,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(993,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(994,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(995,plain,
! [SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( ~ ( ~ ! [SY467: $i] :
( ~ ( ~ ( ! [SY468: $i] :
~ ( in @ ( ordered_pair @ SY468 @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY467 @ SV88 ) @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) ) )
| ( SY467
= ( relation_rng @ SV88 ) ) )
| ~ ! [SY469: $i] :
( ( SY469
!= ( relation_rng @ SV88 ) )
| ~ ( ~ ! [SY470: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY470 ) @ SV88 )
| ( in @ SY470 @ SY469 ) )
| ~ ! [SY472: $i] :
( ~ ( in @ SY472 @ SY469 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY472 @ SY469 @ SV88 ) @ SY472 ) @ SV88 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(996,plain,
( ( empty @ sK35_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(997,plain,
( ( relation @ sK35_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(998,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[853]) ).
thf(999,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)],[854]) ).
thf(1000,plain,
! [SV89: $i] :
( ( ~ ! [SY473: $i,SY474: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
!= SY473 ) ) )
| ~ ( ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
= SV89 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
= SY473 ) ) )
| ( SY474
= ( unordered_pair @ SV89 @ SY473 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(1001,plain,
! [SV89: $i] :
( ( ~ ! [SY475: $i,SY476: $i] :
( ( SY476
!= ( unordered_pair @ SV89 @ SY475 ) )
| ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY476 )
| ( SY477 = SV89 )
| ( SY477 = SY475 ) )
| ~ ~ ( ~ ! [SY478: $i] :
( ( SY478 != SV89 )
| ( in @ SY478 @ SY476 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY475 )
| ( in @ SX3 @ SY476 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(1002,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(1003,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(1004,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)],[858]) ).
thf(1005,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)],[859]) ).
thf(1006,plain,
! [SV90: $i] :
( ( ( relation @ SV90 )
= $false )
| ( ( ! [SY480: $i] :
( ~ ( relation @ SY480 )
| ~ ( ~ ! [SY481: $i] :
( ~ ( relation @ SY481 )
| ~ ( ~ ( ! [SY482: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ SY482 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY482 @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY480 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY481 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK12_SY309 @ SY481 @ SY480 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY480 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY481 @ SY480 @ SV90 ) @ ( sK11_SY305 @ SY481 @ SY480 @ SV90 ) ) @ SY481 ) ) )
| ( SY481
= ( relation_composition @ SV90 @ SY480 ) ) )
| ~ ! [SY483: $i] :
( ~ ( relation @ SY483 )
| ( SY483
!= ( relation_composition @ SV90 @ SY480 ) )
| ~ ( ~ ! [SY484: $i,SY485: $i] :
( ! [SY486: $i] :
( ~ ( in @ ( ordered_pair @ SY484 @ SY486 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY486 @ SY485 ) @ SY480 ) )
| ( in @ ( ordered_pair @ SY484 @ SY485 ) @ SY483 ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ( in @ ( ordered_pair @ SY487 @ SY488 ) @ SY483 )
| ~ ( ~ ( in @ ( ordered_pair @ SY487 @ ( sK9_F @ SY488 @ SY487 @ SY483 @ SY480 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY488 @ SY487 @ SY483 @ SY480 @ SV90 ) @ SY488 ) @ SY480 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(1007,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(1008,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(1009,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)],[863]) ).
thf(1010,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)],[864]) ).
thf(1011,plain,
! [SV91: $i] :
( ( ( relation @ SV91 )
= $false )
| ( ( ~ ( ~ ! [SY489: $i] :
( ~ ( relation @ SY489 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) ) )
| ( SY489
= ( relation_inverse @ SV91 ) ) )
| ~ ! [SY490: $i] :
( ~ ( relation @ SY490 )
| ( SY490
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ ( ordered_pair @ SY491 @ SY492 ) @ SY490 )
| ( in @ ( ordered_pair @ SY492 @ SY491 ) @ SV91 ) )
| ~ ! [SY493: $i,SY494: $i] :
( ~ ( in @ ( ordered_pair @ SY494 @ SY493 ) @ SV91 )
| ( in @ ( ordered_pair @ SY493 @ SY494 ) @ SY490 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(1012,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(1013,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)],[867]) ).
thf(1014,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(1015,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(1016,plain,
! [SV92: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV92 ) @ ( powerset @ SV92 ) )
| ~ ~ ( empty @ ( sK8_B @ SV92 ) ) )
= $false )
| ( ( empty @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(1017,plain,
! [SV93: $i] :
( ( ~ ! [SY495: $i,SY496: $i] :
( ~ ( in @ SV93 @ SY496 )
| ~ ( in @ SY495 @ SY496 )
| ( subset @ ( unordered_pair @ SV93 @ SY495 ) @ SY496 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(1018,plain,
! [SV93: $i] :
( ( ~ ~ ( ~ ! [SY497: $i,SY498: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY497 ) @ SY498 )
| ( in @ SV93 @ SY498 ) )
| ~ ! [SY499: $i,SY500: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY499 ) @ SY500 )
| ( in @ SY499 @ SY500 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(1019,plain,
! [SV94: $i] :
( ( ~ ! [SY501: $i,SY502: $i] :
( ~ ( relation @ SY502 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY501 ) @ SY502 )
| ( in @ SV94 @ ( relation_field @ SY502 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(1020,plain,
! [SV94: $i] :
( ( ~ ! [SY503: $i,SY504: $i] :
( ~ ( relation @ SY504 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY503 ) @ SY504 )
| ( in @ SY503 @ ( relation_field @ SY504 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(1021,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(1022,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(1023,plain,
( ( ( relation_dom @ sK1_A )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(1024,plain,
( ( ( ( relation_rng @ sK1_A )
!= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(1025,plain,
! [SV145: $i,SV95: $i] :
( ( ~ ! [SY538: $i] :
( ! [SY539: $i] :
( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SY538 @ SY539 ) )
| ( SV95 = SY538 ) )
| ~ ! [SY540: $i,SY541: $i] :
( ( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SY540 @ SY541 ) )
| ( SV145 = SY541 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(1026,plain,
! [SV96: $i] :
( ( ( relation @ SV96 )
= $false )
| ( ( ~ ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV96 @ SY510 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SY510 ) ) )
| ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV96 @ SY511 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SY511 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(1027,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)],[879]) ).
thf(1028,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK46_C @ SX1 @ SX0 ) @ ( sK47_SY329 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(1029,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)],[883]) ).
thf(1030,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)],[884]) ).
thf(1031,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)],[885]) ).
thf(1032,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)],[886]) ).
thf(1033,plain,
! [SV9: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_B @ SV9 ) @ ( sK50_SY332 @ SV9 ) ) @ SV9 )
= $true )
| ( ( SV9 = empty_set )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(1034,plain,
! [SV97: $i,SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV13 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(1035,plain,
! [SV98: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV14 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(1036,plain,
! [SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(1037,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( empty @ SV16 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(1038,plain,
! [SV99: $i,SV23: $i] :
( ( ( in @ SV23 @ SV99 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV23 ) @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(1039,plain,
! [SV100: $i,SV24: $i] :
( ( ( disjoint @ ( singleton @ SV24 ) @ SV100 )
= $false )
| ( ( ~ ( in @ SV24 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(1040,plain,
! [SV26: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV26 ) )
= $false )
| ( ( ! [SY512: $i] :
( ~ ( in @ SY512 @ SV102 )
| ( in @ SY512 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(1041,plain,
! [SV103: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV103 )
= $false )
| ( ( ! [SY513: $i] :
( ( in @ SY513 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SY513 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(1042,plain,
! [SV104: $i,SV28: $i] :
( ( ( in @ SV28 @ SV104 )
= $false )
| ( ( subset @ SV28 @ ( union @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(1043,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)],[903]) ).
thf(1044,plain,
! [SV106: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV106 )
= $false )
| ( ( ( set_union2 @ SV30 @ SV106 )
= SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(1045,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)],[905]) ).
thf(1046,plain,
! [SV148: $i,SV109: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV109 )
| ~ ( subset @ SV109 @ SV148 ) )
= $true )
| ( ( subset @ SV33 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1047,plain,
! [SV110: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV110 )
= $false )
| ( ( ! [SY518: $i] : ( subset @ ( set_intersection2 @ SV34 @ SY518 ) @ ( set_intersection2 @ SV110 @ SY518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(1048,plain,
! [SV111: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV111 )
= $false )
| ( ( ( set_intersection2 @ SV35 @ SV111 )
= SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1049,plain,
! [SV112: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV112 )
= $false )
| ( ( ! [SY519: $i] : ( subset @ ( set_difference @ SV36 @ SY519 ) @ ( set_difference @ SV112 @ SY519 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(1050,plain,
! [SV116: $i,SV40: $i] :
( ( ( subset @ SV40 @ SV116 )
= $false )
| ( ( SV116
= ( set_union2 @ SV40 @ ( set_difference @ SV116 @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(1051,plain,
! [SV117: $i,SV41: $i] :
( ( ( in @ SV41 @ SV117 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV41 ) @ SV117 )
= SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1052,plain,
! [SV43: $i,SV119: $i] :
( ( ( proper_subset @ SV119 @ SV43 )
= $false )
| ( ( ~ ( subset @ SV43 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1053,plain,
! [SV44: $i,SV149: $i,SV120: $i] :
( ( ( ~ ( disjoint @ SV120 @ SV149 )
| ~ ( subset @ SV44 @ SV120 ) )
= $true )
| ( ( disjoint @ SV44 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1054,plain,
! [SV121: $i,SV46: $i] :
( ( ( subset @ ( singleton @ SV46 ) @ ( singleton @ SV121 ) )
= $false )
| ( ( SV46 = SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1055,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)],[915]) ).
thf(1056,plain,
! [SV161: $i,SV124: $i,SV49: $i] :
( ( ( ( ( singleton @ SV49 )
!= ( unordered_pair @ SV124 @ SV161 ) ) )
= $true )
| ( ( SV49 = SV124 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1057,plain,
! [SV125: $i,SV50: $i] :
( ( ( in @ SV50 @ SV125 )
= $false )
| ( ( subset @ SV50 @ ( union @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1058,plain,
! [SV151: $i,SV126: $i,SV52: $i] :
( ( ( ( ( singleton @ SV52 )
!= ( unordered_pair @ SV126 @ SV151 ) ) )
= $true )
| ( ( SV126 = SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1059,plain,
! [SV127: $i,SV53: $i] :
( ( ( in @ SV53 @ SV127 )
= $false )
| ( ( ~ ( in @ SV127 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(1060,plain,
! [SV152: $i,SV60: $i] :
( ( ( empty @ ( set_union2 @ SV60 @ SV152 ) )
= $false )
| ( ( empty @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1061,plain,
! [SV62: $i,SV153: $i] :
( ( ( empty @ ( set_union2 @ SV153 @ SV62 ) )
= $false )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1062,plain,
! [SV133: $i,SV63: $i] :
( ( ( empty @ SV63 )
= $true )
| ( ( empty @ SV133 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV63 @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1063,plain,
! [SV134: $i,SV67: $i] :
( ( ( disjoint @ SV67 @ SV134 )
= $false )
| ( ( disjoint @ SV134 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1064,plain,
! [SV135: $i,SV68: $i] :
( ( ( in @ SV68 @ SV135 )
= $false )
| ( ( element @ SV68 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1065,plain,
! [SV136: $i,SV69: $i] :
( ( ( element @ SV69 @ SV136 )
= $false )
| ( ( ( empty @ SV136 )
| ( in @ SV69 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1066,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)],[928]) ).
thf(1067,plain,
! [SV71: $i,SV155: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ ( powerset @ SV155 ) )
| ~ ( in @ SV71 @ SV138 ) )
= $true )
| ( ( ~ ( empty @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1068,plain,
! [SV72: $i,SV139: $i] :
( ( ( empty @ SV139 )
= $false )
| ( ( ~ ( in @ SV72 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1069,plain,
! [SV140: $i,SV73: $i] :
( ( ( SV73 = SV140 )
= $true )
| ( ( ~ ( empty @ SV73 ) )
= $true )
| ( ( ~ ( empty @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1070,plain,
! [SV162: $i] :
( ( ! [SY543: $i] :
( ~ ( in @ SV162 @ SY543 )
| ( subset @ ( singleton @ SV162 ) @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1071,plain,
! [SV163: $i] :
( ( ! [SY544: $i] :
( ~ ( subset @ ( singleton @ SV163 ) @ SY544 )
| ( in @ SV163 @ SY544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1072,plain,
! [SV164: $i] :
( ( ! [SY545: $i] :
( ~ ( subset @ SV164 @ SY545 )
| ~ ( subset @ SY545 @ SV164 )
| ( SV164 = SY545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1073,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)],[935]) ).
thf(1074,plain,
! [SV165: $i] :
( ( ! [SY546: $i] :
( ( SV165 = SY546 )
| ~ ( subset @ SV165 @ SY546 )
| ( proper_subset @ SV165 @ SY546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1075,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)],[937]) ).
thf(1076,plain,
! [SV166: $i] :
( ( ! [SY547: $i] :
( ( disjoint @ SV166 @ SY547 )
| ( in @ ( sK30_C @ SY547 @ SV166 ) @ ( set_intersection2 @ SV166 @ SY547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1077,plain,
! [SV167: $i] :
( ( ! [SY548: $i] :
( ! [SY549: $i] :
~ ( in @ SY549 @ ( set_intersection2 @ SV167 @ SY548 ) )
| ~ ( disjoint @ SV167 @ SY548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1078,plain,
! [SV74: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV74 )
| ~ ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV141 ) )
= $false )
| ( ( element @ SV74 @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1079,plain,
! [SV142: $i,SV75: $i] :
( ( ~ ! [SY526: $i,SY527: $i] :
( ~ ( in @ SV75 @ SY526 )
| ~ ( in @ SV142 @ SY527 )
| ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY526 @ SY527 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(1080,plain,
! [SV142: $i,SV75: $i] :
( ( ~ ~ ( ~ ! [SY528: $i] :
( ! [SY529: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY528 @ SY529 ) )
| ( in @ SV75 @ SY528 ) )
| ~ ! [SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY530 @ SY531 ) )
| ( in @ SV142 @ SY531 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(1081,plain,
! [SV76: $i] :
( ( ! [SY405: $i] :
( ~ ( subset @ SV76 @ SY405 )
| ! [SY406: $i] : ( subset @ ( cartesian_product2 @ SV76 @ SY406 ) @ ( cartesian_product2 @ SY405 @ SY406 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1082,plain,
! [SV76: $i] :
( ( ! [SY407: $i] :
( ~ ( subset @ SV76 @ SY407 )
| ! [SY408: $i] : ( subset @ ( cartesian_product2 @ SY408 @ SV76 ) @ ( cartesian_product2 @ SY408 @ SY407 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1083,plain,
! [SV168: $i] :
( ( ! [SY550: $i] :
( ( ( set_difference @ SV168 @ SY550 )
!= SV168 )
| ( disjoint @ SV168 @ SY550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1084,plain,
! [SV169: $i] :
( ( ! [SY551: $i] :
( ~ ( disjoint @ SV169 @ SY551 )
| ( ( set_difference @ SV169 @ SY551 )
= SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1085,plain,
! [SV77: $i] :
( ( ! [SY409: $i,SY410: $i] :
( ~ ( relation @ SY410 )
| ~ ( in @ ( ordered_pair @ SV77 @ SY409 ) @ SY410 )
| ( in @ SV77 @ ( relation_dom @ SY410 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1086,plain,
! [SV77: $i] :
( ( ! [SY411: $i,SY412: $i] :
( ~ ( relation @ SY412 )
| ~ ( in @ ( ordered_pair @ SV77 @ SY411 ) @ SY412 )
| ( in @ SY411 @ ( relation_rng @ SY412 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(1087,plain,
! [SV170: $i] :
( ( ~ ( empty @ SV170 )
| ( empty @ ( relation_rng @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1088,plain,
! [SV171: $i] :
( ( ~ ( empty @ SV171 )
| ( relation @ ( relation_rng @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1089,plain,
! [SV78: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) )
| ~ ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) ) )
= $false )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1090,plain,
! [SV79: $i] :
( ( ! [SY414: $i,SY415: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ~ ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY414 ) ) )
| ~ ( ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY415 )
| ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SY415 @ SY414 @ SV79 ) @ SY414 ) ) )
| ( SY415
= ( set_union2 @ SV79 @ SY414 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1091,plain,
! [SV79: $i] :
( ( ! [SY416: $i,SY417: $i] :
( ( SY417
!= ( set_union2 @ SV79 @ SY416 ) )
| ~ ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SY417 )
| ( in @ SY418 @ SV79 )
| ( in @ SY418 @ SY416 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV79 )
| ( in @ SY419 @ SY417 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY416 )
| ( in @ SX3 @ SY417 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1092,plain,
! [SV172: $i] :
( ( ! [SY552: $i] :
( ( disjoint @ SV172 @ SY552 )
| ~ ( ~ ( in @ ( sK31_C @ SY552 @ SV172 ) @ SV172 )
| ~ ( in @ ( sK31_C @ SY552 @ SV172 ) @ SY552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1093,plain,
! [SV173: $i] :
( ( ! [SY553: $i] :
( ! [SY554: $i] :
( ~ ( in @ SY554 @ SV173 )
| ~ ( in @ SY554 @ SY553 ) )
| ~ ( disjoint @ SV173 @ SY553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1094,plain,
! [SV80: $i] :
( ( ! [SY421: $i,SY422: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY421 )
| ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY421 )
| ( in @ ( sK15_D @ SY422 @ SY421 @ SV80 ) @ SY422 ) ) ) )
| ( SY422
= ( set_difference @ SV80 @ SY421 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(1095,plain,
! [SV80: $i] :
( ( ! [SY423: $i,SY424: $i] :
( ( SY424
!= ( set_difference @ SV80 @ SY423 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV80 )
| ( in @ SY425 @ SY423 )
| ( in @ SY425 @ SY424 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY424 )
| ( in @ SY426 @ SV80 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY424 )
| ~ ( in @ SX3 @ SY423 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(1096,plain,
! [SV174: $i] :
( ( ! [SY555: $i] :
( ( ( set_difference @ SV174 @ SY555 )
!= empty_set )
| ( subset @ SV174 @ SY555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1097,plain,
! [SV175: $i] :
( ( ! [SY556: $i] :
( ~ ( subset @ SV175 @ SY556 )
| ( ( set_difference @ SV175 @ SY556 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1098,plain,
( ( empty @ sK34_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1099,plain,
! [SV176: $i] :
( ( ! [SY557: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SY557 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( sK20_C @ SY557 @ SV176 ) @ SY557 ) )
| ( subset @ SV176 @ SY557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1100,plain,
! [SV177: $i] :
( ( ! [SY558: $i] :
( ~ ( subset @ SV177 @ SY558 )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SV177 )
| ( in @ SY559 @ SY558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1101,plain,
! [SV81: $i] :
( ( ! [SY428: $i,SY429: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY428 )
| ~ ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) )
| ~ ( ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY428 )
| ( in @ ( sK19_D @ SY429 @ SY428 @ SV81 ) @ SY429 ) ) ) )
| ( SY429
= ( set_intersection2 @ SV81 @ SY428 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1102,plain,
! [SV81: $i] :
( ( ! [SY430: $i,SY431: $i] :
( ( SY431
!= ( set_intersection2 @ SV81 @ SY430 ) )
| ~ ( ~ ! [SY432: $i] :
( ~ ( in @ SY432 @ SV81 )
| ~ ( in @ SY432 @ SY430 )
| ( in @ SY432 @ SY431 ) )
| ~ ~ ( ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SY431 )
| ( in @ SY433 @ SV81 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY431 )
| ( in @ SX3 @ SY430 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1103,plain,
! [SV178: $i] :
( ( ! [SY560: $i] :
( ( ( set_difference @ SV178 @ SY560 )
!= empty_set )
| ( subset @ SV178 @ SY560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1104,plain,
! [SV179: $i] :
( ( ! [SY561: $i] :
( ~ ( subset @ SV179 @ SY561 )
| ( ( set_difference @ SV179 @ SY561 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1105,plain,
! [SV82: $i] :
( ( ! [SY435: $i] :
( ~ ( subset @ SY435 @ ( sK32_B @ SV82 ) )
| ( are_equipotent @ SY435 @ ( sK32_B @ SV82 ) )
| ( in @ SY435 @ ( sK32_B @ SV82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(1106,plain,
! [SV82: $i] :
( ( ~ ( ~ ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK32_B @ SV82 ) )
| ( in @ ( powerset @ SY436 ) @ ( sK32_B @ SV82 ) ) )
| ~ ~ ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) )
| ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1107,plain,
! [SV144: $i,SV83: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SV83 @ SY532 )
| ~ ( in @ SV144 @ SY533 )
| ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY532 @ SY533 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1108,plain,
! [SV144: $i,SV83: $i] :
( ( ~ ~ ( ~ ! [SY534: $i] :
( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY534 @ SY535 ) )
| ( in @ SV83 @ SY534 ) )
| ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY536 @ SY537 ) )
| ( in @ SV144 @ SY537 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1109,plain,
! [SV180: $i] :
( ( ! [SY562: $i] :
( ~ ( ~ ( ( ( sK29_C @ SY562 @ SV180 )
!= SV180 )
| ~ ( in @ ( sK29_C @ SY562 @ SV180 ) @ SY562 ) )
| ~ ( ( ( sK29_C @ SY562 @ SV180 )
= SV180 )
| ( in @ ( sK29_C @ SY562 @ SV180 ) @ SY562 ) ) )
| ( SY562
= ( singleton @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1110,plain,
! [SV181: $i] :
( ( ! [SY563: $i] :
( ( SY563
!= ( singleton @ SV181 ) )
| ~ ( ~ ! [SY564: $i] :
( ( SY564 != SV181 )
| ( in @ SY564 @ SY563 ) )
| ~ ! [SY565: $i] :
( ~ ( in @ SY565 @ SY563 )
| ( SY565 = SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1111,plain,
! [SV182: $i] :
( ( ! [SY566: $i] :
( ~ ( ~ ( ! [SY567: $i] :
( ~ ( in @ ( sK17_C @ SY566 @ SV182 ) @ SY567 )
| ~ ( in @ SY567 @ SV182 ) )
| ~ ( in @ ( sK17_C @ SY566 @ SV182 ) @ SY566 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SY566 @ SV182 ) @ ( sK18_SY312 @ SY566 @ SV182 ) )
| ~ ( in @ ( sK18_SY312 @ SY566 @ SV182 ) @ SV182 ) )
| ( in @ ( sK17_C @ SY566 @ SV182 ) @ SY566 ) ) )
| ( SY566
= ( union @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1112,plain,
! [SV183: $i] :
( ( ! [SY568: $i] :
( ( SY568
!= ( union @ SV183 ) )
| ~ ( ~ ! [SY569: $i] :
( ! [SY570: $i] :
( ~ ( in @ SY569 @ SY570 )
| ~ ( in @ SY570 @ SV183 ) )
| ( in @ SY569 @ SY568 ) )
| ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ SY568 )
| ~ ( ~ ( in @ SY571 @ ( sK16_D @ SY571 @ SY568 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SY571 @ SY568 @ SV183 ) @ SV183 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1113,plain,
! [SV184: $i] :
( ( ~ ( relation @ SV184 )
| ( ( relation_dom @ SV184 )
!= empty_set )
| ( SV184 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1114,plain,
! [SV185: $i] :
( ( ~ ( relation @ SV185 )
| ( ( relation_rng @ SV185 )
!= empty_set )
| ( SV185 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1115,plain,
! [SV186: $i] :
( ( ! [SY572: $i] :
( ~ ( subset @ SV186 @ ( singleton @ SY572 ) )
| ( SV186 = empty_set )
| ( SV186
= ( singleton @ SY572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1116,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)],[981]) ).
thf(1117,plain,
! [SV84: $i] :
( ( ! [SY446: $i] :
( ~ ( subset @ SY446 @ ( sK2_B @ SV84 ) )
| ( are_equipotent @ SY446 @ ( sK2_B @ SV84 ) )
| ( in @ SY446 @ ( sK2_B @ SV84 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1118,plain,
! [SV84: $i] :
( ( ~ ( ~ ! [SY447: $i] :
( ~ ( ~ ! [SY448: $i] :
( ~ ( subset @ SY448 @ SY447 )
| ( in @ SY448 @ ( sK3_SY300 @ SY447 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY447 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SY447 @ ( sK2_B @ SV84 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1119,plain,
! [SV187: $i] :
( ( ~ ( relation @ SV187 )
| ( ( relation_rng @ SV187 )
= ( relation_dom @ ( relation_inverse @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1120,plain,
! [SV188: $i] :
( ( ~ ( relation @ SV188 )
| ( ( relation_dom @ SV188 )
= ( relation_rng @ ( relation_inverse @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1121,plain,
! [SV85: $i] :
( ( ! [SY451: $i,SY452: $i] :
( ~ ( ~ ( ! [SY453: $i,SY454: $i] :
( ~ ( in @ SY453 @ SV85 )
| ~ ( in @ SY454 @ SY451 )
| ( ( sK23_D @ SY452 @ SY451 @ SV85 )
!= ( ordered_pair @ SY453 @ SY454 ) ) )
| ~ ( in @ ( sK23_D @ SY452 @ SY451 @ SV85 ) @ SY452 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY452 @ SY451 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SY452 @ SY451 @ SV85 ) @ SY451 ) )
| ( ( sK23_D @ SY452 @ SY451 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SY452 @ SY451 @ SV85 ) @ ( sK25_SY318 @ SY452 @ SY451 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SY452 @ SY451 @ SV85 ) @ SY452 ) ) )
| ( SY452
= ( cartesian_product2 @ SV85 @ SY451 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1122,plain,
! [SV85: $i] :
( ( ! [SY455: $i,SY456: $i] :
( ( SY456
!= ( cartesian_product2 @ SV85 @ SY455 ) )
| ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i,SY459: $i] :
( ~ ( in @ SY458 @ SV85 )
| ~ ( in @ SY459 @ SY455 )
| ( SY457
!= ( ordered_pair @ SY458 @ SY459 ) ) )
| ( in @ SY457 @ SY456 ) )
| ~ ! [SY460: $i] :
( ~ ( in @ SY460 @ SY456 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY460 @ SY456 @ SY455 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY460 @ SY456 @ SY455 @ SV85 ) @ SY455 ) )
| ( SY460
!= ( ordered_pair @ ( sK21_E @ SY460 @ SY456 @ SY455 @ SV85 ) @ ( sK22_SY313 @ SY460 @ SY456 @ SY455 @ SV85 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1123,plain,
! [SV86: $i] :
( ( ( ~ ! [SY461: $i] :
( ~ ( ~ ( ! [SY462: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ SY462 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ ( sK41_SY326 @ SY461 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) ) )
| ( SY461
= ( relation_dom @ SV86 ) ) )
| ~ ! [SY463: $i] :
( ( SY463
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY464: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY464 @ SY465 ) @ SV86 )
| ( in @ SY464 @ SY463 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SY463 )
| ( in @ ( ordered_pair @ SY466 @ ( sK39_D @ SY466 @ SY463 @ SV86 ) ) @ SV86 ) ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1124,plain,
! [SV87: $i] :
( ( element @ ( sK6_B @ SV87 ) @ ( powerset @ SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1125,plain,
! [SV87: $i] :
( ( empty @ ( sK6_B @ SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1126,plain,
! [SV189: $i] :
( ( ! [SY573: $i] :
( ~ ( in @ SV189 @ SY573 )
| ( subset @ ( singleton @ SV189 ) @ SY573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1127,plain,
! [SV190: $i] :
( ( ! [SY574: $i] :
( ~ ( subset @ ( singleton @ SV190 ) @ SY574 )
| ( in @ SV190 @ SY574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1128,plain,
! [SV191: $i] :
( ( ! [SY575: $i] :
( ( ( set_intersection2 @ SV191 @ SY575 )
!= empty_set )
| ( disjoint @ SV191 @ SY575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1129,plain,
! [SV192: $i] :
( ( ! [SY576: $i] :
( ~ ( disjoint @ SV192 @ SY576 )
| ( ( set_intersection2 @ SV192 @ SY576 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1130,plain,
! [SV88: $i] :
( ( ( ~ ! [SY467: $i] :
( ~ ( ~ ( ! [SY468: $i] :
~ ( in @ ( ordered_pair @ SY468 @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY467 @ SV88 ) @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) ) )
| ( SY467
= ( relation_rng @ SV88 ) ) )
| ~ ! [SY469: $i] :
( ( SY469
!= ( relation_rng @ SV88 ) )
| ~ ( ~ ! [SY470: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY470 ) @ SV88 )
| ( in @ SY470 @ SY469 ) )
| ~ ! [SY472: $i] :
( ~ ( in @ SY472 @ SY469 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY472 @ SY469 @ SV88 ) @ SY472 ) @ SV88 ) ) ) ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1131,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[998]) ).
thf(1132,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)],[999]) ).
thf(1133,plain,
! [SV89: $i] :
( ( ! [SY473: $i,SY474: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
!= SY473 ) ) )
| ~ ( ( in @ ( sK27_D @ SY474 @ SY473 @ SV89 ) @ SY474 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
= SV89 )
| ( ( sK27_D @ SY474 @ SY473 @ SV89 )
= SY473 ) ) )
| ( SY474
= ( unordered_pair @ SV89 @ SY473 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1134,plain,
! [SV89: $i] :
( ( ! [SY475: $i,SY476: $i] :
( ( SY476
!= ( unordered_pair @ SV89 @ SY475 ) )
| ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY476 )
| ( SY477 = SV89 )
| ( SY477 = SY475 ) )
| ~ ~ ( ~ ! [SY478: $i] :
( ( SY478 != SV89 )
| ( in @ SY478 @ SY476 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY475 )
| ( in @ SX3 @ SY476 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1135,plain,
! [SV193: $i] :
( ( ! [SY577: $i] :
( ( ( set_difference @ SV193 @ ( singleton @ SY577 ) )
!= SV193 )
| ~ ( in @ SY577 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1136,plain,
! [SV194: $i] :
( ( ! [SY578: $i] :
( ( in @ SY578 @ SV194 )
| ( ( set_difference @ SV194 @ ( singleton @ SY578 ) )
= SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1137,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)],[1004]) ).
thf(1138,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)],[1005]) ).
thf(1139,plain,
! [SV90: $i,SV195: $i] :
( ( ( ~ ( relation @ SV195 )
| ~ ( ~ ! [SY579: $i] :
( ~ ( relation @ SY579 )
| ~ ( ~ ( ! [SY580: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ SY580 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY580 @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) ) )
| ( SY579
= ( relation_composition @ SV90 @ SV195 ) ) )
| ~ ! [SY581: $i] :
( ~ ( relation @ SY581 )
| ( SY581
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY582: $i,SY583: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY582 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY583 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY582 @ SY583 ) @ SY581 ) )
| ~ ! [SY585: $i,SY586: $i] :
( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SY581 )
| ~ ( ~ ( in @ ( ordered_pair @ SY585 @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) @ SY586 ) @ SV195 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1140,plain,
! [SV196: $i] :
( ( ~ ( empty @ SV196 )
| ( empty @ ( relation_dom @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1141,plain,
! [SV197: $i] :
( ( ~ ( empty @ SV197 )
| ( relation @ ( relation_dom @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1142,plain,
! [SV198: $i] :
( ( ! [SY587: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SY587 @ SV198 ) @ SY587 )
| ~ ( subset @ ( sK28_C @ SY587 @ SV198 ) @ SV198 ) )
| ~ ( ( in @ ( sK28_C @ SY587 @ SV198 ) @ SY587 )
| ( subset @ ( sK28_C @ SY587 @ SV198 ) @ SV198 ) ) )
| ( SY587
= ( powerset @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1143,plain,
! [SV199: $i] :
( ( ! [SY588: $i] :
( ( SY588
!= ( powerset @ SV199 ) )
| ~ ( ~ ! [SY589: $i] :
( ~ ( in @ SY589 @ SY588 )
| ( subset @ SY589 @ SV199 ) )
| ~ ! [SY590: $i] :
( ~ ( subset @ SY590 @ SV199 )
| ( in @ SY590 @ SY588 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1144,plain,
! [SV91: $i] :
( ( ( ~ ! [SY489: $i] :
( ~ ( relation @ SY489 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) ) )
| ( SY489
= ( relation_inverse @ SV91 ) ) )
| ~ ! [SY490: $i] :
( ~ ( relation @ SY490 )
| ( SY490
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ ( ordered_pair @ SY491 @ SY492 ) @ SY490 )
| ( in @ ( ordered_pair @ SY492 @ SY491 ) @ SV91 ) )
| ~ ! [SY493: $i,SY494: $i] :
( ~ ( in @ ( ordered_pair @ SY494 @ SY493 ) @ SV91 )
| ( in @ ( ordered_pair @ SY493 @ SY494 ) @ SY490 ) ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1145,plain,
! [SV200: $i] :
( ( ! [SY591: $i] :
( ~ ( subset @ SV200 @ ( singleton @ SY591 ) )
| ( SV200 = empty_set )
| ( SV200
= ( singleton @ SY591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1146,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)],[1013]) ).
thf(1147,plain,
! [SV201: $i] :
( ( ! [SY592: $i] :
( ~ ( element @ SV201 @ ( powerset @ SY592 ) )
| ( subset @ SV201 @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1148,plain,
! [SV202: $i] :
( ( ! [SY593: $i] :
( ~ ( subset @ SV202 @ SY593 )
| ( element @ SV202 @ ( powerset @ SY593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1149,plain,
! [SV92: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV92 ) @ ( powerset @ SV92 ) ) )
= $false )
| ( ( empty @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1150,plain,
! [SV92: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV92 ) ) )
= $false )
| ( ( empty @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1151,plain,
! [SV93: $i] :
( ( ! [SY495: $i,SY496: $i] :
( ~ ( in @ SV93 @ SY496 )
| ~ ( in @ SY495 @ SY496 )
| ( subset @ ( unordered_pair @ SV93 @ SY495 ) @ SY496 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1152,plain,
! [SV93: $i] :
( ( ~ ( ~ ! [SY497: $i,SY498: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY497 ) @ SY498 )
| ( in @ SV93 @ SY498 ) )
| ~ ! [SY499: $i,SY500: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY499 ) @ SY500 )
| ( in @ SY499 @ SY500 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1153,plain,
! [SV94: $i] :
( ( ! [SY501: $i,SY502: $i] :
( ~ ( relation @ SY502 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY501 ) @ SY502 )
| ( in @ SV94 @ ( relation_field @ SY502 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1154,plain,
! [SV94: $i] :
( ( ! [SY503: $i,SY504: $i] :
( ~ ( relation @ SY504 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY503 ) @ SY504 )
| ( in @ SY503 @ ( relation_field @ SY504 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1155,plain,
! [SV203: $i] :
( ( ( in @ ( sK42_B @ SV203 ) @ SV203 )
| ( SV203 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1156,plain,
! [SV204: $i] :
( ( ( SV204 != empty_set )
| ! [SY594: $i] :
~ ( in @ SY594 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1157,plain,
( ( ( relation_rng @ sK1_A )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1158,plain,
! [SV145: $i,SV95: $i] :
( ( ~ ! [SY538: $i] :
( ! [SY539: $i] :
( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SY538 @ SY539 ) )
| ( SV95 = SY538 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1025]) ).
thf(1159,plain,
! [SV145: $i,SV95: $i] :
( ( ~ ! [SY540: $i,SY541: $i] :
( ( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SY540 @ SY541 ) )
| ( SV145 = SY541 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1025]) ).
thf(1160,plain,
! [SV96: $i] :
( ( ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV96 @ SY510 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SY510 ) ) )
| ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV96 @ SY511 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SY511 ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1161,plain,
! [SV205: $i] :
( ( ~ ( ~ ! [SY595: $i,SY596: $i] :
( ( sK48_B @ SV205 )
!= ( ordered_pair @ SY595 @ SY596 ) )
| ~ ( in @ ( sK48_B @ SV205 ) @ SV205 ) )
| ( relation @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1162,plain,
! [SV206: $i] :
( ( ~ ( relation @ SV206 )
| ! [SY597: $i] :
( ( SY597
= ( ordered_pair @ ( sK46_C @ SY597 @ SV206 ) @ ( sK47_SY329 @ SY597 @ SV206 ) ) )
| ~ ( in @ SY597 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1163,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)],[1029]) ).
thf(1164,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)],[1030]) ).
thf(1165,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)],[1031]) ).
thf(1166,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)],[1032]) ).
thf(1167,plain,
! [SV97: $i,SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV13 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1168,plain,
! [SV98: $i,SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV14 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1169,plain,
! [SV15: $i] :
( ( ( empty @ ( relation_dom @ SV15 ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1170,plain,
! [SV16: $i] :
( ( ( empty @ ( relation_rng @ SV16 ) )
= $false )
| ( ( empty @ SV16 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1171,plain,
! [SV100: $i,SV24: $i] :
( ( ( in @ SV24 @ SV100 )
= $false )
| ( ( disjoint @ ( singleton @ SV24 ) @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1172,plain,
! [SV26: $i,SV102: $i,SV207: $i] :
( ( ( ~ ( in @ SV207 @ SV102 )
| ( in @ SV207 @ SV26 ) )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1173,plain,
! [SV103: $i,SV27: $i,SV208: $i] :
( ( ( ( in @ SV208 @ SV27 )
| ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SV208 ) ) ) )
= $true )
| ( ( subset @ SV27 @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1174,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)],[1043]) ).
thf(1175,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)],[1045]) ).
thf(1176,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)],[1046]) ).
thf(1177,plain,
! [SV110: $i,SV209: $i,SV34: $i] :
( ( ( subset @ ( set_intersection2 @ SV34 @ SV209 ) @ ( set_intersection2 @ SV110 @ SV209 ) )
= $true )
| ( ( subset @ SV34 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1178,plain,
! [SV112: $i,SV210: $i,SV36: $i] :
( ( ( subset @ ( set_difference @ SV36 @ SV210 ) @ ( set_difference @ SV112 @ SV210 ) )
= $true )
| ( ( subset @ SV36 @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1179,plain,
! [SV119: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV119 )
= $false )
| ( ( proper_subset @ SV119 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1180,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)],[1053]) ).
thf(1181,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)],[1055]) ).
thf(1182,plain,
! [SV161: $i,SV124: $i,SV49: $i] :
( ( ( ( singleton @ SV49 )
= ( unordered_pair @ SV124 @ SV161 ) )
= $false )
| ( ( SV49 = SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1183,plain,
! [SV151: $i,SV126: $i,SV52: $i] :
( ( ( ( singleton @ SV52 )
= ( unordered_pair @ SV126 @ SV151 ) )
= $false )
| ( ( SV126 = SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1184,plain,
! [SV53: $i,SV127: $i] :
( ( ( in @ SV127 @ SV53 )
= $false )
| ( ( in @ SV53 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1185,plain,
! [SV133: $i,SV63: $i] :
( ( ( empty @ ( cartesian_product2 @ SV63 @ SV133 ) )
= $false )
| ( ( empty @ SV133 )
= $true )
| ( ( empty @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1186,plain,
! [SV69: $i,SV136: $i] :
( ( ( empty @ SV136 )
= $true )
| ( ( in @ SV69 @ SV136 )
= $true )
| ( ( element @ SV69 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1187,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)],[1066]) ).
thf(1188,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)],[1067]) ).
thf(1189,plain,
! [SV139: $i,SV72: $i] :
( ( ( in @ SV72 @ SV139 )
= $false )
| ( ( empty @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1190,plain,
! [SV140: $i,SV73: $i] :
( ( ( empty @ SV73 )
= $false )
| ( ( SV73 = SV140 )
= $true )
| ( ( ~ ( empty @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1191,plain,
! [SV211: $i,SV162: $i] :
( ( ~ ( in @ SV162 @ SV211 )
| ( subset @ ( singleton @ SV162 ) @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1192,plain,
! [SV212: $i,SV163: $i] :
( ( ~ ( subset @ ( singleton @ SV163 ) @ SV212 )
| ( in @ SV163 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1193,plain,
! [SV213: $i,SV164: $i] :
( ( ~ ( subset @ SV164 @ SV213 )
| ~ ( subset @ SV213 @ SV164 )
| ( SV164 = SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1194,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1195,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1196,plain,
! [SV214: $i,SV165: $i] :
( ( ( SV165 = SV214 )
| ~ ( subset @ SV165 @ SV214 )
| ( proper_subset @ SV165 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1197,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1198,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1199,plain,
! [SV215: $i,SV166: $i] :
( ( ( disjoint @ SV166 @ SV215 )
| ( in @ ( sK30_C @ SV215 @ SV166 ) @ ( set_intersection2 @ SV166 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1200,plain,
! [SV216: $i,SV167: $i] :
( ( ! [SY598: $i] :
~ ( in @ SY598 @ ( set_intersection2 @ SV167 @ SV216 ) )
| ~ ( disjoint @ SV167 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1201,plain,
! [SV74: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV74 ) )
= $false )
| ( ( element @ SV74 @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1202,plain,
! [SV74: $i,SV141: $i] :
( ( ( ~ ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV141 ) )
= $false )
| ( ( element @ SV74 @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1203,plain,
! [SV142: $i,SV75: $i] :
( ( ! [SY526: $i,SY527: $i] :
( ~ ( in @ SV75 @ SY526 )
| ~ ( in @ SV142 @ SY527 )
| ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY526 @ SY527 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1204,plain,
! [SV142: $i,SV75: $i] :
( ( ~ ( ~ ! [SY528: $i] :
( ! [SY529: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY528 @ SY529 ) )
| ( in @ SV75 @ SY528 ) )
| ~ ! [SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY530 @ SY531 ) )
| ( in @ SV142 @ SY531 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1205,plain,
! [SV217: $i,SV76: $i] :
( ( ~ ( subset @ SV76 @ SV217 )
| ! [SY599: $i] : ( subset @ ( cartesian_product2 @ SV76 @ SY599 ) @ ( cartesian_product2 @ SV217 @ SY599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1206,plain,
! [SV218: $i,SV76: $i] :
( ( ~ ( subset @ SV76 @ SV218 )
| ! [SY600: $i] : ( subset @ ( cartesian_product2 @ SY600 @ SV76 ) @ ( cartesian_product2 @ SY600 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1207,plain,
! [SV219: $i,SV168: $i] :
( ( ( ( set_difference @ SV168 @ SV219 )
!= SV168 )
| ( disjoint @ SV168 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1208,plain,
! [SV220: $i,SV169: $i] :
( ( ~ ( disjoint @ SV169 @ SV220 )
| ( ( set_difference @ SV169 @ SV220 )
= SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1209,plain,
! [SV221: $i,SV77: $i] :
( ( ! [SY601: $i] :
( ~ ( relation @ SY601 )
| ~ ( in @ ( ordered_pair @ SV77 @ SV221 ) @ SY601 )
| ( in @ SV77 @ ( relation_dom @ SY601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1210,plain,
! [SV222: $i,SV77: $i] :
( ( ! [SY602: $i] :
( ~ ( relation @ SY602 )
| ~ ( in @ ( ordered_pair @ SV77 @ SV222 ) @ SY602 )
| ( in @ SV222 @ ( relation_rng @ SY602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1211,plain,
! [SV170: $i] :
( ( ( ~ ( empty @ SV170 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1212,plain,
! [SV171: $i] :
( ( ( ~ ( empty @ SV171 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1213,plain,
! [SV78: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) ) )
= $false )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1214,plain,
! [SV78: $i,SV143: $i] :
( ( ( ~ ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) ) )
= $false )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1215,plain,
! [SV79: $i,SV223: $i] :
( ( ! [SY603: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY603 @ SV223 @ SV79 ) @ SY603 )
| ~ ( in @ ( sK26_D @ SY603 @ SV223 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY603 @ SV223 @ SV79 ) @ SY603 )
| ~ ( in @ ( sK26_D @ SY603 @ SV223 @ SV79 ) @ SV223 ) ) )
| ~ ( ( in @ ( sK26_D @ SY603 @ SV223 @ SV79 ) @ SY603 )
| ( in @ ( sK26_D @ SY603 @ SV223 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SY603 @ SV223 @ SV79 ) @ SV223 ) ) )
| ( SY603
= ( set_union2 @ SV79 @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1216,plain,
! [SV224: $i,SV79: $i] :
( ( ! [SY604: $i] :
( ( SY604
!= ( set_union2 @ SV79 @ SV224 ) )
| ~ ( ~ ! [SY605: $i] :
( ~ ( in @ SY605 @ SY604 )
| ( in @ SY605 @ SV79 )
| ( in @ SY605 @ SV224 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV79 )
| ( in @ SY419 @ SY604 ) )
| ~ ! [SY607: $i] :
( ~ ( in @ SY607 @ SV224 )
| ( in @ SY607 @ SY604 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1217,plain,
! [SV225: $i,SV172: $i] :
( ( ( disjoint @ SV172 @ SV225 )
| ~ ( ~ ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV172 )
| ~ ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1218,plain,
! [SV226: $i,SV173: $i] :
( ( ! [SY608: $i] :
( ~ ( in @ SY608 @ SV173 )
| ~ ( in @ SY608 @ SV226 ) )
| ~ ( disjoint @ SV173 @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1219,plain,
! [SV80: $i,SV227: $i] :
( ( ! [SY609: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY609 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY609 @ SV227 @ SV80 ) @ SV227 )
| ~ ( in @ ( sK15_D @ SY609 @ SV227 @ SV80 ) @ SY609 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY609 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SY609 @ SV227 @ SV80 ) @ SY609 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY609 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SY609 @ SV227 @ SV80 ) @ SY609 ) ) ) )
| ( SY609
= ( set_difference @ SV80 @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1220,plain,
! [SV228: $i,SV80: $i] :
( ( ! [SY610: $i] :
( ( SY610
!= ( set_difference @ SV80 @ SV228 ) )
| ~ ( ~ ! [SY611: $i] :
( ~ ( in @ SY611 @ SV80 )
| ( in @ SY611 @ SV228 )
| ( in @ SY611 @ SY610 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SY610 )
| ( in @ SY426 @ SV80 ) )
| ~ ! [SY613: $i] :
( ~ ( in @ SY613 @ SY610 )
| ~ ( in @ SY613 @ SV228 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1221,plain,
! [SV229: $i,SV174: $i] :
( ( ( ( set_difference @ SV174 @ SV229 )
!= empty_set )
| ( subset @ SV174 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1222,plain,
! [SV230: $i,SV175: $i] :
( ( ~ ( subset @ SV175 @ SV230 )
| ( ( set_difference @ SV175 @ SV230 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1223,plain,
! [SV176: $i,SV231: $i] :
( ( ~ ( ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV231 ) )
| ( subset @ SV176 @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1224,plain,
! [SV232: $i,SV177: $i] :
( ( ~ ( subset @ SV177 @ SV232 )
| ! [SY614: $i] :
( ~ ( in @ SY614 @ SV177 )
| ( in @ SY614 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1225,plain,
! [SV81: $i,SV233: $i] :
( ( ! [SY615: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY615 @ SV233 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SY615 @ SV233 @ SV81 ) @ SV233 )
| ~ ( in @ ( sK19_D @ SY615 @ SV233 @ SV81 ) @ SY615 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY615 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SY615 @ SV233 @ SV81 ) @ SY615 ) )
| ~ ( ( in @ ( sK19_D @ SY615 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SY615 @ SV233 @ SV81 ) @ SY615 ) ) ) )
| ( SY615
= ( set_intersection2 @ SV81 @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1226,plain,
! [SV234: $i,SV81: $i] :
( ( ! [SY616: $i] :
( ( SY616
!= ( set_intersection2 @ SV81 @ SV234 ) )
| ~ ( ~ ! [SY617: $i] :
( ~ ( in @ SY617 @ SV81 )
| ~ ( in @ SY617 @ SV234 )
| ( in @ SY617 @ SY616 ) )
| ~ ~ ( ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SY616 )
| ( in @ SY433 @ SV81 ) )
| ~ ! [SY619: $i] :
( ~ ( in @ SY619 @ SY616 )
| ( in @ SY619 @ SV234 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1227,plain,
! [SV235: $i,SV178: $i] :
( ( ( ( set_difference @ SV178 @ SV235 )
!= empty_set )
| ( subset @ SV178 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1228,plain,
! [SV236: $i,SV179: $i] :
( ( ~ ( subset @ SV179 @ SV236 )
| ( ( set_difference @ SV179 @ SV236 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1229,plain,
! [SV82: $i,SV237: $i] :
( ( ~ ( subset @ SV237 @ ( sK32_B @ SV82 ) )
| ( are_equipotent @ SV237 @ ( sK32_B @ SV82 ) )
| ( in @ SV237 @ ( sK32_B @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1230,plain,
! [SV82: $i] :
( ( ~ ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK32_B @ SV82 ) )
| ( in @ ( powerset @ SY436 ) @ ( sK32_B @ SV82 ) ) )
| ~ ~ ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) )
| ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1231,plain,
! [SV144: $i,SV83: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( in @ SV83 @ SY532 )
| ~ ( in @ SV144 @ SY533 )
| ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY532 @ SY533 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1232,plain,
! [SV144: $i,SV83: $i] :
( ( ~ ( ~ ! [SY534: $i] :
( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY534 @ SY535 ) )
| ( in @ SV83 @ SY534 ) )
| ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY536 @ SY537 ) )
| ( in @ SV144 @ SY537 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1233,plain,
! [SV180: $i,SV238: $i] :
( ( ~ ( ~ ( ( ( sK29_C @ SV238 @ SV180 )
!= SV180 )
| ~ ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) )
| ~ ( ( ( sK29_C @ SV238 @ SV180 )
= SV180 )
| ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) ) )
| ( SV238
= ( singleton @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1234,plain,
! [SV181: $i,SV239: $i] :
( ( ( SV239
!= ( singleton @ SV181 ) )
| ~ ( ~ ! [SY620: $i] :
( ( SY620 != SV181 )
| ( in @ SY620 @ SV239 ) )
| ~ ! [SY621: $i] :
( ~ ( in @ SY621 @ SV239 )
| ( SY621 = SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1235,plain,
! [SV182: $i,SV240: $i] :
( ( ~ ( ~ ( ! [SY622: $i] :
( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SY622 )
| ~ ( in @ SY622 @ SV182 ) )
| ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) )
| ~ ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 ) )
| ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) ) )
| ( SV240
= ( union @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1236,plain,
! [SV183: $i,SV241: $i] :
( ( ( SV241
!= ( union @ SV183 ) )
| ~ ( ~ ! [SY623: $i] :
( ! [SY570: $i] :
( ~ ( in @ SY623 @ SY570 )
| ~ ( in @ SY570 @ SV183 ) )
| ( in @ SY623 @ SV241 ) )
| ~ ! [SY625: $i] :
( ~ ( in @ SY625 @ SV241 )
| ~ ( ~ ( in @ SY625 @ ( sK16_D @ SY625 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SY625 @ SV241 @ SV183 ) @ SV183 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1237,plain,
! [SV184: $i] :
( ( ( ~ ( relation @ SV184 ) )
= $true )
| ( ( ( ( relation_dom @ SV184 )
!= empty_set )
| ( SV184 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1238,plain,
! [SV185: $i] :
( ( ( ~ ( relation @ SV185 ) )
= $true )
| ( ( ( ( relation_rng @ SV185 )
!= empty_set )
| ( SV185 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1239,plain,
! [SV242: $i,SV186: $i] :
( ( ~ ( subset @ SV186 @ ( singleton @ SV242 ) )
| ( SV186 = empty_set )
| ( SV186
= ( singleton @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1240,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1116]) ).
thf(1241,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1116]) ).
thf(1242,plain,
! [SV84: $i,SV243: $i] :
( ( ~ ( subset @ SV243 @ ( sK2_B @ SV84 ) )
| ( are_equipotent @ SV243 @ ( sK2_B @ SV84 ) )
| ( in @ SV243 @ ( sK2_B @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1243,plain,
! [SV84: $i] :
( ( ~ ! [SY447: $i] :
( ~ ( ~ ! [SY448: $i] :
( ~ ( subset @ SY448 @ SY447 )
| ( in @ SY448 @ ( sK3_SY300 @ SY447 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY447 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SY447 @ ( sK2_B @ SV84 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1244,plain,
! [SV187: $i] :
( ( ( ~ ( relation @ SV187 ) )
= $true )
| ( ( ( relation_rng @ SV187 )
= ( relation_dom @ ( relation_inverse @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1245,plain,
! [SV188: $i] :
( ( ( ~ ( relation @ SV188 ) )
= $true )
| ( ( ( relation_dom @ SV188 )
= ( relation_rng @ ( relation_inverse @ SV188 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1246,plain,
! [SV244: $i,SV85: $i] :
( ( ! [SY626: $i] :
( ~ ( ~ ( ! [SY627: $i,SY628: $i] :
( ~ ( in @ SY627 @ SV85 )
| ~ ( in @ SY628 @ SV244 )
| ( ( sK23_D @ SY626 @ SV244 @ SV85 )
!= ( ordered_pair @ SY627 @ SY628 ) ) )
| ~ ( in @ ( sK23_D @ SY626 @ SV244 @ SV85 ) @ SY626 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY626 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SY626 @ SV244 @ SV85 ) @ SV244 ) )
| ( ( sK23_D @ SY626 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SY626 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SY626 @ SV244 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SY626 @ SV244 @ SV85 ) @ SY626 ) ) )
| ( SY626
= ( cartesian_product2 @ SV85 @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1247,plain,
! [SV245: $i,SV85: $i] :
( ( ! [SY629: $i] :
( ( SY629
!= ( cartesian_product2 @ SV85 @ SV245 ) )
| ~ ( ~ ! [SY630: $i] :
( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ SV85 )
| ~ ( in @ SY632 @ SV245 )
| ( SY630
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ( in @ SY630 @ SY629 ) )
| ~ ! [SY633: $i] :
( ~ ( in @ SY633 @ SY629 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY633 @ SY629 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY633 @ SY629 @ SV245 @ SV85 ) @ SV245 ) )
| ( SY633
!= ( ordered_pair @ ( sK21_E @ SY633 @ SY629 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SY633 @ SY629 @ SV245 @ SV85 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1248,plain,
! [SV86: $i] :
( ( ( ~ ! [SY461: $i] :
( ~ ( ~ ( ! [SY462: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ SY462 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ ( sK41_SY326 @ SY461 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) ) )
| ( SY461
= ( relation_dom @ SV86 ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1249,plain,
! [SV86: $i] :
( ( ( ~ ! [SY463: $i] :
( ( SY463
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY464: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY464 @ SY465 ) @ SV86 )
| ( in @ SY464 @ SY463 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SY463 )
| ( in @ ( ordered_pair @ SY466 @ ( sK39_D @ SY466 @ SY463 @ SV86 ) ) @ SV86 ) ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1250,plain,
! [SV246: $i,SV189: $i] :
( ( ~ ( in @ SV189 @ SV246 )
| ( subset @ ( singleton @ SV189 ) @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1251,plain,
! [SV247: $i,SV190: $i] :
( ( ~ ( subset @ ( singleton @ SV190 ) @ SV247 )
| ( in @ SV190 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1252,plain,
! [SV248: $i,SV191: $i] :
( ( ( ( set_intersection2 @ SV191 @ SV248 )
!= empty_set )
| ( disjoint @ SV191 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1253,plain,
! [SV249: $i,SV192: $i] :
( ( ~ ( disjoint @ SV192 @ SV249 )
| ( ( set_intersection2 @ SV192 @ SV249 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1254,plain,
! [SV88: $i] :
( ( ( ~ ! [SY467: $i] :
( ~ ( ~ ( ! [SY468: $i] :
~ ( in @ ( ordered_pair @ SY468 @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY467 @ SV88 ) @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) ) )
| ( SY467
= ( relation_rng @ SV88 ) ) ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1255,plain,
! [SV88: $i] :
( ( ( ~ ! [SY469: $i] :
( ( SY469
!= ( relation_rng @ SV88 ) )
| ~ ( ~ ! [SY470: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY470 ) @ SV88 )
| ( in @ SY470 @ SY469 ) )
| ~ ! [SY472: $i] :
( ~ ( in @ SY472 @ SY469 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY472 @ SY469 @ SV88 ) @ SY472 ) @ SV88 ) ) ) ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1256,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[1131]) ).
thf(1257,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)],[1131]) ).
thf(1258,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1259,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1260,plain,
! [SV89: $i,SV250: $i] :
( ( ! [SY634: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY634 @ SV250 @ SV89 ) @ SY634 )
| ( ( sK27_D @ SY634 @ SV250 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY634 @ SV250 @ SV89 ) @ SY634 )
| ( ( sK27_D @ SY634 @ SV250 @ SV89 )
!= SV250 ) ) )
| ~ ( ( in @ ( sK27_D @ SY634 @ SV250 @ SV89 ) @ SY634 )
| ( ( sK27_D @ SY634 @ SV250 @ SV89 )
= SV89 )
| ( ( sK27_D @ SY634 @ SV250 @ SV89 )
= SV250 ) ) )
| ( SY634
= ( unordered_pair @ SV89 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1261,plain,
! [SV251: $i,SV89: $i] :
( ( ! [SY635: $i] :
( ( SY635
!= ( unordered_pair @ SV89 @ SV251 ) )
| ~ ( ~ ! [SY636: $i] :
( ~ ( in @ SY636 @ SY635 )
| ( SY636 = SV89 )
| ( SY636 = SV251 ) )
| ~ ~ ( ~ ! [SY478: $i] :
( ( SY478 != SV89 )
| ( in @ SY478 @ SY635 ) )
| ~ ! [SY638: $i] :
( ( SY638 != SV251 )
| ( in @ SY638 @ SY635 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1262,plain,
! [SV252: $i,SV193: $i] :
( ( ( ( set_difference @ SV193 @ ( singleton @ SV252 ) )
!= SV193 )
| ~ ( in @ SV252 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1263,plain,
! [SV194: $i,SV253: $i] :
( ( ( in @ SV253 @ SV194 )
| ( ( set_difference @ SV194 @ ( singleton @ SV253 ) )
= SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1264,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1137]) ).
thf(1265,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1137]) ).
thf(1266,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1267,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1268,plain,
! [SV90: $i,SV195: $i] :
( ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( ~ ! [SY579: $i] :
( ~ ( relation @ SY579 )
| ~ ( ~ ( ! [SY580: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ SY580 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY580 @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) ) )
| ( SY579
= ( relation_composition @ SV90 @ SV195 ) ) )
| ~ ! [SY581: $i] :
( ~ ( relation @ SY581 )
| ( SY581
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY582: $i,SY583: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY582 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY583 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY582 @ SY583 ) @ SY581 ) )
| ~ ! [SY585: $i,SY586: $i] :
( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SY581 )
| ~ ( ~ ( in @ ( ordered_pair @ SY585 @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) @ SY586 ) @ SV195 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1269,plain,
! [SV196: $i] :
( ( ( ~ ( empty @ SV196 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1270,plain,
! [SV197: $i] :
( ( ( ~ ( empty @ SV197 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1271,plain,
! [SV198: $i,SV254: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ~ ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) )
| ~ ( ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) ) )
| ( SV254
= ( powerset @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1272,plain,
! [SV199: $i,SV255: $i] :
( ( ( SV255
!= ( powerset @ SV199 ) )
| ~ ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV255 )
| ( subset @ SY639 @ SV199 ) )
| ~ ! [SY640: $i] :
( ~ ( subset @ SY640 @ SV199 )
| ( in @ SY640 @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1273,plain,
! [SV91: $i] :
( ( ( ~ ! [SY489: $i] :
( ~ ( relation @ SY489 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) ) )
| ( SY489
= ( relation_inverse @ SV91 ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1274,plain,
! [SV91: $i] :
( ( ( ~ ! [SY490: $i] :
( ~ ( relation @ SY490 )
| ( SY490
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ ( ordered_pair @ SY491 @ SY492 ) @ SY490 )
| ( in @ ( ordered_pair @ SY492 @ SY491 ) @ SV91 ) )
| ~ ! [SY493: $i,SY494: $i] :
( ~ ( in @ ( ordered_pair @ SY494 @ SY493 ) @ SV91 )
| ( in @ ( ordered_pair @ SY493 @ SY494 ) @ SY490 ) ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1275,plain,
! [SV256: $i,SV200: $i] :
( ( ~ ( subset @ SV200 @ ( singleton @ SV256 ) )
| ( SV200 = empty_set )
| ( SV200
= ( singleton @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1276,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1277,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1278,plain,
! [SV257: $i,SV201: $i] :
( ( ~ ( element @ SV201 @ ( powerset @ SV257 ) )
| ( subset @ SV201 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1279,plain,
! [SV258: $i,SV202: $i] :
( ( ~ ( subset @ SV202 @ SV258 )
| ( element @ SV202 @ ( powerset @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1280,plain,
! [SV92: $i] :
( ( ( element @ ( sK8_B @ SV92 ) @ ( powerset @ SV92 ) )
= $true )
| ( ( empty @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1281,plain,
! [SV92: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV92 ) ) )
= $true )
| ( ( empty @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1282,plain,
! [SV259: $i,SV93: $i] :
( ( ! [SY641: $i] :
( ~ ( in @ SV93 @ SY641 )
| ~ ( in @ SV259 @ SY641 )
| ( subset @ ( unordered_pair @ SV93 @ SV259 ) @ SY641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1283,plain,
! [SV93: $i] :
( ( ~ ! [SY497: $i,SY498: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY497 ) @ SY498 )
| ( in @ SV93 @ SY498 ) )
| ~ ! [SY499: $i,SY500: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY499 ) @ SY500 )
| ( in @ SY499 @ SY500 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1284,plain,
! [SV260: $i,SV94: $i] :
( ( ! [SY642: $i] :
( ~ ( relation @ SY642 )
| ~ ( in @ ( ordered_pair @ SV94 @ SV260 ) @ SY642 )
| ( in @ SV94 @ ( relation_field @ SY642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1285,plain,
! [SV261: $i,SV94: $i] :
( ( ! [SY643: $i] :
( ~ ( relation @ SY643 )
| ~ ( in @ ( ordered_pair @ SV94 @ SV261 ) @ SY643 )
| ( in @ SV261 @ ( relation_field @ SY643 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1286,plain,
! [SV203: $i] :
( ( ( in @ ( sK42_B @ SV203 ) @ SV203 )
= $true )
| ( ( SV203 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1287,plain,
! [SV204: $i] :
( ( ( ( SV204 != empty_set ) )
= $true )
| ( ( ! [SY594: $i] :
~ ( in @ SY594 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1288,plain,
! [SV145: $i,SV95: $i] :
( ( ! [SY538: $i] :
( ! [SY539: $i] :
( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SY538 @ SY539 ) )
| ( SV95 = SY538 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1289,plain,
! [SV145: $i,SV95: $i] :
( ( ! [SY540: $i,SY541: $i] :
( ( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SY540 @ SY541 ) )
| ( SV145 = SY541 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1290,plain,
! [SV96: $i] :
( ( ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV96 @ SY510 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SY510 ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1291,plain,
! [SV96: $i] :
( ( ( ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV96 @ SY511 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SY511 ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1292,plain,
! [SV205: $i] :
( ( ( ~ ( ~ ! [SY595: $i,SY596: $i] :
( ( sK48_B @ SV205 )
!= ( ordered_pair @ SY595 @ SY596 ) )
| ~ ( in @ ( sK48_B @ SV205 ) @ SV205 ) ) )
= $true )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1293,plain,
! [SV206: $i] :
( ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( ! [SY597: $i] :
( ( SY597
= ( ordered_pair @ ( sK46_C @ SY597 @ SV206 ) @ ( sK47_SY329 @ SY597 @ SV206 ) ) )
| ~ ( in @ SY597 @ SV206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1294,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)],[1163]) ).
thf(1295,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)],[1164]) ).
thf(1296,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)],[1165]) ).
thf(1297,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)],[1166]) ).
thf(1298,plain,
! [SV13: $i,SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( relation @ ( relation_composition @ SV13 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1299,plain,
! [SV14: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV14 )
= $false )
| ( ( relation @ ( set_union2 @ SV14 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1300,plain,
! [SV26: $i,SV102: $i,SV207: $i] :
( ( ( ~ ( in @ SV207 @ SV102 ) )
= $true )
| ( ( in @ SV207 @ SV26 )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1301,plain,
! [SV103: $i,SV27: $i,SV208: $i] :
( ( ( in @ SV208 @ SV27 )
= $true )
| ( ( subset @ SV27 @ ( set_difference @ SV103 @ ( singleton @ SV208 ) ) )
= $true )
| ( ( subset @ SV27 @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1302,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)],[1174]) ).
thf(1303,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)],[1175]) ).
thf(1304,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)],[1176]) ).
thf(1305,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)],[1180]) ).
thf(1306,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)],[1181]) ).
thf(1307,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)],[1187]) ).
thf(1308,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)],[1188]) ).
thf(1309,plain,
! [SV73: $i,SV140: $i] :
( ( ( empty @ SV140 )
= $false )
| ( ( SV73 = SV140 )
= $true )
| ( ( empty @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1310,plain,
! [SV211: $i,SV162: $i] :
( ( ( ~ ( in @ SV162 @ SV211 ) )
= $true )
| ( ( subset @ ( singleton @ SV162 ) @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1311,plain,
! [SV212: $i,SV163: $i] :
( ( ( ~ ( subset @ ( singleton @ SV163 ) @ SV212 ) )
= $true )
| ( ( in @ SV163 @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1312,plain,
! [SV213: $i,SV164: $i] :
( ( ( ~ ( subset @ SV164 @ SV213 )
| ~ ( subset @ SV213 @ SV164 ) )
= $true )
| ( ( SV164 = SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1313,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1314,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1195]) ).
thf(1315,plain,
! [SV214: $i,SV165: $i] :
( ( ( ( SV165 = SV214 )
| ~ ( subset @ SV165 @ SV214 ) )
= $true )
| ( ( proper_subset @ SV165 @ SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1316,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1317,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1318,plain,
! [SV215: $i,SV166: $i] :
( ( ( disjoint @ SV166 @ SV215 )
= $true )
| ( ( in @ ( sK30_C @ SV215 @ SV166 ) @ ( set_intersection2 @ SV166 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1319,plain,
! [SV216: $i,SV167: $i] :
( ( ( ! [SY598: $i] :
~ ( in @ SY598 @ ( set_intersection2 @ SV167 @ SV216 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV167 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1320,plain,
! [SV74: $i,SV141: $i] :
( ( ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV74 )
= $true )
| ( ( element @ SV74 @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1321,plain,
! [SV74: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV141 ) )
= $true )
| ( ( element @ SV74 @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1202]) ).
thf(1322,plain,
! [SV142: $i,SV262: $i,SV75: $i] :
( ( ! [SY644: $i] :
( ~ ( in @ SV75 @ SV262 )
| ~ ( in @ SV142 @ SY644 )
| ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV262 @ SY644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1323,plain,
! [SV142: $i,SV75: $i] :
( ( ~ ! [SY528: $i] :
( ! [SY529: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY528 @ SY529 ) )
| ( in @ SV75 @ SY528 ) )
| ~ ! [SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY530 @ SY531 ) )
| ( in @ SV142 @ SY531 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1324,plain,
! [SV217: $i,SV76: $i] :
( ( ( ~ ( subset @ SV76 @ SV217 ) )
= $true )
| ( ( ! [SY599: $i] : ( subset @ ( cartesian_product2 @ SV76 @ SY599 ) @ ( cartesian_product2 @ SV217 @ SY599 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1325,plain,
! [SV218: $i,SV76: $i] :
( ( ( ~ ( subset @ SV76 @ SV218 ) )
= $true )
| ( ( ! [SY600: $i] : ( subset @ ( cartesian_product2 @ SY600 @ SV76 ) @ ( cartesian_product2 @ SY600 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1326,plain,
! [SV219: $i,SV168: $i] :
( ( ( ( ( set_difference @ SV168 @ SV219 )
!= SV168 ) )
= $true )
| ( ( disjoint @ SV168 @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1327,plain,
! [SV220: $i,SV169: $i] :
( ( ( ~ ( disjoint @ SV169 @ SV220 ) )
= $true )
| ( ( ( set_difference @ SV169 @ SV220 )
= SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1328,plain,
! [SV221: $i,SV77: $i,SV263: $i] :
( ( ~ ( relation @ SV263 )
| ~ ( in @ ( ordered_pair @ SV77 @ SV221 ) @ SV263 )
| ( in @ SV77 @ ( relation_dom @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1329,plain,
! [SV222: $i,SV77: $i,SV264: $i] :
( ( ~ ( relation @ SV264 )
| ~ ( in @ ( ordered_pair @ SV77 @ SV222 ) @ SV264 )
| ( in @ SV222 @ ( relation_rng @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1330,plain,
! [SV170: $i] :
( ( ( empty @ SV170 )
= $false )
| ( ( empty @ ( relation_rng @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1331,plain,
! [SV171: $i] :
( ( ( empty @ SV171 )
= $false )
| ( ( relation @ ( relation_rng @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1332,plain,
! [SV78: $i,SV143: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) )
= $true )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1333,plain,
! [SV78: $i,SV143: $i] :
( ( ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
| ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) )
= $true )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1334,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) )
| ~ ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) )
| ( SV265
= ( set_union2 @ SV79 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1335,plain,
! [SV224: $i,SV79: $i,SV266: $i] :
( ( ( SV266
!= ( set_union2 @ SV79 @ SV224 ) )
| ~ ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV266 )
| ( in @ SY645 @ SV79 )
| ( in @ SY645 @ SV224 ) )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1336,plain,
! [SV225: $i,SV172: $i] :
( ( ( disjoint @ SV172 @ SV225 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV172 )
| ~ ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1337,plain,
! [SV226: $i,SV173: $i] :
( ( ( ! [SY608: $i] :
( ~ ( in @ SY608 @ SV173 )
| ~ ( in @ SY608 @ SV226 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV173 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1338,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) ) )
| ( SV267
= ( set_difference @ SV80 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1339,plain,
! [SV228: $i,SV80: $i,SV268: $i] :
( ( ( SV268
!= ( set_difference @ SV80 @ SV228 ) )
| ~ ( ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV80 )
| ( in @ SY648 @ SV228 )
| ( in @ SY648 @ SV268 ) )
| ~ ~ ( ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) )
| ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1340,plain,
! [SV229: $i,SV174: $i] :
( ( ( ( ( set_difference @ SV174 @ SV229 )
!= empty_set ) )
= $true )
| ( ( subset @ SV174 @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1341,plain,
! [SV230: $i,SV175: $i] :
( ( ( ~ ( subset @ SV175 @ SV230 ) )
= $true )
| ( ( ( set_difference @ SV175 @ SV230 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1342,plain,
! [SV176: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV231 ) ) )
= $true )
| ( ( subset @ SV176 @ SV231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1343,plain,
! [SV232: $i,SV177: $i] :
( ( ( ~ ( subset @ SV177 @ SV232 ) )
= $true )
| ( ( ! [SY614: $i] :
( ~ ( in @ SY614 @ SV177 )
| ( in @ SY614 @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1344,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) ) )
| ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1345,plain,
! [SV234: $i,SV81: $i,SV270: $i] :
( ( ( SV270
!= ( set_intersection2 @ SV81 @ SV234 ) )
| ~ ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SV81 )
| ~ ( in @ SY651 @ SV234 )
| ( in @ SY651 @ SV270 ) )
| ~ ~ ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) )
| ~ ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1346,plain,
! [SV235: $i,SV178: $i] :
( ( ( ( ( set_difference @ SV178 @ SV235 )
!= empty_set ) )
= $true )
| ( ( subset @ SV178 @ SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1347,plain,
! [SV236: $i,SV179: $i] :
( ( ( ~ ( subset @ SV179 @ SV236 ) )
= $true )
| ( ( ( set_difference @ SV179 @ SV236 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1348,plain,
! [SV82: $i,SV237: $i] :
( ( ( ~ ( subset @ SV237 @ ( sK32_B @ SV82 ) )
| ( are_equipotent @ SV237 @ ( sK32_B @ SV82 ) ) )
= $true )
| ( ( in @ SV237 @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1349,plain,
! [SV82: $i] :
( ( ~ ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK32_B @ SV82 ) )
| ( in @ ( powerset @ SY436 ) @ ( sK32_B @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1350,plain,
! [SV82: $i] :
( ( ~ ~ ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) )
| ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1351,plain,
! [SV144: $i,SV271: $i,SV83: $i] :
( ( ! [SY654: $i] :
( ~ ( in @ SV83 @ SV271 )
| ~ ( in @ SV144 @ SY654 )
| ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV271 @ SY654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1352,plain,
! [SV144: $i,SV83: $i] :
( ( ~ ! [SY534: $i] :
( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY534 @ SY535 ) )
| ( in @ SV83 @ SY534 ) )
| ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY536 @ SY537 ) )
| ( in @ SV144 @ SY537 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1353,plain,
! [SV180: $i,SV238: $i] :
( ( ( ~ ( ~ ( ( ( sK29_C @ SV238 @ SV180 )
!= SV180 )
| ~ ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) )
| ~ ( ( ( sK29_C @ SV238 @ SV180 )
= SV180 )
| ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) ) ) )
= $true )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1354,plain,
! [SV181: $i,SV239: $i] :
( ( ( ( SV239
!= ( singleton @ SV181 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY620: $i] :
( ( SY620 != SV181 )
| ( in @ SY620 @ SV239 ) )
| ~ ! [SY621: $i] :
( ~ ( in @ SY621 @ SV239 )
| ( SY621 = SV181 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1355,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( ~ ( ! [SY622: $i] :
( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SY622 )
| ~ ( in @ SY622 @ SV182 ) )
| ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) )
| ~ ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 ) )
| ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) ) ) )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1356,plain,
! [SV183: $i,SV241: $i] :
( ( ( ( SV241
!= ( union @ SV183 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY623: $i] :
( ! [SY570: $i] :
( ~ ( in @ SY623 @ SY570 )
| ~ ( in @ SY570 @ SV183 ) )
| ( in @ SY623 @ SV241 ) )
| ~ ! [SY625: $i] :
( ~ ( in @ SY625 @ SV241 )
| ~ ( ~ ( in @ SY625 @ ( sK16_D @ SY625 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SY625 @ SV241 @ SV183 ) @ SV183 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1357,plain,
! [SV184: $i] :
( ( ( relation @ SV184 )
= $false )
| ( ( ( ( relation_dom @ SV184 )
!= empty_set )
| ( SV184 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1358,plain,
! [SV185: $i] :
( ( ( relation @ SV185 )
= $false )
| ( ( ( ( relation_rng @ SV185 )
!= empty_set )
| ( SV185 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1359,plain,
! [SV242: $i,SV186: $i] :
( ( ( ~ ( subset @ SV186 @ ( singleton @ SV242 ) ) )
= $true )
| ( ( ( SV186 = empty_set )
| ( SV186
= ( singleton @ SV242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1360,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1361,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1362,plain,
! [SV84: $i,SV243: $i] :
( ( ( ~ ( subset @ SV243 @ ( sK2_B @ SV84 ) )
| ( are_equipotent @ SV243 @ ( sK2_B @ SV84 ) ) )
= $true )
| ( ( in @ SV243 @ ( sK2_B @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1363,plain,
! [SV84: $i] :
( ( ~ ! [SY447: $i] :
( ~ ( ~ ! [SY448: $i] :
( ~ ( subset @ SY448 @ SY447 )
| ( in @ SY448 @ ( sK3_SY300 @ SY447 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY447 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SY447 @ ( sK2_B @ SV84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1364,plain,
! [SV84: $i] :
( ( ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1365,plain,
! [SV187: $i] :
( ( ( relation @ SV187 )
= $false )
| ( ( ( relation_rng @ SV187 )
= ( relation_dom @ ( relation_inverse @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1366,plain,
! [SV188: $i] :
( ( ( relation @ SV188 )
= $false )
| ( ( ( relation_dom @ SV188 )
= ( relation_rng @ ( relation_inverse @ SV188 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1367,plain,
! [SV272: $i,SV244: $i,SV85: $i] :
( ( ~ ( ~ ( ! [SY655: $i,SY656: $i] :
( ~ ( in @ SY655 @ SV85 )
| ~ ( in @ SY656 @ SV244 )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SY655 @ SY656 ) ) )
| ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) ) )
| ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1368,plain,
! [SV245: $i,SV85: $i,SV273: $i] :
( ( ( SV273
!= ( cartesian_product2 @ SV85 @ SV245 ) )
| ~ ( ~ ! [SY657: $i] :
( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ SV85 )
| ~ ( in @ SY632 @ SV245 )
| ( SY657
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ( in @ SY657 @ SV273 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV273 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SY660
!= ( ordered_pair @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1369,plain,
! [SV86: $i] :
( ( ( ! [SY461: $i] :
( ~ ( ~ ( ! [SY462: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ SY462 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY461 @ SV86 ) @ ( sK41_SY326 @ SY461 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SY461 @ SV86 ) @ SY461 ) ) )
| ( SY461
= ( relation_dom @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1370,plain,
! [SV86: $i] :
( ( ( ! [SY463: $i] :
( ( SY463
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY464: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY464 @ SY465 ) @ SV86 )
| ( in @ SY464 @ SY463 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SY463 )
| ( in @ ( ordered_pair @ SY466 @ ( sK39_D @ SY466 @ SY463 @ SV86 ) ) @ SV86 ) ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1371,plain,
! [SV246: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ SV246 ) )
= $true )
| ( ( subset @ ( singleton @ SV189 ) @ SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1372,plain,
! [SV247: $i,SV190: $i] :
( ( ( ~ ( subset @ ( singleton @ SV190 ) @ SV247 ) )
= $true )
| ( ( in @ SV190 @ SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1373,plain,
! [SV248: $i,SV191: $i] :
( ( ( ( ( set_intersection2 @ SV191 @ SV248 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV191 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1374,plain,
! [SV249: $i,SV192: $i] :
( ( ( ~ ( disjoint @ SV192 @ SV249 ) )
= $true )
| ( ( ( set_intersection2 @ SV192 @ SV249 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1375,plain,
! [SV88: $i] :
( ( ( ! [SY467: $i] :
( ~ ( ~ ( ! [SY468: $i] :
~ ( in @ ( ordered_pair @ SY468 @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY467 @ SV88 ) @ ( sK37_C @ SY467 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SY467 @ SV88 ) @ SY467 ) ) )
| ( SY467
= ( relation_rng @ SV88 ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1376,plain,
! [SV88: $i] :
( ( ( ! [SY469: $i] :
( ( SY469
!= ( relation_rng @ SV88 ) )
| ~ ( ~ ! [SY470: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY470 ) @ SV88 )
| ( in @ SY470 @ SY469 ) )
| ~ ! [SY472: $i] :
( ~ ( in @ SY472 @ SY469 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY472 @ SY469 @ SV88 ) @ SY472 ) @ SV88 ) ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1377,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[1256]) ).
thf(1378,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)],[1257]) ).
thf(1379,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1380,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1381,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) ) )
| ~ ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV89 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV250 ) ) )
| ( SV274
= ( unordered_pair @ SV89 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1382,plain,
! [SV251: $i,SV89: $i,SV275: $i] :
( ( ( SV275
!= ( unordered_pair @ SV89 @ SV251 ) )
| ~ ( ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ SV275 )
| ( SY661 = SV89 )
| ( SY661 = SV251 ) )
| ~ ~ ( ~ ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) )
| ~ ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1383,plain,
! [SV252: $i,SV193: $i] :
( ( ( ( ( set_difference @ SV193 @ ( singleton @ SV252 ) )
!= SV193 ) )
= $true )
| ( ( ~ ( in @ SV252 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1384,plain,
! [SV194: $i,SV253: $i] :
( ( ( in @ SV253 @ SV194 )
= $true )
| ( ( ( set_difference @ SV194 @ ( singleton @ SV253 ) )
= SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1385,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1386,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1387,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1388,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1389,plain,
! [SV90: $i,SV195: $i] :
( ( ( relation @ SV195 )
= $false )
| ( ( ~ ( ~ ! [SY579: $i] :
( ~ ( relation @ SY579 )
| ~ ( ~ ( ! [SY580: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ SY580 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY580 @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) ) )
| ( SY579
= ( relation_composition @ SV90 @ SV195 ) ) )
| ~ ! [SY581: $i] :
( ~ ( relation @ SY581 )
| ( SY581
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY582: $i,SY583: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY582 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY583 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY582 @ SY583 ) @ SY581 ) )
| ~ ! [SY585: $i,SY586: $i] :
( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SY581 )
| ~ ( ~ ( in @ ( ordered_pair @ SY585 @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) @ SY586 ) @ SV195 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1390,plain,
! [SV196: $i] :
( ( ( empty @ SV196 )
= $false )
| ( ( empty @ ( relation_dom @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1391,plain,
! [SV197: $i] :
( ( ( empty @ SV197 )
= $false )
| ( ( relation @ ( relation_dom @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1392,plain,
! [SV198: $i,SV254: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ~ ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) )
| ~ ( ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) ) ) )
= $true )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1393,plain,
! [SV199: $i,SV255: $i] :
( ( ( ( SV255
!= ( powerset @ SV199 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV255 )
| ( subset @ SY639 @ SV199 ) )
| ~ ! [SY640: $i] :
( ~ ( subset @ SY640 @ SV199 )
| ( in @ SY640 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1394,plain,
! [SV91: $i] :
( ( ( ! [SY489: $i] :
( ~ ( relation @ SY489 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY489 @ SV91 ) @ ( sK14_SY310 @ SY489 @ SV91 ) ) @ SY489 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY489 @ SV91 ) @ ( sK13_C @ SY489 @ SV91 ) ) @ SV91 ) ) )
| ( SY489
= ( relation_inverse @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1395,plain,
! [SV91: $i] :
( ( ( ! [SY490: $i] :
( ~ ( relation @ SY490 )
| ( SY490
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ ( ordered_pair @ SY491 @ SY492 ) @ SY490 )
| ( in @ ( ordered_pair @ SY492 @ SY491 ) @ SV91 ) )
| ~ ! [SY493: $i,SY494: $i] :
( ~ ( in @ ( ordered_pair @ SY494 @ SY493 ) @ SV91 )
| ( in @ ( ordered_pair @ SY493 @ SY494 ) @ SY490 ) ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1274]) ).
thf(1396,plain,
! [SV256: $i,SV200: $i] :
( ( ( ~ ( subset @ SV200 @ ( singleton @ SV256 ) ) )
= $true )
| ( ( ( SV200 = empty_set )
| ( SV200
= ( singleton @ SV256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1397,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1398,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1399,plain,
! [SV257: $i,SV201: $i] :
( ( ( ~ ( element @ SV201 @ ( powerset @ SV257 ) ) )
= $true )
| ( ( subset @ SV201 @ SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1400,plain,
! [SV258: $i,SV202: $i] :
( ( ( ~ ( subset @ SV202 @ SV258 ) )
= $true )
| ( ( element @ SV202 @ ( powerset @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1401,plain,
! [SV92: $i] :
( ( ( empty @ ( sK8_B @ SV92 ) )
= $false )
| ( ( empty @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1402,plain,
! [SV259: $i,SV276: $i,SV93: $i] :
( ( ~ ( in @ SV93 @ SV276 )
| ~ ( in @ SV259 @ SV276 )
| ( subset @ ( unordered_pair @ SV93 @ SV259 ) @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1403,plain,
! [SV93: $i] :
( ( ~ ! [SY497: $i,SY498: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY497 ) @ SY498 )
| ( in @ SV93 @ SY498 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1404,plain,
! [SV93: $i] :
( ( ~ ! [SY499: $i,SY500: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY499 ) @ SY500 )
| ( in @ SY499 @ SY500 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1405,plain,
! [SV260: $i,SV94: $i,SV277: $i] :
( ( ~ ( relation @ SV277 )
| ~ ( in @ ( ordered_pair @ SV94 @ SV260 ) @ SV277 )
| ( in @ SV94 @ ( relation_field @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1406,plain,
! [SV261: $i,SV94: $i,SV278: $i] :
( ( ~ ( relation @ SV278 )
| ~ ( in @ ( ordered_pair @ SV94 @ SV261 ) @ SV278 )
| ( in @ SV261 @ ( relation_field @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1407,plain,
! [SV204: $i] :
( ( ( SV204 = empty_set )
= $false )
| ( ( ! [SY594: $i] :
~ ( in @ SY594 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1408,plain,
! [SV279: $i,SV145: $i,SV95: $i] :
( ( ! [SY664: $i] :
( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SV279 @ SY664 ) )
| ( SV95 = SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1409,plain,
! [SV280: $i,SV145: $i,SV95: $i] :
( ( ! [SY665: $i] :
( ( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SV280 @ SY665 ) )
| ( SV145 = SY665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1410,plain,
! [SV96: $i] :
( ( ( ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV96 @ SY510 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SY510 ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1290]) ).
thf(1411,plain,
! [SV96: $i] :
( ( ( ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV96 @ SY511 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SY511 ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1291]) ).
thf(1412,plain,
! [SV205: $i] :
( ( ( ~ ! [SY595: $i,SY596: $i] :
( ( sK48_B @ SV205 )
!= ( ordered_pair @ SY595 @ SY596 ) )
| ~ ( in @ ( sK48_B @ SV205 ) @ SV205 ) )
= $false )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1413,plain,
! [SV206: $i] :
( ( ( relation @ SV206 )
= $false )
| ( ( ! [SY597: $i] :
( ( SY597
= ( ordered_pair @ ( sK46_C @ SY597 @ SV206 ) @ ( sK47_SY329 @ SY597 @ SV206 ) ) )
| ~ ( in @ SY597 @ SV206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1414,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)],[1296]) ).
thf(1415,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)],[1297]) ).
thf(1416,plain,
! [SV26: $i,SV102: $i,SV207: $i] :
( ( ( in @ SV207 @ SV102 )
= $false )
| ( ( in @ SV207 @ SV26 )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1417,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)],[1302]) ).
thf(1418,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)],[1303]) ).
thf(1419,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)],[1304]) ).
thf(1420,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)],[1305]) ).
thf(1421,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)],[1306]) ).
thf(1422,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)],[1307]) ).
thf(1423,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)],[1308]) ).
thf(1424,plain,
! [SV211: $i,SV162: $i] :
( ( ( in @ SV162 @ SV211 )
= $false )
| ( ( subset @ ( singleton @ SV162 ) @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1425,plain,
! [SV212: $i,SV163: $i] :
( ( ( subset @ ( singleton @ SV163 ) @ SV212 )
= $false )
| ( ( in @ SV163 @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1426,plain,
! [SV213: $i,SV164: $i] :
( ( ( ~ ( subset @ SV164 @ SV213 ) )
= $true )
| ( ( ~ ( subset @ SV213 @ SV164 ) )
= $true )
| ( ( SV164 = SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1427,plain,
! [SV281: $i] :
( ( ! [SY666: $i] :
( ( SV281 != SY666 )
| ( subset @ SV281 @ SY666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1428,plain,
! [SV282: $i] :
( ( ! [SY667: $i] :
( ( SV282 != SY667 )
| ( subset @ SY667 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1429,plain,
! [SV214: $i,SV165: $i] :
( ( ( SV165 = SV214 )
= $true )
| ( ( ~ ( subset @ SV165 @ SV214 ) )
= $true )
| ( ( proper_subset @ SV165 @ SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1430,plain,
! [SV283: $i] :
( ( ! [SY668: $i] :
( ~ ( proper_subset @ SV283 @ SY668 )
| ( SV283 != SY668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1431,plain,
! [SV284: $i] :
( ( ! [SY669: $i] :
( ~ ( proper_subset @ SV284 @ SY669 )
| ( subset @ SV284 @ SY669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1432,plain,
! [SV216: $i,SV167: $i,SV285: $i] :
( ( ( ~ ( in @ SV285 @ ( set_intersection2 @ SV167 @ SV216 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV167 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1433,plain,
! [SV74: $i,SV141: $i] :
( ( ( in @ ( sK33_C @ SV141 @ SV74 ) @ SV141 )
= $false )
| ( ( element @ SV74 @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1434,plain,
! [SV286: $i,SV142: $i,SV262: $i,SV75: $i] :
( ( ~ ( in @ SV75 @ SV262 )
| ~ ( in @ SV142 @ SV286 )
| ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV262 @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1435,plain,
! [SV142: $i,SV75: $i] :
( ( ~ ! [SY528: $i] :
( ! [SY529: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY528 @ SY529 ) )
| ( in @ SV75 @ SY528 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1436,plain,
! [SV142: $i,SV75: $i] :
( ( ~ ! [SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY530 @ SY531 ) )
| ( in @ SV142 @ SY531 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1437,plain,
! [SV217: $i,SV76: $i] :
( ( ( subset @ SV76 @ SV217 )
= $false )
| ( ( ! [SY599: $i] : ( subset @ ( cartesian_product2 @ SV76 @ SY599 ) @ ( cartesian_product2 @ SV217 @ SY599 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1438,plain,
! [SV218: $i,SV76: $i] :
( ( ( subset @ SV76 @ SV218 )
= $false )
| ( ( ! [SY600: $i] : ( subset @ ( cartesian_product2 @ SY600 @ SV76 ) @ ( cartesian_product2 @ SY600 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1439,plain,
! [SV219: $i,SV168: $i] :
( ( ( ( set_difference @ SV168 @ SV219 )
= SV168 )
= $false )
| ( ( disjoint @ SV168 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1440,plain,
! [SV220: $i,SV169: $i] :
( ( ( disjoint @ SV169 @ SV220 )
= $false )
| ( ( ( set_difference @ SV169 @ SV220 )
= SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1441,plain,
! [SV221: $i,SV77: $i,SV263: $i] :
( ( ( ~ ( relation @ SV263 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV77 @ SV221 ) @ SV263 )
| ( in @ SV77 @ ( relation_dom @ SV263 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1442,plain,
! [SV222: $i,SV77: $i,SV264: $i] :
( ( ( ~ ( relation @ SV264 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV77 @ SV222 ) @ SV264 )
| ( in @ SV222 @ ( relation_rng @ SV264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1443,plain,
! [SV78: $i,SV143: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) )
= $true )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1444,plain,
! [SV78: $i,SV143: $i] :
( ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
= $true )
| ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 )
= $true )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1445,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) )
| ~ ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1446,plain,
! [SV224: $i,SV79: $i,SV266: $i] :
( ( ( ( SV266
!= ( set_union2 @ SV79 @ SV224 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV266 )
| ( in @ SY645 @ SV79 )
| ( in @ SY645 @ SV224 ) )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1447,plain,
! [SV172: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV172 )
| ~ ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV225 ) )
= $false )
| ( ( disjoint @ SV172 @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1448,plain,
! [SV226: $i,SV173: $i,SV287: $i] :
( ( ( ~ ( in @ SV287 @ SV173 )
| ~ ( in @ SV287 @ SV226 ) )
= $true )
| ( ( ~ ( disjoint @ SV173 @ SV226 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1449,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) ) ) )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1450,plain,
! [SV228: $i,SV80: $i,SV268: $i] :
( ( ( ( SV268
!= ( set_difference @ SV80 @ SV228 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV80 )
| ( in @ SY648 @ SV228 )
| ( in @ SY648 @ SV268 ) )
| ~ ~ ( ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) )
| ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1451,plain,
! [SV229: $i,SV174: $i] :
( ( ( ( set_difference @ SV174 @ SV229 )
= empty_set )
= $false )
| ( ( subset @ SV174 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1452,plain,
! [SV230: $i,SV175: $i] :
( ( ( subset @ SV175 @ SV230 )
= $false )
| ( ( ( set_difference @ SV175 @ SV230 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1453,plain,
! [SV176: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV231 ) )
= $false )
| ( ( subset @ SV176 @ SV231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1454,plain,
! [SV232: $i,SV177: $i] :
( ( ( subset @ SV177 @ SV232 )
= $false )
| ( ( ! [SY614: $i] :
( ~ ( in @ SY614 @ SV177 )
| ( in @ SY614 @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1455,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) ) ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1456,plain,
! [SV234: $i,SV81: $i,SV270: $i] :
( ( ( ( SV270
!= ( set_intersection2 @ SV81 @ SV234 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SV81 )
| ~ ( in @ SY651 @ SV234 )
| ( in @ SY651 @ SV270 ) )
| ~ ~ ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) )
| ~ ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1457,plain,
! [SV235: $i,SV178: $i] :
( ( ( ( set_difference @ SV178 @ SV235 )
= empty_set )
= $false )
| ( ( subset @ SV178 @ SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1458,plain,
! [SV236: $i,SV179: $i] :
( ( ( subset @ SV179 @ SV236 )
= $false )
| ( ( ( set_difference @ SV179 @ SV236 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1459,plain,
! [SV82: $i,SV237: $i] :
( ( ( ~ ( subset @ SV237 @ ( sK32_B @ SV82 ) ) )
= $true )
| ( ( are_equipotent @ SV237 @ ( sK32_B @ SV82 ) )
= $true )
| ( ( in @ SV237 @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1460,plain,
! [SV82: $i] :
( ( ! [SY436: $i] :
( ~ ( in @ SY436 @ ( sK32_B @ SV82 ) )
| ( in @ ( powerset @ SY436 ) @ ( sK32_B @ SV82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1461,plain,
! [SV82: $i] :
( ( ~ ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) )
| ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1462,plain,
! [SV288: $i,SV144: $i,SV271: $i,SV83: $i] :
( ( ~ ( in @ SV83 @ SV271 )
| ~ ( in @ SV144 @ SV288 )
| ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV271 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1463,plain,
! [SV144: $i,SV83: $i] :
( ( ~ ! [SY534: $i] :
( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY534 @ SY535 ) )
| ( in @ SV83 @ SY534 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1464,plain,
! [SV144: $i,SV83: $i] :
( ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY536 @ SY537 ) )
| ( in @ SV144 @ SY537 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1465,plain,
! [SV180: $i,SV238: $i] :
( ( ( ~ ( ( ( sK29_C @ SV238 @ SV180 )
!= SV180 )
| ~ ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) )
| ~ ( ( ( sK29_C @ SV238 @ SV180 )
= SV180 )
| ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) ) )
= $false )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1466,plain,
! [SV181: $i,SV239: $i] :
( ( ( SV239
= ( singleton @ SV181 ) )
= $false )
| ( ( ~ ( ~ ! [SY620: $i] :
( ( SY620 != SV181 )
| ( in @ SY620 @ SV239 ) )
| ~ ! [SY621: $i] :
( ~ ( in @ SY621 @ SV239 )
| ( SY621 = SV181 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1467,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( ! [SY622: $i] :
( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SY622 )
| ~ ( in @ SY622 @ SV182 ) )
| ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) )
| ~ ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 ) )
| ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) ) )
= $false )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1468,plain,
! [SV183: $i,SV241: $i] :
( ( ( SV241
= ( union @ SV183 ) )
= $false )
| ( ( ~ ( ~ ! [SY623: $i] :
( ! [SY570: $i] :
( ~ ( in @ SY623 @ SY570 )
| ~ ( in @ SY570 @ SV183 ) )
| ( in @ SY623 @ SV241 ) )
| ~ ! [SY625: $i] :
( ~ ( in @ SY625 @ SV241 )
| ~ ( ~ ( in @ SY625 @ ( sK16_D @ SY625 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SY625 @ SV241 @ SV183 ) @ SV183 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1469,plain,
! [SV184: $i] :
( ( ( ( ( relation_dom @ SV184 )
!= empty_set ) )
= $true )
| ( ( SV184 = empty_set )
= $true )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1470,plain,
! [SV185: $i] :
( ( ( ( ( relation_rng @ SV185 )
!= empty_set ) )
= $true )
| ( ( SV185 = empty_set )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1471,plain,
! [SV242: $i,SV186: $i] :
( ( ( subset @ SV186 @ ( singleton @ SV242 ) )
= $false )
| ( ( ( SV186 = empty_set )
| ( SV186
= ( singleton @ SV242 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1472,plain,
! [SV289: $i] :
( ( ( SV289 != empty_set )
| ! [SY670: $i] : ( subset @ SV289 @ ( singleton @ SY670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1473,plain,
! [SV290: $i] :
( ( ! [SY671: $i] :
( ( SV290
!= ( singleton @ SY671 ) )
| ( subset @ SV290 @ ( singleton @ SY671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1474,plain,
! [SV84: $i,SV243: $i] :
( ( ( ~ ( subset @ SV243 @ ( sK2_B @ SV84 ) ) )
= $true )
| ( ( are_equipotent @ SV243 @ ( sK2_B @ SV84 ) )
= $true )
| ( ( in @ SV243 @ ( sK2_B @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1475,plain,
! [SV84: $i] :
( ( ! [SY447: $i] :
( ~ ( ~ ! [SY448: $i] :
( ~ ( subset @ SY448 @ SY447 )
| ( in @ SY448 @ ( sK3_SY300 @ SY447 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY447 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SY447 @ ( sK2_B @ SV84 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1476,plain,
! [SV84: $i] :
( ( ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1477,plain,
! [SV272: $i,SV244: $i,SV85: $i] :
( ( ( ~ ( ~ ( ! [SY655: $i,SY656: $i] :
( ~ ( in @ SY655 @ SV85 )
| ~ ( in @ SY656 @ SV244 )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SY655 @ SY656 ) ) )
| ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) ) ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1478,plain,
! [SV245: $i,SV85: $i,SV273: $i] :
( ( ( ( SV273
!= ( cartesian_product2 @ SV85 @ SV245 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY657: $i] :
( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ SV85 )
| ~ ( in @ SY632 @ SV245 )
| ( SY657
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ( in @ SY657 @ SV273 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV273 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SY660
!= ( ordered_pair @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1479,plain,
! [SV86: $i,SV291: $i] :
( ( ( ~ ( ~ ( ! [SY672: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SY672 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ ( sK41_SY326 @ SV291 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) ) )
| ( SV291
= ( relation_dom @ SV86 ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1480,plain,
! [SV86: $i,SV292: $i] :
( ( ( ( SV292
!= ( relation_dom @ SV86 ) )
| ~ ( ~ ! [SY673: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY673 @ SY465 ) @ SV86 )
| ( in @ SY673 @ SV292 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV292 )
| ( in @ ( ordered_pair @ SY675 @ ( sK39_D @ SY675 @ SV292 @ SV86 ) ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1481,plain,
! [SV246: $i,SV189: $i] :
( ( ( in @ SV189 @ SV246 )
= $false )
| ( ( subset @ ( singleton @ SV189 ) @ SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1482,plain,
! [SV247: $i,SV190: $i] :
( ( ( subset @ ( singleton @ SV190 ) @ SV247 )
= $false )
| ( ( in @ SV190 @ SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1483,plain,
! [SV248: $i,SV191: $i] :
( ( ( ( set_intersection2 @ SV191 @ SV248 )
= empty_set )
= $false )
| ( ( disjoint @ SV191 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1484,plain,
! [SV249: $i,SV192: $i] :
( ( ( disjoint @ SV192 @ SV249 )
= $false )
| ( ( ( set_intersection2 @ SV192 @ SV249 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1485,plain,
! [SV88: $i,SV293: $i] :
( ( ( ~ ( ~ ( ! [SY676: $i] :
~ ( in @ ( ordered_pair @ SY676 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV293 @ SV88 ) @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) ) )
| ( SV293
= ( relation_rng @ SV88 ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1486,plain,
! [SV88: $i,SV294: $i] :
( ( ( ( SV294
!= ( relation_rng @ SV88 ) )
| ~ ( ~ ! [SY677: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY677 ) @ SV88 )
| ( in @ SY677 @ SV294 ) )
| ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV294 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY679 @ SV294 @ SV88 ) @ SY679 ) @ SV88 ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1487,plain,
! [SV295: $i] :
( ( ( SV295 = empty_set )
| ! [SY680: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SY680 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SY680 @ SV295 ) @ ( sK45_SY327 @ SY680 @ SV295 ) ) )
| ~ ( in @ ( sK44_C @ SY680 @ SV295 ) @ SY680 ) )
| ~ ( ! [SY681: $i] :
( ~ ( in @ SY681 @ SV295 )
| ( in @ ( sK44_C @ SY680 @ SV295 ) @ SY681 ) )
| ( in @ ( sK44_C @ SY680 @ SV295 ) @ SY680 ) ) )
| ( SY680
= ( set_meet @ SV295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1488,plain,
! [SV296: $i] :
( ( ( SV296 = empty_set )
| ! [SY682: $i] :
( ( SY682
!= ( set_meet @ SV296 ) )
| ~ ( ~ ! [SY683: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY683 @ SY682 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SY683 @ ( sK43_D @ SY683 @ SY682 @ SV296 ) ) )
| ( in @ SY683 @ SY682 ) )
| ~ ! [SY684: $i] :
( ~ ( in @ SY684 @ SY682 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SV296 )
| ( in @ SY684 @ SY685 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1489,plain,
! [SV297: $i] :
( ( ( SV297 != empty_set )
| ! [SY686: $i] :
( ( SY686
!= ( set_meet @ SV297 ) )
| ( SY686 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1490,plain,
! [SV298: $i] :
( ( ( SV298 != empty_set )
| ! [SY687: $i] :
( ( SY687 != empty_set )
| ( SY687
= ( set_meet @ SV298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1491,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) ) )
| ~ ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV89 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV250 ) ) ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1492,plain,
! [SV251: $i,SV89: $i,SV275: $i] :
( ( ( ( SV275
!= ( unordered_pair @ SV89 @ SV251 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ SV275 )
| ( SY661 = SV89 )
| ( SY661 = SV251 ) )
| ~ ~ ( ~ ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) )
| ~ ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1493,plain,
! [SV252: $i,SV193: $i] :
( ( ( ( set_difference @ SV193 @ ( singleton @ SV252 ) )
= SV193 )
= $false )
| ( ( ~ ( in @ SV252 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1494,plain,
! [SV299: $i] :
( ( ( empty @ SV299 )
| ! [SY688: $i] :
( ~ ( element @ SY688 @ SV299 )
| ( in @ SY688 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1495,plain,
! [SV300: $i] :
( ( ( empty @ SV300 )
| ! [SY689: $i] :
( ~ ( in @ SY689 @ SV300 )
| ( element @ SY689 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1496,plain,
! [SV301: $i] :
( ( ~ ( empty @ SV301 )
| ! [SY690: $i] :
( ~ ( element @ SY690 @ SV301 )
| ( empty @ SY690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1497,plain,
! [SV302: $i] :
( ( ~ ( empty @ SV302 )
| ! [SY691: $i] :
( ~ ( empty @ SY691 )
| ( element @ SY691 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1498,plain,
! [SV90: $i,SV195: $i] :
( ( ( ~ ! [SY579: $i] :
( ~ ( relation @ SY579 )
| ~ ( ~ ( ! [SY580: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ SY580 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY580 @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) ) )
| ( SY579
= ( relation_composition @ SV90 @ SV195 ) ) )
| ~ ! [SY581: $i] :
( ~ ( relation @ SY581 )
| ( SY581
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY582: $i,SY583: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY582 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY583 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY582 @ SY583 ) @ SY581 ) )
| ~ ! [SY585: $i,SY586: $i] :
( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SY581 )
| ~ ( ~ ( in @ ( ordered_pair @ SY585 @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) @ SY586 ) @ SV195 ) ) ) ) ) )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1499,plain,
! [SV198: $i,SV254: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ~ ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) )
| ~ ( ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) ) )
= $false )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1500,plain,
! [SV199: $i,SV255: $i] :
( ( ( SV255
= ( powerset @ SV199 ) )
= $false )
| ( ( ~ ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV255 )
| ( subset @ SY639 @ SV199 ) )
| ~ ! [SY640: $i] :
( ~ ( subset @ SY640 @ SV199 )
| ( in @ SY640 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1501,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ( relation @ SV303 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) ) )
| ( SV303
= ( relation_inverse @ SV91 ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1502,plain,
! [SV91: $i,SV304: $i] :
( ( ( ~ ( relation @ SV304 )
| ( SV304
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY692: $i,SY693: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SV304 )
| ( in @ ( ordered_pair @ SY693 @ SY692 ) @ SV91 ) )
| ~ ! [SY694: $i,SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ SY694 ) @ SV91 )
| ( in @ ( ordered_pair @ SY694 @ SY695 ) @ SV304 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1503,plain,
! [SV256: $i,SV200: $i] :
( ( ( subset @ SV200 @ ( singleton @ SV256 ) )
= $false )
| ( ( ( SV200 = empty_set )
| ( SV200
= ( singleton @ SV256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1504,plain,
! [SV305: $i] :
( ( ( SV305 != empty_set )
| ! [SY696: $i] : ( subset @ SV305 @ ( singleton @ SY696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1505,plain,
! [SV306: $i] :
( ( ! [SY697: $i] :
( ( SV306
!= ( singleton @ SY697 ) )
| ( subset @ SV306 @ ( singleton @ SY697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1506,plain,
! [SV257: $i,SV201: $i] :
( ( ( element @ SV201 @ ( powerset @ SV257 ) )
= $false )
| ( ( subset @ SV201 @ SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1507,plain,
! [SV258: $i,SV202: $i] :
( ( ( subset @ SV202 @ SV258 )
= $false )
| ( ( element @ SV202 @ ( powerset @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1508,plain,
! [SV259: $i,SV276: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ SV276 )
| ~ ( in @ SV259 @ SV276 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV93 @ SV259 ) @ SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1509,plain,
! [SV93: $i] :
( ( ! [SY497: $i,SY498: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY497 ) @ SY498 )
| ( in @ SV93 @ SY498 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1510,plain,
! [SV93: $i] :
( ( ! [SY499: $i,SY500: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY499 ) @ SY500 )
| ( in @ SY499 @ SY500 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1511,plain,
! [SV260: $i,SV94: $i,SV277: $i] :
( ( ( ~ ( relation @ SV277 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV260 ) @ SV277 )
| ( in @ SV94 @ ( relation_field @ SV277 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1512,plain,
! [SV261: $i,SV94: $i,SV278: $i] :
( ( ( ~ ( relation @ SV278 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV261 ) @ SV278 )
| ( in @ SV261 @ ( relation_field @ SV278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1513,plain,
! [SV204: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ SV204 ) )
= $true )
| ( ( SV204 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1514,plain,
! [SV279: $i,SV145: $i,SV95: $i] :
( ( ( ! [SY664: $i] :
( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SV279 @ SY664 ) ) )
= $true )
| ( ( SV95 = SV279 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1515,plain,
! [SV308: $i,SV280: $i,SV145: $i,SV95: $i] :
( ( ( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SV280 @ SV308 ) )
| ( SV145 = SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1516,plain,
! [SV96: $i,SV309: $i] :
( ( ( ~ ( relation @ SV309 )
| ~ ( subset @ SV96 @ SV309 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SV309 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1517,plain,
! [SV96: $i,SV310: $i] :
( ( ( ~ ( relation @ SV310 )
| ~ ( subset @ SV96 @ SV310 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SV310 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1518,plain,
! [SV205: $i] :
( ( ( ~ ! [SY595: $i,SY596: $i] :
( ( sK48_B @ SV205 )
!= ( ordered_pair @ SY595 @ SY596 ) ) )
= $false )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1519,plain,
! [SV205: $i] :
( ( ( ~ ( in @ ( sK48_B @ SV205 ) @ SV205 ) )
= $false )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1520,plain,
! [SV206: $i,SV311: $i] :
( ( ( ( SV311
= ( ordered_pair @ ( sK46_C @ SV311 @ SV206 ) @ ( sK47_SY329 @ SV311 @ SV206 ) ) )
| ~ ( in @ SV311 @ SV206 ) )
= $true )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1521,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)],[1414]) ).
thf(1522,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)],[1415]) ).
thf(1523,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)],[1417]) ).
thf(1524,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)],[1423]) ).
thf(1525,plain,
! [SV213: $i,SV164: $i] :
( ( ( subset @ SV164 @ SV213 )
= $false )
| ( ( ~ ( subset @ SV213 @ SV164 ) )
= $true )
| ( ( SV164 = SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1526,plain,
! [SV312: $i,SV281: $i] :
( ( ( SV281 != SV312 )
| ( subset @ SV281 @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1527,plain,
! [SV313: $i,SV282: $i] :
( ( ( SV282 != SV313 )
| ( subset @ SV313 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1528,plain,
! [SV214: $i,SV165: $i] :
( ( ( subset @ SV165 @ SV214 )
= $false )
| ( ( SV165 = SV214 )
= $true )
| ( ( proper_subset @ SV165 @ SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1529,plain,
! [SV314: $i,SV283: $i] :
( ( ~ ( proper_subset @ SV283 @ SV314 )
| ( SV283 != SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1530,plain,
! [SV315: $i,SV284: $i] :
( ( ~ ( proper_subset @ SV284 @ SV315 )
| ( subset @ SV284 @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1531,plain,
! [SV216: $i,SV167: $i,SV285: $i] :
( ( ( in @ SV285 @ ( set_intersection2 @ SV167 @ SV216 ) )
= $false )
| ( ( ~ ( disjoint @ SV167 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1532,plain,
! [SV286: $i,SV142: $i,SV262: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV262 )
| ~ ( in @ SV142 @ SV286 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV262 @ SV286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1533,plain,
! [SV142: $i,SV75: $i] :
( ( ! [SY528: $i] :
( ! [SY529: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY528 @ SY529 ) )
| ( in @ SV75 @ SY528 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1534,plain,
! [SV142: $i,SV75: $i] :
( ( ! [SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SY530 @ SY531 ) )
| ( in @ SV142 @ SY531 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1535,plain,
! [SV217: $i,SV316: $i,SV76: $i] :
( ( ( subset @ ( cartesian_product2 @ SV76 @ SV316 ) @ ( cartesian_product2 @ SV217 @ SV316 ) )
= $true )
| ( ( subset @ SV76 @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1536,plain,
! [SV218: $i,SV76: $i,SV317: $i] :
( ( ( subset @ ( cartesian_product2 @ SV317 @ SV76 ) @ ( cartesian_product2 @ SV317 @ SV218 ) )
= $true )
| ( ( subset @ SV76 @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1537,plain,
! [SV221: $i,SV77: $i,SV263: $i] :
( ( ( relation @ SV263 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV77 @ SV221 ) @ SV263 )
| ( in @ SV77 @ ( relation_dom @ SV263 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1538,plain,
! [SV222: $i,SV77: $i,SV264: $i] :
( ( ( relation @ SV264 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV77 @ SV222 ) @ SV264 )
| ( in @ SV222 @ ( relation_rng @ SV264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1539,plain,
! [SV78: $i,SV143: $i] :
( ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 ) )
= $true )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1540,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) )
| ~ ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) )
= $false )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1541,plain,
! [SV224: $i,SV79: $i,SV266: $i] :
( ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false )
| ( ( ~ ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV266 )
| ( in @ SY645 @ SV79 )
| ( in @ SY645 @ SV224 ) )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1542,plain,
! [SV172: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV172 ) )
= $false )
| ( ( disjoint @ SV172 @ SV225 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1543,plain,
! [SV172: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV225 ) )
= $false )
| ( ( disjoint @ SV172 @ SV225 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1544,plain,
! [SV226: $i,SV173: $i,SV287: $i] :
( ( ( ~ ( in @ SV287 @ SV173 ) )
= $true )
| ( ( ~ ( in @ SV287 @ SV226 ) )
= $true )
| ( ( ~ ( disjoint @ SV173 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1545,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) ) )
= $false )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1546,plain,
! [SV228: $i,SV80: $i,SV268: $i] :
( ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false )
| ( ( ~ ( ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV80 )
| ( in @ SY648 @ SV228 )
| ( in @ SY648 @ SV268 ) )
| ~ ~ ( ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) )
| ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1547,plain,
! [SV176: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV176 ) )
= $false )
| ( ( subset @ SV176 @ SV231 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1548,plain,
! [SV176: $i,SV231: $i] :
( ( ( ~ ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV231 ) )
= $false )
| ( ( subset @ SV176 @ SV231 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1549,plain,
! [SV232: $i,SV177: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV177 )
| ( in @ SV318 @ SV232 ) )
= $true )
| ( ( subset @ SV177 @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1550,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) ) )
= $false )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1551,plain,
! [SV234: $i,SV81: $i,SV270: $i] :
( ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false )
| ( ( ~ ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SV81 )
| ~ ( in @ SY651 @ SV234 )
| ( in @ SY651 @ SV270 ) )
| ~ ~ ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) )
| ~ ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1552,plain,
! [SV82: $i,SV237: $i] :
( ( ( subset @ SV237 @ ( sK32_B @ SV82 ) )
= $false )
| ( ( are_equipotent @ SV237 @ ( sK32_B @ SV82 ) )
= $true )
| ( ( in @ SV237 @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1553,plain,
! [SV82: $i,SV319: $i] :
( ( ~ ( in @ SV319 @ ( sK32_B @ SV82 ) )
| ( in @ ( powerset @ SV319 ) @ ( sK32_B @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1554,plain,
! [SV82: $i] :
( ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) )
| ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1555,plain,
! [SV288: $i,SV144: $i,SV271: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV271 )
| ~ ( in @ SV144 @ SV288 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV271 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1556,plain,
! [SV144: $i,SV83: $i] :
( ( ! [SY534: $i] :
( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY534 @ SY535 ) )
| ( in @ SV83 @ SY534 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1557,plain,
! [SV144: $i,SV83: $i] :
( ( ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SY536 @ SY537 ) )
| ( in @ SV144 @ SY537 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1558,plain,
! [SV180: $i,SV238: $i] :
( ( ( ~ ( ( ( sK29_C @ SV238 @ SV180 )
!= SV180 )
| ~ ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) ) )
= $false )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1559,plain,
! [SV180: $i,SV238: $i] :
( ( ( ~ ( ( ( sK29_C @ SV238 @ SV180 )
= SV180 )
| ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) ) )
= $false )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1560,plain,
! [SV239: $i,SV181: $i] :
( ( ( ~ ! [SY620: $i] :
( ( SY620 != SV181 )
| ( in @ SY620 @ SV239 ) )
| ~ ! [SY621: $i] :
( ~ ( in @ SY621 @ SV239 )
| ( SY621 = SV181 ) ) )
= $false )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1561,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( ! [SY622: $i] :
( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SY622 )
| ~ ( in @ SY622 @ SV182 ) )
| ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) ) )
= $false )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1562,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) )
| ~ ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 ) )
| ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) ) )
= $false )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1563,plain,
! [SV241: $i,SV183: $i] :
( ( ( ~ ! [SY623: $i] :
( ! [SY570: $i] :
( ~ ( in @ SY623 @ SY570 )
| ~ ( in @ SY570 @ SV183 ) )
| ( in @ SY623 @ SV241 ) )
| ~ ! [SY625: $i] :
( ~ ( in @ SY625 @ SV241 )
| ~ ( ~ ( in @ SY625 @ ( sK16_D @ SY625 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SY625 @ SV241 @ SV183 ) @ SV183 ) ) ) )
= $false )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1564,plain,
! [SV184: $i] :
( ( ( ( relation_dom @ SV184 )
= empty_set )
= $false )
| ( ( SV184 = empty_set )
= $true )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1565,plain,
! [SV185: $i] :
( ( ( ( relation_rng @ SV185 )
= empty_set )
= $false )
| ( ( SV185 = empty_set )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1566,plain,
! [SV242: $i,SV186: $i] :
( ( ( SV186 = empty_set )
= $true )
| ( ( SV186
= ( singleton @ SV242 ) )
= $true )
| ( ( subset @ SV186 @ ( singleton @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1567,plain,
! [SV289: $i] :
( ( ( ( SV289 != empty_set ) )
= $true )
| ( ( ! [SY670: $i] : ( subset @ SV289 @ ( singleton @ SY670 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1568,plain,
! [SV320: $i,SV290: $i] :
( ( ( SV290
!= ( singleton @ SV320 ) )
| ( subset @ SV290 @ ( singleton @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1569,plain,
! [SV84: $i,SV243: $i] :
( ( ( subset @ SV243 @ ( sK2_B @ SV84 ) )
= $false )
| ( ( are_equipotent @ SV243 @ ( sK2_B @ SV84 ) )
= $true )
| ( ( in @ SV243 @ ( sK2_B @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1570,plain,
! [SV84: $i,SV321: $i] :
( ( ~ ( ~ ! [SY698: $i] :
( ~ ( subset @ SY698 @ SV321 )
| ( in @ SY698 @ ( sK3_SY300 @ SV321 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SV321 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1571,plain,
! [SV84: $i] :
( ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) )
| ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1572,plain,
! [SV272: $i,SV244: $i,SV85: $i] :
( ( ( ~ ( ! [SY655: $i,SY656: $i] :
( ~ ( in @ SY655 @ SV85 )
| ~ ( in @ SY656 @ SV244 )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SY655 @ SY656 ) ) )
| ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) ) )
= $false )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1573,plain,
! [SV245: $i,SV85: $i,SV273: $i] :
( ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false )
| ( ( ~ ( ~ ! [SY657: $i] :
( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ SV85 )
| ~ ( in @ SY632 @ SV245 )
| ( SY657
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ( in @ SY657 @ SV273 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV273 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SY660
!= ( ordered_pair @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1574,plain,
! [SV86: $i,SV291: $i] :
( ( ( ~ ( ~ ( ! [SY672: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SY672 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ ( sK41_SY326 @ SV291 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) ) ) )
= $true )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1575,plain,
! [SV86: $i,SV292: $i] :
( ( ( ( SV292
!= ( relation_dom @ SV86 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY673: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY673 @ SY465 ) @ SV86 )
| ( in @ SY673 @ SV292 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV292 )
| ( in @ ( ordered_pair @ SY675 @ ( sK39_D @ SY675 @ SV292 @ SV86 ) ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1576,plain,
! [SV88: $i,SV293: $i] :
( ( ( ~ ( ~ ( ! [SY676: $i] :
~ ( in @ ( ordered_pair @ SY676 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV293 @ SV88 ) @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) ) ) )
= $true )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1577,plain,
! [SV88: $i,SV294: $i] :
( ( ( ( SV294
!= ( relation_rng @ SV88 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY677: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY677 ) @ SV88 )
| ( in @ SY677 @ SV294 ) )
| ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV294 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY679 @ SV294 @ SV88 ) @ SY679 ) @ SV88 ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1578,plain,
! [SV295: $i] :
( ( ( SV295 = empty_set )
= $true )
| ( ( ! [SY680: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SY680 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SY680 @ SV295 ) @ ( sK45_SY327 @ SY680 @ SV295 ) ) )
| ~ ( in @ ( sK44_C @ SY680 @ SV295 ) @ SY680 ) )
| ~ ( ! [SY681: $i] :
( ~ ( in @ SY681 @ SV295 )
| ( in @ ( sK44_C @ SY680 @ SV295 ) @ SY681 ) )
| ( in @ ( sK44_C @ SY680 @ SV295 ) @ SY680 ) ) )
| ( SY680
= ( set_meet @ SV295 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1579,plain,
! [SV296: $i] :
( ( ( SV296 = empty_set )
= $true )
| ( ( ! [SY682: $i] :
( ( SY682
!= ( set_meet @ SV296 ) )
| ~ ( ~ ! [SY683: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY683 @ SY682 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SY683 @ ( sK43_D @ SY683 @ SY682 @ SV296 ) ) )
| ( in @ SY683 @ SY682 ) )
| ~ ! [SY684: $i] :
( ~ ( in @ SY684 @ SY682 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SV296 )
| ( in @ SY684 @ SY685 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1580,plain,
! [SV297: $i] :
( ( ( ( SV297 != empty_set ) )
= $true )
| ( ( ! [SY686: $i] :
( ( SY686
!= ( set_meet @ SV297 ) )
| ( SY686 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1581,plain,
! [SV298: $i] :
( ( ( ( SV298 != empty_set ) )
= $true )
| ( ( ! [SY687: $i] :
( ( SY687 != empty_set )
| ( SY687
= ( set_meet @ SV298 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1582,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) ) )
| ~ ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV89 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV250 ) ) )
= $false )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1583,plain,
! [SV251: $i,SV89: $i,SV275: $i] :
( ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false )
| ( ( ~ ( ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ SV275 )
| ( SY661 = SV89 )
| ( SY661 = SV251 ) )
| ~ ~ ( ~ ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) )
| ~ ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1584,plain,
! [SV193: $i,SV252: $i] :
( ( ( in @ SV252 @ SV193 )
= $false )
| ( ( ( set_difference @ SV193 @ ( singleton @ SV252 ) )
= SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1585,plain,
! [SV299: $i] :
( ( ( empty @ SV299 )
= $true )
| ( ( ! [SY688: $i] :
( ~ ( element @ SY688 @ SV299 )
| ( in @ SY688 @ SV299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1494]) ).
thf(1586,plain,
! [SV300: $i] :
( ( ( empty @ SV300 )
= $true )
| ( ( ! [SY689: $i] :
( ~ ( in @ SY689 @ SV300 )
| ( element @ SY689 @ SV300 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1495]) ).
thf(1587,plain,
! [SV301: $i] :
( ( ( ~ ( empty @ SV301 ) )
= $true )
| ( ( ! [SY690: $i] :
( ~ ( element @ SY690 @ SV301 )
| ( empty @ SY690 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1588,plain,
! [SV302: $i] :
( ( ( ~ ( empty @ SV302 ) )
= $true )
| ( ( ! [SY691: $i] :
( ~ ( empty @ SY691 )
| ( element @ SY691 @ SV302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1589,plain,
! [SV90: $i,SV195: $i] :
( ( ( ~ ! [SY579: $i] :
( ~ ( relation @ SY579 )
| ~ ( ~ ( ! [SY580: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ SY580 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY580 @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) ) )
| ( SY579
= ( relation_composition @ SV90 @ SV195 ) ) ) )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1498]) ).
thf(1590,plain,
! [SV195: $i,SV90: $i] :
( ( ( ~ ! [SY581: $i] :
( ~ ( relation @ SY581 )
| ( SY581
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY582: $i,SY583: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY582 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY583 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY582 @ SY583 ) @ SY581 ) )
| ~ ! [SY585: $i,SY586: $i] :
( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SY581 )
| ~ ( ~ ( in @ ( ordered_pair @ SY585 @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) @ SY586 ) @ SV195 ) ) ) ) ) )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1498]) ).
thf(1591,plain,
! [SV198: $i,SV254: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ~ ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) ) )
= $false )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1592,plain,
! [SV198: $i,SV254: $i] :
( ( ( ~ ( ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) ) )
= $false )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1593,plain,
! [SV199: $i,SV255: $i] :
( ( ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV255 )
| ( subset @ SY639 @ SV199 ) )
| ~ ! [SY640: $i] :
( ~ ( subset @ SY640 @ SV199 )
| ( in @ SY640 @ SV255 ) ) )
= $false )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1594,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ( relation @ SV303 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) ) )
| ( SV303
= ( relation_inverse @ SV91 ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1595,plain,
! [SV91: $i,SV304: $i] :
( ( ( ~ ( relation @ SV304 ) )
= $true )
| ( ( ( SV304
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY692: $i,SY693: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SV304 )
| ( in @ ( ordered_pair @ SY693 @ SY692 ) @ SV91 ) )
| ~ ! [SY694: $i,SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ SY694 ) @ SV91 )
| ( in @ ( ordered_pair @ SY694 @ SY695 ) @ SV304 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1596,plain,
! [SV256: $i,SV200: $i] :
( ( ( SV200 = empty_set )
= $true )
| ( ( SV200
= ( singleton @ SV256 ) )
= $true )
| ( ( subset @ SV200 @ ( singleton @ SV256 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1597,plain,
! [SV305: $i] :
( ( ( ( SV305 != empty_set ) )
= $true )
| ( ( ! [SY696: $i] : ( subset @ SV305 @ ( singleton @ SY696 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1598,plain,
! [SV322: $i,SV306: $i] :
( ( ( SV306
!= ( singleton @ SV322 ) )
| ( subset @ SV306 @ ( singleton @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1599,plain,
! [SV259: $i,SV276: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ SV276 ) )
= $true )
| ( ( ~ ( in @ SV259 @ SV276 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV93 @ SV259 ) @ SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1600,plain,
! [SV323: $i,SV93: $i] :
( ( ! [SY699: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SV323 ) @ SY699 )
| ( in @ SV93 @ SY699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1601,plain,
! [SV324: $i,SV93: $i] :
( ( ! [SY700: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SV324 ) @ SY700 )
| ( in @ SV324 @ SY700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1602,plain,
! [SV260: $i,SV94: $i,SV277: $i] :
( ( ( relation @ SV277 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV260 ) @ SV277 )
| ( in @ SV94 @ ( relation_field @ SV277 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1603,plain,
! [SV261: $i,SV94: $i,SV278: $i] :
( ( ( relation @ SV278 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV261 ) @ SV278 )
| ( in @ SV261 @ ( relation_field @ SV278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1604,plain,
! [SV204: $i,SV307: $i] :
( ( ( in @ SV307 @ SV204 )
= $false )
| ( ( SV204 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1605,plain,
! [SV325: $i,SV279: $i,SV145: $i,SV95: $i] :
( ( ( ( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SV279 @ SV325 ) ) )
= $true )
| ( ( SV95 = SV279 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1606,plain,
! [SV308: $i,SV280: $i,SV145: $i,SV95: $i] :
( ( ( ( ( ordered_pair @ SV95 @ SV145 )
!= ( ordered_pair @ SV280 @ SV308 ) ) )
= $true )
| ( ( SV145 = SV308 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1607,plain,
! [SV96: $i,SV309: $i] :
( ( ( ~ ( relation @ SV309 ) )
= $true )
| ( ( ~ ( subset @ SV96 @ SV309 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SV309 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1608,plain,
! [SV96: $i,SV310: $i] :
( ( ( ~ ( relation @ SV310 ) )
= $true )
| ( ( ~ ( subset @ SV96 @ SV310 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SV310 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1609,plain,
! [SV205: $i] :
( ( ( ! [SY595: $i,SY596: $i] :
( ( sK48_B @ SV205 )
!= ( ordered_pair @ SY595 @ SY596 ) ) )
= $true )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1610,plain,
! [SV205: $i] :
( ( ( in @ ( sK48_B @ SV205 ) @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1519]) ).
thf(1611,plain,
! [SV206: $i,SV311: $i] :
( ( ( SV311
= ( ordered_pair @ ( sK46_C @ SV311 @ SV206 ) @ ( sK47_SY329 @ SV311 @ SV206 ) ) )
= $true )
| ( ( ~ ( in @ SV311 @ SV206 ) )
= $true )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1612,plain,
! [SV164: $i,SV213: $i] :
( ( ( subset @ SV213 @ SV164 )
= $false )
| ( ( subset @ SV164 @ SV213 )
= $false )
| ( ( SV164 = SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1613,plain,
! [SV312: $i,SV281: $i] :
( ( ( ( SV281 != SV312 ) )
= $true )
| ( ( subset @ SV281 @ SV312 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1614,plain,
! [SV313: $i,SV282: $i] :
( ( ( ( SV282 != SV313 ) )
= $true )
| ( ( subset @ SV313 @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1615,plain,
! [SV314: $i,SV283: $i] :
( ( ( ~ ( proper_subset @ SV283 @ SV314 ) )
= $true )
| ( ( ( SV283 != SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1616,plain,
! [SV315: $i,SV284: $i] :
( ( ( ~ ( proper_subset @ SV284 @ SV315 ) )
= $true )
| ( ( subset @ SV284 @ SV315 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1617,plain,
! [SV285: $i,SV216: $i,SV167: $i] :
( ( ( disjoint @ SV167 @ SV216 )
= $false )
| ( ( in @ SV285 @ ( set_intersection2 @ SV167 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1618,plain,
! [SV286: $i,SV142: $i,SV262: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV262 ) )
= $true )
| ( ( ~ ( in @ SV142 @ SV286 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV262 @ SV286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1619,plain,
! [SV326: $i,SV142: $i,SV75: $i] :
( ( ! [SY701: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV326 @ SY701 ) )
| ( in @ SV75 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1620,plain,
! [SV327: $i,SV142: $i,SV75: $i] :
( ( ! [SY702: $i] :
( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV327 @ SY702 ) )
| ( in @ SV142 @ SY702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1621,plain,
! [SV263: $i,SV221: $i,SV77: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV77 @ SV221 ) @ SV263 ) )
= $true )
| ( ( in @ SV77 @ ( relation_dom @ SV263 ) )
= $true )
| ( ( relation @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1622,plain,
! [SV264: $i,SV222: $i,SV77: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV77 @ SV222 ) @ SV264 ) )
= $true )
| ( ( in @ SV222 @ ( relation_rng @ SV264 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1623,plain,
! [SV78: $i,SV143: $i] :
( ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV143 )
= $false )
| ( ( in @ ( sK4_C @ SV143 @ SV78 ) @ SV78 )
= $false )
| ( ( SV78 = SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1624,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) ) )
= $false )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1625,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) )
= $false )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1626,plain,
! [SV224: $i,SV79: $i,SV266: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV266 )
| ( in @ SY645 @ SV79 )
| ( in @ SY645 @ SV224 ) )
| ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) ) )
= $false )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1627,plain,
! [SV172: $i,SV225: $i] :
( ( ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV172 )
= $true )
| ( ( disjoint @ SV172 @ SV225 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1628,plain,
! [SV172: $i,SV225: $i] :
( ( ( in @ ( sK31_C @ SV225 @ SV172 ) @ SV225 )
= $true )
| ( ( disjoint @ SV172 @ SV225 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1629,plain,
! [SV226: $i,SV173: $i,SV287: $i] :
( ( ( in @ SV287 @ SV173 )
= $false )
| ( ( ~ ( in @ SV287 @ SV226 ) )
= $true )
| ( ( ~ ( disjoint @ SV173 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1630,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) )
= $false )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1631,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) ) )
= $false )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1632,plain,
! [SV268: $i,SV228: $i,SV80: $i] :
( ( ( ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV80 )
| ( in @ SY648 @ SV228 )
| ( in @ SY648 @ SV268 ) )
| ~ ~ ( ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) )
| ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) ) )
= $false )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1633,plain,
! [SV176: $i,SV231: $i] :
( ( ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV176 @ SV231 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1634,plain,
! [SV176: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV231 ) )
= $true )
| ( ( subset @ SV176 @ SV231 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1548]) ).
thf(1635,plain,
! [SV232: $i,SV177: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV177 ) )
= $true )
| ( ( in @ SV318 @ SV232 )
= $true )
| ( ( subset @ SV177 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1636,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) )
= $false )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1637,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) ) )
= $false )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1638,plain,
! [SV270: $i,SV234: $i,SV81: $i] :
( ( ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SV81 )
| ~ ( in @ SY651 @ SV234 )
| ( in @ SY651 @ SV270 ) )
| ~ ~ ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) )
| ~ ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) ) )
= $false )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1639,plain,
! [SV82: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ ( sK32_B @ SV82 ) ) )
= $true )
| ( ( in @ ( powerset @ SV319 ) @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1640,plain,
! [SV82: $i] :
( ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1641,plain,
! [SV82: $i] :
( ( ~ ( in @ SV82 @ ( sK32_B @ SV82 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1642,plain,
! [SV288: $i,SV144: $i,SV271: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV271 ) )
= $true )
| ( ( ~ ( in @ SV144 @ SV288 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV271 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1643,plain,
! [SV328: $i,SV144: $i,SV83: $i] :
( ( ! [SY703: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV328 @ SY703 ) )
| ( in @ SV83 @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1644,plain,
! [SV329: $i,SV144: $i,SV83: $i] :
( ( ! [SY704: $i] :
( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV329 @ SY704 ) )
| ( in @ SV144 @ SY704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1645,plain,
! [SV180: $i,SV238: $i] :
( ( ( ( ( sK29_C @ SV238 @ SV180 )
!= SV180 )
| ~ ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) )
= $true )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1646,plain,
! [SV180: $i,SV238: $i] :
( ( ( ( ( sK29_C @ SV238 @ SV180 )
= SV180 )
| ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) )
= $true )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1647,plain,
! [SV239: $i,SV181: $i] :
( ( ( ~ ! [SY620: $i] :
( ( SY620 != SV181 )
| ( in @ SY620 @ SV239 ) ) )
= $false )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1648,plain,
! [SV181: $i,SV239: $i] :
( ( ( ~ ! [SY621: $i] :
( ~ ( in @ SY621 @ SV239 )
| ( SY621 = SV181 ) ) )
= $false )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1649,plain,
! [SV182: $i,SV240: $i] :
( ( ( ! [SY622: $i] :
( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SY622 )
| ~ ( in @ SY622 @ SV182 ) )
| ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1650,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) )
| ~ ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 ) )
| ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1651,plain,
! [SV241: $i,SV183: $i] :
( ( ( ~ ! [SY623: $i] :
( ! [SY570: $i] :
( ~ ( in @ SY623 @ SY570 )
| ~ ( in @ SY570 @ SV183 ) )
| ( in @ SY623 @ SV241 ) ) )
= $false )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1652,plain,
! [SV183: $i,SV241: $i] :
( ( ( ~ ! [SY625: $i] :
( ~ ( in @ SY625 @ SV241 )
| ~ ( ~ ( in @ SY625 @ ( sK16_D @ SY625 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SY625 @ SV241 @ SV183 ) @ SV183 ) ) ) )
= $false )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1653,plain,
! [SV289: $i] :
( ( ( SV289 = empty_set )
= $false )
| ( ( ! [SY670: $i] : ( subset @ SV289 @ ( singleton @ SY670 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1654,plain,
! [SV320: $i,SV290: $i] :
( ( ( ( SV290
!= ( singleton @ SV320 ) ) )
= $true )
| ( ( subset @ SV290 @ ( singleton @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1655,plain,
! [SV84: $i,SV321: $i] :
( ( ( ~ ( ~ ! [SY698: $i] :
( ~ ( subset @ SY698 @ SV321 )
| ( in @ SY698 @ ( sK3_SY300 @ SV321 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SV321 @ SV84 ) @ ( sK2_B @ SV84 ) ) ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1656,plain,
! [SV84: $i] :
( ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1571]) ).
thf(1657,plain,
! [SV84: $i] :
( ( ~ ( in @ SV84 @ ( sK2_B @ SV84 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1571]) ).
thf(1658,plain,
! [SV272: $i,SV244: $i,SV85: $i] :
( ( ( ~ ( ! [SY655: $i,SY656: $i] :
( ~ ( in @ SY655 @ SV85 )
| ~ ( in @ SY656 @ SV244 )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SY655 @ SY656 ) ) )
| ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) ) )
= $false )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1659,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) ) )
= $false )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1660,plain,
! [SV273: $i,SV245: $i,SV85: $i] :
( ( ( ~ ! [SY657: $i] :
( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ SV85 )
| ~ ( in @ SY632 @ SV245 )
| ( SY657
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ( in @ SY657 @ SV273 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV273 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SY660
!= ( ordered_pair @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) ) ) ) ) )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1661,plain,
! [SV86: $i,SV291: $i] :
( ( ( ~ ( ! [SY672: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SY672 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ ( sK41_SY326 @ SV291 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) ) )
= $false )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1662,plain,
! [SV86: $i,SV292: $i] :
( ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( ~ ( ~ ! [SY673: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY673 @ SY465 ) @ SV86 )
| ( in @ SY673 @ SV292 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV292 )
| ( in @ ( ordered_pair @ SY675 @ ( sK39_D @ SY675 @ SV292 @ SV86 ) ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1663,plain,
! [SV88: $i,SV293: $i] :
( ( ( ~ ( ! [SY676: $i] :
~ ( in @ ( ordered_pair @ SY676 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV293 @ SV88 ) @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) ) )
= $false )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1664,plain,
! [SV88: $i,SV294: $i] :
( ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( ~ ( ~ ! [SY677: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY677 ) @ SV88 )
| ( in @ SY677 @ SV294 ) )
| ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV294 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY679 @ SV294 @ SV88 ) @ SY679 ) @ SV88 ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1665,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) )
| ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
| ~ ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV295 )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) ) )
| ( SV330
= ( set_meet @ SV295 ) ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1666,plain,
! [SV296: $i,SV331: $i] :
( ( ( ( SV331
!= ( set_meet @ SV296 ) )
| ~ ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV331 @ SV296 ) ) )
| ( in @ SY706 @ SV331 ) )
| ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV331 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SV296 )
| ( in @ SY707 @ SY685 ) ) ) ) )
= $true )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1667,plain,
! [SV297: $i] :
( ( ( SV297 = empty_set )
= $false )
| ( ( ! [SY686: $i] :
( ( SY686
!= ( set_meet @ SV297 ) )
| ( SY686 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1668,plain,
! [SV298: $i] :
( ( ( SV298 = empty_set )
= $false )
| ( ( ! [SY687: $i] :
( ( SY687 != empty_set )
| ( SY687
= ( set_meet @ SV298 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1669,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) ) ) )
= $false )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1670,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV89 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV250 ) ) )
= $false )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1671,plain,
! [SV251: $i,SV89: $i,SV275: $i] :
( ( ( ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ SV275 )
| ( SY661 = SV89 )
| ( SY661 = SV251 ) )
| ~ ~ ( ~ ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) )
| ~ ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) ) )
= $false )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1672,plain,
! [SV299: $i,SV332: $i] :
( ( ( ~ ( element @ SV332 @ SV299 )
| ( in @ SV332 @ SV299 ) )
= $true )
| ( ( empty @ SV299 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1673,plain,
! [SV300: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV300 )
| ( element @ SV333 @ SV300 ) )
= $true )
| ( ( empty @ SV300 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1674,plain,
! [SV301: $i] :
( ( ( empty @ SV301 )
= $false )
| ( ( ! [SY690: $i] :
( ~ ( element @ SY690 @ SV301 )
| ( empty @ SY690 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1675,plain,
! [SV302: $i] :
( ( ( empty @ SV302 )
= $false )
| ( ( ! [SY691: $i] :
( ~ ( empty @ SY691 )
| ( element @ SY691 @ SV302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1676,plain,
! [SV90: $i,SV195: $i] :
( ( ( ! [SY579: $i] :
( ~ ( relation @ SY579 )
| ~ ( ~ ( ! [SY580: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ SY580 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY580 @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY579 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SY579 @ SV195 @ SV90 ) ) @ SY579 ) ) )
| ( SY579
= ( relation_composition @ SV90 @ SV195 ) ) ) )
= $true )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1677,plain,
! [SV195: $i,SV90: $i] :
( ( ( ! [SY581: $i] :
( ~ ( relation @ SY581 )
| ( SY581
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY582: $i,SY583: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY582 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY583 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY582 @ SY583 ) @ SY581 ) )
| ~ ! [SY585: $i,SY586: $i] :
( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SY581 )
| ~ ( ~ ( in @ ( ordered_pair @ SY585 @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY586 @ SY585 @ SY581 @ SV195 @ SV90 ) @ SY586 ) @ SV195 ) ) ) ) ) )
= $true )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1678,plain,
! [SV198: $i,SV254: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ~ ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) )
= $true )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1679,plain,
! [SV198: $i,SV254: $i] :
( ( ( ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
| ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) )
= $true )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1680,plain,
! [SV199: $i,SV255: $i] :
( ( ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV255 )
| ( subset @ SY639 @ SV199 ) ) )
= $false )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1681,plain,
! [SV255: $i,SV199: $i] :
( ( ( ~ ! [SY640: $i] :
( ~ ( subset @ SY640 @ SV199 )
| ( in @ SY640 @ SV255 ) ) )
= $false )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1682,plain,
! [SV91: $i,SV303: $i] :
( ( ( relation @ SV303 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) ) )
| ( SV303
= ( relation_inverse @ SV91 ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1683,plain,
! [SV91: $i,SV304: $i] :
( ( ( relation @ SV304 )
= $false )
| ( ( ( SV304
!= ( relation_inverse @ SV91 ) )
| ~ ( ~ ! [SY692: $i,SY693: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SV304 )
| ( in @ ( ordered_pair @ SY693 @ SY692 ) @ SV91 ) )
| ~ ! [SY694: $i,SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ SY694 ) @ SV91 )
| ( in @ ( ordered_pair @ SY694 @ SY695 ) @ SV304 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1684,plain,
! [SV305: $i] :
( ( ( SV305 = empty_set )
= $false )
| ( ( ! [SY696: $i] : ( subset @ SV305 @ ( singleton @ SY696 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1685,plain,
! [SV322: $i,SV306: $i] :
( ( ( ( SV306
!= ( singleton @ SV322 ) ) )
= $true )
| ( ( subset @ SV306 @ ( singleton @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1686,plain,
! [SV259: $i,SV276: $i,SV93: $i] :
( ( ( in @ SV93 @ SV276 )
= $false )
| ( ( ~ ( in @ SV259 @ SV276 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV93 @ SV259 ) @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1687,plain,
! [SV334: $i,SV323: $i,SV93: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV93 @ SV323 ) @ SV334 )
| ( in @ SV93 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1688,plain,
! [SV335: $i,SV324: $i,SV93: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV93 @ SV324 ) @ SV335 )
| ( in @ SV324 @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1689,plain,
! [SV277: $i,SV260: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV260 ) @ SV277 ) )
= $true )
| ( ( in @ SV94 @ ( relation_field @ SV277 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1690,plain,
! [SV278: $i,SV261: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV261 ) @ SV278 ) )
= $true )
| ( ( in @ SV261 @ ( relation_field @ SV278 ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1603]) ).
thf(1691,plain,
! [SV325: $i,SV279: $i,SV145: $i,SV95: $i] :
( ( ( ( ordered_pair @ SV95 @ SV145 )
= ( ordered_pair @ SV279 @ SV325 ) )
= $false )
| ( ( SV95 = SV279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1692,plain,
! [SV308: $i,SV280: $i,SV145: $i,SV95: $i] :
( ( ( ( ordered_pair @ SV95 @ SV145 )
= ( ordered_pair @ SV280 @ SV308 ) )
= $false )
| ( ( SV145 = SV308 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1693,plain,
! [SV96: $i,SV309: $i] :
( ( ( relation @ SV309 )
= $false )
| ( ( ~ ( subset @ SV96 @ SV309 )
| ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SV309 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1694,plain,
! [SV96: $i,SV310: $i] :
( ( ( relation @ SV310 )
= $false )
| ( ( ~ ( subset @ SV96 @ SV310 )
| ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SV310 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1695,plain,
! [SV336: $i,SV205: $i] :
( ( ( ! [SY709: $i] :
( ( sK48_B @ SV205 )
!= ( ordered_pair @ SV336 @ SY709 ) ) )
= $true )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1696,plain,
! [SV206: $i,SV311: $i] :
( ( ( in @ SV311 @ SV206 )
= $false )
| ( ( SV311
= ( ordered_pair @ ( sK46_C @ SV311 @ SV206 ) @ ( sK47_SY329 @ SV311 @ SV206 ) ) )
= $true )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1697,plain,
! [SV312: $i,SV281: $i] :
( ( ( SV281 = SV312 )
= $false )
| ( ( subset @ SV281 @ SV312 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1698,plain,
! [SV313: $i,SV282: $i] :
( ( ( SV282 = SV313 )
= $false )
| ( ( subset @ SV313 @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1699,plain,
! [SV314: $i,SV283: $i] :
( ( ( proper_subset @ SV283 @ SV314 )
= $false )
| ( ( ( SV283 != SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1700,plain,
! [SV315: $i,SV284: $i] :
( ( ( proper_subset @ SV284 @ SV315 )
= $false )
| ( ( subset @ SV284 @ SV315 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1701,plain,
! [SV286: $i,SV142: $i,SV262: $i,SV75: $i] :
( ( ( in @ SV75 @ SV262 )
= $false )
| ( ( ~ ( in @ SV142 @ SV286 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV262 @ SV286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1702,plain,
! [SV326: $i,SV142: $i,SV75: $i] :
( ( ( ! [SY701: $i] :
~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV326 @ SY701 ) ) )
= $true )
| ( ( in @ SV75 @ SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1703,plain,
! [SV337: $i,SV327: $i,SV142: $i,SV75: $i] :
( ( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV327 @ SV337 ) )
| ( in @ SV142 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1704,plain,
! [SV263: $i,SV221: $i,SV77: $i] :
( ( ( in @ ( ordered_pair @ SV77 @ SV221 ) @ SV263 )
= $false )
| ( ( in @ SV77 @ ( relation_dom @ SV263 ) )
= $true )
| ( ( relation @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1705,plain,
! [SV264: $i,SV222: $i,SV77: $i] :
( ( ( in @ ( ordered_pair @ SV77 @ SV222 ) @ SV264 )
= $false )
| ( ( in @ SV222 @ ( relation_rng @ SV264 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1706,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1707,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1708,plain,
! [SV224: $i,SV79: $i,SV266: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV266 )
| ( in @ SY645 @ SV79 )
| ( in @ SY645 @ SV224 ) ) )
= $false )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1709,plain,
! [SV224: $i,SV266: $i,SV79: $i] :
( ( ( ~ ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) ) )
= $false )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1710,plain,
! [SV173: $i,SV226: $i,SV287: $i] :
( ( ( in @ SV287 @ SV226 )
= $false )
| ( ( in @ SV287 @ SV173 )
= $false )
| ( ( ~ ( disjoint @ SV173 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1711,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1712,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) ) )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1713,plain,
! [SV268: $i,SV228: $i,SV80: $i] :
( ( ( ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV80 )
| ( in @ SY648 @ SV228 )
| ( in @ SY648 @ SV268 ) ) )
= $false )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1714,plain,
! [SV228: $i,SV80: $i,SV268: $i] :
( ( ( ~ ~ ( ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) )
| ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) ) )
= $false )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1715,plain,
! [SV176: $i,SV231: $i] :
( ( ( in @ ( sK20_C @ SV231 @ SV176 ) @ SV231 )
= $false )
| ( ( subset @ SV176 @ SV231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1716,plain,
! [SV232: $i,SV177: $i,SV318: $i] :
( ( ( in @ SV318 @ SV177 )
= $false )
| ( ( in @ SV318 @ SV232 )
= $true )
| ( ( subset @ SV177 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1717,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1718,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1719,plain,
! [SV270: $i,SV234: $i,SV81: $i] :
( ( ( ~ ! [SY651: $i] :
( ~ ( in @ SY651 @ SV81 )
| ~ ( in @ SY651 @ SV234 )
| ( in @ SY651 @ SV270 ) ) )
= $false )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1720,plain,
! [SV234: $i,SV81: $i,SV270: $i] :
( ( ( ~ ~ ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) )
| ~ ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) ) )
= $false )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1721,plain,
! [SV82: $i,SV319: $i] :
( ( ( in @ SV319 @ ( sK32_B @ SV82 ) )
= $false )
| ( ( in @ ( powerset @ SV319 ) @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1722,plain,
! [SV82: $i] :
( ( ! [SY437: $i,SY438: $i] :
( ~ ( in @ SY437 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY438 @ SY437 )
| ( in @ SY438 @ ( sK32_B @ SV82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1640]) ).
thf(1723,plain,
! [SV82: $i] :
( ( in @ SV82 @ ( sK32_B @ SV82 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1641]) ).
thf(1724,plain,
! [SV288: $i,SV144: $i,SV271: $i,SV83: $i] :
( ( ( in @ SV83 @ SV271 )
= $false )
| ( ( ~ ( in @ SV144 @ SV288 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV271 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1725,plain,
! [SV328: $i,SV144: $i,SV83: $i] :
( ( ( ! [SY703: $i] :
~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV328 @ SY703 ) ) )
= $true )
| ( ( in @ SV83 @ SV328 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1726,plain,
! [SV338: $i,SV329: $i,SV144: $i,SV83: $i] :
( ( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV329 @ SV338 ) )
| ( in @ SV144 @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1727,plain,
! [SV180: $i,SV238: $i] :
( ( ( ( ( sK29_C @ SV238 @ SV180 )
!= SV180 ) )
= $true )
| ( ( ~ ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) )
= $true )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1728,plain,
! [SV180: $i,SV238: $i] :
( ( ( ( sK29_C @ SV238 @ SV180 )
= SV180 )
= $true )
| ( ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 )
= $true )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1729,plain,
! [SV239: $i,SV181: $i] :
( ( ( ! [SY620: $i] :
( ( SY620 != SV181 )
| ( in @ SY620 @ SV239 ) ) )
= $true )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1730,plain,
! [SV181: $i,SV239: $i] :
( ( ( ! [SY621: $i] :
( ~ ( in @ SY621 @ SV239 )
| ( SY621 = SV181 ) ) )
= $true )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1731,plain,
! [SV182: $i,SV240: $i] :
( ( ( ! [SY622: $i] :
( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SY622 )
| ~ ( in @ SY622 @ SV182 ) ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1732,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) )
| ~ ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1733,plain,
! [SV241: $i,SV183: $i] :
( ( ( ! [SY623: $i] :
( ! [SY570: $i] :
( ~ ( in @ SY623 @ SY570 )
| ~ ( in @ SY570 @ SV183 ) )
| ( in @ SY623 @ SV241 ) ) )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1734,plain,
! [SV183: $i,SV241: $i] :
( ( ( ! [SY625: $i] :
( ~ ( in @ SY625 @ SV241 )
| ~ ( ~ ( in @ SY625 @ ( sK16_D @ SY625 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SY625 @ SV241 @ SV183 ) @ SV183 ) ) ) )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1735,plain,
! [SV339: $i,SV289: $i] :
( ( ( subset @ SV289 @ ( singleton @ SV339 ) )
= $true )
| ( ( SV289 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1736,plain,
! [SV320: $i,SV290: $i] :
( ( ( SV290
= ( singleton @ SV320 ) )
= $false )
| ( ( subset @ SV290 @ ( singleton @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1737,plain,
! [SV84: $i,SV321: $i] :
( ( ( ~ ! [SY698: $i] :
( ~ ( subset @ SY698 @ SV321 )
| ( in @ SY698 @ ( sK3_SY300 @ SV321 @ SV84 ) ) )
| ~ ( in @ ( sK3_SY300 @ SV321 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
= $false )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1738,plain,
! [SV84: $i] :
( ( ! [SY449: $i,SY450: $i] :
( ~ ( in @ SY449 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY450 @ SY449 )
| ( in @ SY450 @ ( sK2_B @ SV84 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1739,plain,
! [SV84: $i] :
( ( in @ SV84 @ ( sK2_B @ SV84 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1740,plain,
! [SV272: $i,SV244: $i,SV85: $i] :
( ( ( ! [SY655: $i,SY656: $i] :
( ~ ( in @ SY655 @ SV85 )
| ~ ( in @ SY656 @ SV244 )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SY655 @ SY656 ) ) )
| ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1741,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) ) )
| ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1742,plain,
! [SV273: $i,SV245: $i,SV85: $i] :
( ( ( ~ ! [SY657: $i] :
( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ SV85 )
| ~ ( in @ SY632 @ SV245 )
| ( SY657
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ( in @ SY657 @ SV273 ) ) )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1743,plain,
! [SV85: $i,SV245: $i,SV273: $i] :
( ( ( ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV273 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SY660
!= ( ordered_pair @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) ) ) ) ) )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1744,plain,
! [SV86: $i,SV291: $i] :
( ( ( ~ ( ! [SY672: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SY672 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) ) )
= $false )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1745,plain,
! [SV86: $i,SV291: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ ( sK41_SY326 @ SV291 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) ) )
= $false )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1746,plain,
! [SV292: $i,SV86: $i] :
( ( ( ~ ! [SY673: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY673 @ SY465 ) @ SV86 )
| ( in @ SY673 @ SV292 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV292 )
| ( in @ ( ordered_pair @ SY675 @ ( sK39_D @ SY675 @ SV292 @ SV86 ) ) @ SV86 ) ) )
= $false )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1747,plain,
! [SV88: $i,SV293: $i] :
( ( ( ~ ( ! [SY676: $i] :
~ ( in @ ( ordered_pair @ SY676 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) ) )
= $false )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1663]) ).
thf(1748,plain,
! [SV88: $i,SV293: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV293 @ SV88 ) @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) ) )
= $false )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1663]) ).
thf(1749,plain,
! [SV294: $i,SV88: $i] :
( ( ( ~ ! [SY677: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY677 ) @ SV88 )
| ( in @ SY677 @ SV294 ) )
| ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV294 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY679 @ SV294 @ SV88 ) @ SY679 ) @ SV88 ) ) )
= $false )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1750,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) )
| ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
| ~ ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV295 )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) ) ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1751,plain,
! [SV296: $i,SV331: $i] :
( ( ( ( SV331
!= ( set_meet @ SV296 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV331 @ SV296 ) ) )
| ( in @ SY706 @ SV331 ) )
| ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV331 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SV296 )
| ( in @ SY707 @ SY685 ) ) ) ) )
= $true )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1752,plain,
! [SV297: $i,SV340: $i] :
( ( ( ( SV340
!= ( set_meet @ SV297 ) )
| ( SV340 = empty_set ) )
= $true )
| ( ( SV297 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1753,plain,
! [SV298: $i,SV341: $i] :
( ( ( ( SV341 != empty_set )
| ( SV341
= ( set_meet @ SV298 ) ) )
= $true )
| ( ( SV298 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1754,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) ) ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1755,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV89 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV250 ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1756,plain,
! [SV251: $i,SV89: $i,SV275: $i] :
( ( ( ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ SV275 )
| ( SY661 = SV89 )
| ( SY661 = SV251 ) ) )
= $false )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1757,plain,
! [SV251: $i,SV275: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) )
| ~ ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) ) )
= $false )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1758,plain,
! [SV299: $i,SV332: $i] :
( ( ( ~ ( element @ SV332 @ SV299 ) )
= $true )
| ( ( in @ SV332 @ SV299 )
= $true )
| ( ( empty @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1759,plain,
! [SV300: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV300 ) )
= $true )
| ( ( element @ SV333 @ SV300 )
= $true )
| ( ( empty @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1760,plain,
! [SV301: $i,SV342: $i] :
( ( ( ~ ( element @ SV342 @ SV301 )
| ( empty @ SV342 ) )
= $true )
| ( ( empty @ SV301 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1761,plain,
! [SV302: $i,SV343: $i] :
( ( ( ~ ( empty @ SV343 )
| ( element @ SV343 @ SV302 ) )
= $true )
| ( ( empty @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1762,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( relation @ SV344 )
| ~ ( ~ ( ! [SY710: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SY710 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY710 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) ) )
| ( SV344
= ( relation_composition @ SV90 @ SV195 ) ) )
= $true )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1763,plain,
! [SV195: $i,SV90: $i,SV345: $i] :
( ( ( ~ ( relation @ SV345 )
| ( SV345
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY711: $i,SY712: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY711 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY712 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY711 @ SY712 ) @ SV345 ) )
| ~ ! [SY714: $i,SY715: $i] :
( ~ ( in @ ( ordered_pair @ SY714 @ SY715 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SY714 @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) @ SY715 ) @ SV195 ) ) ) ) )
= $true )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(1764,plain,
! [SV198: $i,SV254: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 ) )
= $true )
| ( ( ~ ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) )
= $true )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1765,plain,
! [SV198: $i,SV254: $i] :
( ( ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
= $true )
| ( ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 )
= $true )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1766,plain,
! [SV199: $i,SV255: $i] :
( ( ( ! [SY639: $i] :
( ~ ( in @ SY639 @ SV255 )
| ( subset @ SY639 @ SV199 ) ) )
= $true )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1767,plain,
! [SV255: $i,SV199: $i] :
( ( ( ! [SY640: $i] :
( ~ ( subset @ SY640 @ SV199 )
| ( in @ SY640 @ SV255 ) ) )
= $true )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1768,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) ) ) )
= $true )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1769,plain,
! [SV91: $i,SV304: $i] :
( ( ( ( SV304
!= ( relation_inverse @ SV91 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY692: $i,SY693: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SV304 )
| ( in @ ( ordered_pair @ SY693 @ SY692 ) @ SV91 ) )
| ~ ! [SY694: $i,SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ SY694 ) @ SV91 )
| ( in @ ( ordered_pair @ SY694 @ SY695 ) @ SV304 ) ) ) )
= $true )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1770,plain,
! [SV346: $i,SV305: $i] :
( ( ( subset @ SV305 @ ( singleton @ SV346 ) )
= $true )
| ( ( SV305 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1771,plain,
! [SV322: $i,SV306: $i] :
( ( ( SV306
= ( singleton @ SV322 ) )
= $false )
| ( ( subset @ SV306 @ ( singleton @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1772,plain,
! [SV93: $i,SV276: $i,SV259: $i] :
( ( ( in @ SV259 @ SV276 )
= $false )
| ( ( in @ SV93 @ SV276 )
= $false )
| ( ( subset @ ( unordered_pair @ SV93 @ SV259 ) @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1773,plain,
! [SV334: $i,SV323: $i,SV93: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV93 @ SV323 ) @ SV334 ) )
= $true )
| ( ( in @ SV93 @ SV334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1774,plain,
! [SV335: $i,SV324: $i,SV93: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV93 @ SV324 ) @ SV335 ) )
= $true )
| ( ( in @ SV324 @ SV335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1775,plain,
! [SV277: $i,SV260: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ SV94 @ SV260 ) @ SV277 )
= $false )
| ( ( in @ SV94 @ ( relation_field @ SV277 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1776,plain,
! [SV278: $i,SV261: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ SV94 @ SV261 ) @ SV278 )
= $false )
| ( ( in @ SV261 @ ( relation_field @ SV278 ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1777,plain,
! [SV309: $i,SV96: $i] :
( ( ( ~ ( subset @ SV96 @ SV309 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SV309 ) )
= $true )
| ( ( relation @ SV309 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1778,plain,
! [SV310: $i,SV96: $i] :
( ( ( ~ ( subset @ SV96 @ SV310 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SV310 ) )
= $true )
| ( ( relation @ SV310 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1779,plain,
! [SV347: $i,SV336: $i,SV205: $i] :
( ( ( ( ( sK48_B @ SV205 )
!= ( ordered_pair @ SV336 @ SV347 ) ) )
= $true )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1780,plain,
! [SV314: $i,SV283: $i] :
( ( ( SV283 = SV314 )
= $false )
| ( ( proper_subset @ SV283 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1781,plain,
! [SV262: $i,SV75: $i,SV286: $i,SV142: $i] :
( ( ( in @ SV142 @ SV286 )
= $false )
| ( ( in @ SV75 @ SV262 )
= $false )
| ( ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV262 @ SV286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1782,plain,
! [SV348: $i,SV326: $i,SV142: $i,SV75: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV326 @ SV348 ) ) )
= $true )
| ( ( in @ SV75 @ SV326 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1783,plain,
! [SV337: $i,SV327: $i,SV142: $i,SV75: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV327 @ SV337 ) ) )
= $true )
| ( ( in @ SV142 @ SV337 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1784,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) )
= $false )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1785,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
= $true )
| ( ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 )
| ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1786,plain,
! [SV224: $i,SV79: $i,SV266: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ SV266 )
| ( in @ SY645 @ SV79 )
| ( in @ SY645 @ SV224 ) ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1787,plain,
! [SV224: $i,SV266: $i,SV79: $i] :
( ( ( ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1788,plain,
! [SV287: $i,SV226: $i,SV173: $i] :
( ( ( disjoint @ SV173 @ SV226 )
= $false )
| ( ( in @ SV287 @ SV173 )
= $false )
| ( ( in @ SV287 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1789,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1790,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) )
= $false )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1791,plain,
! [SV268: $i,SV228: $i,SV80: $i] :
( ( ( ! [SY648: $i] :
( ~ ( in @ SY648 @ SV80 )
| ( in @ SY648 @ SV228 )
| ( in @ SY648 @ SV268 ) ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1792,plain,
! [SV228: $i,SV80: $i,SV268: $i] :
( ( ( ~ ( ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) )
| ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1793,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1794,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
| ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) )
= $false )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1795,plain,
! [SV270: $i,SV234: $i,SV81: $i] :
( ( ( ! [SY651: $i] :
( ~ ( in @ SY651 @ SV81 )
| ~ ( in @ SY651 @ SV234 )
| ( in @ SY651 @ SV270 ) ) )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1796,plain,
! [SV234: $i,SV81: $i,SV270: $i] :
( ( ( ~ ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) )
| ~ ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) ) )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1797,plain,
! [SV82: $i,SV349: $i] :
( ( ! [SY716: $i] :
( ~ ( in @ SV349 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SY716 @ SV349 )
| ( in @ SY716 @ ( sK32_B @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(1798,plain,
! [SV271: $i,SV83: $i,SV288: $i,SV144: $i] :
( ( ( in @ SV144 @ SV288 )
= $false )
| ( ( in @ SV83 @ SV271 )
= $false )
| ( ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV271 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1799,plain,
! [SV350: $i,SV328: $i,SV144: $i,SV83: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV328 @ SV350 ) ) )
= $true )
| ( ( in @ SV83 @ SV328 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(1800,plain,
! [SV338: $i,SV329: $i,SV144: $i,SV83: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV329 @ SV338 ) ) )
= $true )
| ( ( in @ SV144 @ SV338 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1801,plain,
! [SV180: $i,SV238: $i] :
( ( ( ( sK29_C @ SV238 @ SV180 )
= SV180 )
= $false )
| ( ( ~ ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 ) )
= $true )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1802,plain,
! [SV239: $i,SV181: $i,SV351: $i] :
( ( ( ( SV351 != SV181 )
| ( in @ SV351 @ SV239 ) )
= $true )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1803,plain,
! [SV181: $i,SV239: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ SV239 )
| ( SV352 = SV181 ) )
= $true )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(1804,plain,
! [SV353: $i,SV182: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV353 )
| ~ ( in @ SV353 @ SV182 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1805,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) )
| ~ ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 ) )
= $false )
| ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1806,plain,
! [SV241: $i,SV183: $i,SV354: $i] :
( ( ( ! [SY717: $i] :
( ~ ( in @ SV354 @ SY717 )
| ~ ( in @ SY717 @ SV183 ) )
| ( in @ SV354 @ SV241 ) )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(1807,plain,
! [SV183: $i,SV241: $i,SV355: $i] :
( ( ( ~ ( in @ SV355 @ SV241 )
| ~ ( ~ ( in @ SV355 @ ( sK16_D @ SV355 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SV355 @ SV241 @ SV183 ) @ SV183 ) ) )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(1808,plain,
! [SV84: $i,SV321: $i] :
( ( ( ~ ! [SY698: $i] :
( ~ ( subset @ SY698 @ SV321 )
| ( in @ SY698 @ ( sK3_SY300 @ SV321 @ SV84 ) ) ) )
= $false )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1737]) ).
thf(1809,plain,
! [SV84: $i,SV321: $i] :
( ( ( ~ ( in @ ( sK3_SY300 @ SV321 @ SV84 ) @ ( sK2_B @ SV84 ) ) )
= $false )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1737]) ).
thf(1810,plain,
! [SV84: $i,SV356: $i] :
( ( ! [SY718: $i] :
( ~ ( in @ SV356 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SY718 @ SV356 )
| ( in @ SY718 @ ( sK2_B @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(1811,plain,
! [SV272: $i,SV244: $i,SV85: $i] :
( ( ( ! [SY655: $i,SY656: $i] :
( ~ ( in @ SY655 @ SV85 )
| ~ ( in @ SY656 @ SV244 )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SY655 @ SY656 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1812,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1813,plain,
! [SV273: $i,SV245: $i,SV85: $i] :
( ( ( ! [SY657: $i] :
( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ SV85 )
| ~ ( in @ SY632 @ SV245 )
| ( SY657
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ( in @ SY657 @ SV273 ) ) )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1814,plain,
! [SV85: $i,SV245: $i,SV273: $i] :
( ( ( ! [SY660: $i] :
( ~ ( in @ SY660 @ SV273 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SY660
!= ( ordered_pair @ ( sK21_E @ SY660 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SY660 @ SV273 @ SV245 @ SV85 ) ) ) ) ) )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1815,plain,
! [SV86: $i,SV291: $i] :
( ( ( ! [SY672: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SY672 ) @ SV86 )
| ~ ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1816,plain,
! [SV86: $i,SV291: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ ( sK41_SY326 @ SV291 @ SV86 ) ) @ SV86 )
| ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1817,plain,
! [SV292: $i,SV86: $i] :
( ( ( ~ ! [SY673: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY673 @ SY465 ) @ SV86 )
| ( in @ SY673 @ SV292 ) ) )
= $false )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1818,plain,
! [SV86: $i,SV292: $i] :
( ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV292 )
| ( in @ ( ordered_pair @ SY675 @ ( sK39_D @ SY675 @ SV292 @ SV86 ) ) @ SV86 ) ) )
= $false )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1819,plain,
! [SV88: $i,SV293: $i] :
( ( ( ! [SY676: $i] :
~ ( in @ ( ordered_pair @ SY676 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ~ ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) )
= $true )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1820,plain,
! [SV88: $i,SV293: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV293 @ SV88 ) @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
| ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) )
= $true )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1821,plain,
! [SV294: $i,SV88: $i] :
( ( ( ~ ! [SY677: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY677 ) @ SV88 )
| ( in @ SY677 @ SV294 ) ) )
= $false )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1822,plain,
! [SV88: $i,SV294: $i] :
( ( ( ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV294 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY679 @ SV294 @ SV88 ) @ SY679 ) @ SV88 ) ) )
= $false )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1823,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) )
| ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
| ~ ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV295 )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) ) )
= $false )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1824,plain,
! [SV296: $i,SV331: $i] :
( ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( ~ ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV331 @ SV296 ) ) )
| ( in @ SY706 @ SV331 ) )
| ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV331 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SV296 )
| ( in @ SY707 @ SY685 ) ) ) ) )
= $true )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1825,plain,
! [SV297: $i,SV340: $i] :
( ( ( ( SV340
!= ( set_meet @ SV297 ) ) )
= $true )
| ( ( SV340 = empty_set )
= $true )
| ( ( SV297 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1826,plain,
! [SV298: $i,SV341: $i] :
( ( ( ( SV341 != empty_set ) )
= $true )
| ( ( SV341
= ( set_meet @ SV298 ) )
= $true )
| ( ( SV298 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1827,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) ) )
= $false )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1828,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
= $true )
| ( ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV89 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV250 ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1829,plain,
! [SV251: $i,SV89: $i,SV275: $i] :
( ( ( ! [SY661: $i] :
( ~ ( in @ SY661 @ SV275 )
| ( SY661 = SV89 )
| ( SY661 = SV251 ) ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1830,plain,
! [SV251: $i,SV275: $i,SV89: $i] :
( ( ( ~ ( ~ ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) )
| ~ ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1757]) ).
thf(1831,plain,
! [SV299: $i,SV332: $i] :
( ( ( element @ SV332 @ SV299 )
= $false )
| ( ( in @ SV332 @ SV299 )
= $true )
| ( ( empty @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1832,plain,
! [SV300: $i,SV333: $i] :
( ( ( in @ SV333 @ SV300 )
= $false )
| ( ( element @ SV333 @ SV300 )
= $true )
| ( ( empty @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1833,plain,
! [SV301: $i,SV342: $i] :
( ( ( ~ ( element @ SV342 @ SV301 ) )
= $true )
| ( ( empty @ SV342 )
= $true )
| ( ( empty @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1834,plain,
! [SV302: $i,SV343: $i] :
( ( ( ~ ( empty @ SV343 ) )
= $true )
| ( ( element @ SV343 @ SV302 )
= $true )
| ( ( empty @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(1835,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( relation @ SV344 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY710: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SY710 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY710 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) ) )
| ( SV344
= ( relation_composition @ SV90 @ SV195 ) ) )
= $true )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(1836,plain,
! [SV195: $i,SV90: $i,SV345: $i] :
( ( ( ~ ( relation @ SV345 ) )
= $true )
| ( ( ( SV345
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY711: $i,SY712: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY711 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY712 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY711 @ SY712 ) @ SV345 ) )
| ~ ! [SY714: $i,SY715: $i] :
( ~ ( in @ ( ordered_pair @ SY714 @ SY715 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SY714 @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) @ SY715 ) @ SV195 ) ) ) ) )
= $true )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(1837,plain,
! [SV198: $i,SV254: $i] :
( ( ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
= $false )
| ( ( ~ ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 ) )
= $true )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1838,plain,
! [SV199: $i,SV255: $i,SV357: $i] :
( ( ( ~ ( in @ SV357 @ SV255 )
| ( subset @ SV357 @ SV199 ) )
= $true )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(1839,plain,
! [SV255: $i,SV199: $i,SV358: $i] :
( ( ( ~ ( subset @ SV358 @ SV199 )
| ( in @ SV358 @ SV255 ) )
= $true )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(1840,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) ) )
= $false )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1841,plain,
! [SV91: $i,SV304: $i] :
( ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( ~ ( ~ ! [SY692: $i,SY693: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SV304 )
| ( in @ ( ordered_pair @ SY693 @ SY692 ) @ SV91 ) )
| ~ ! [SY694: $i,SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ SY694 ) @ SV91 )
| ( in @ ( ordered_pair @ SY694 @ SY695 ) @ SV304 ) ) ) )
= $true )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1842,plain,
! [SV334: $i,SV323: $i,SV93: $i] :
( ( ( subset @ ( unordered_pair @ SV93 @ SV323 ) @ SV334 )
= $false )
| ( ( in @ SV93 @ SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1843,plain,
! [SV335: $i,SV324: $i,SV93: $i] :
( ( ( subset @ ( unordered_pair @ SV93 @ SV324 ) @ SV335 )
= $false )
| ( ( in @ SV324 @ SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1844,plain,
! [SV309: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV309 )
= $false )
| ( ( subset @ ( relation_dom @ SV96 ) @ ( relation_dom @ SV309 ) )
= $true )
| ( ( relation @ SV309 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1845,plain,
! [SV310: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV310 )
= $false )
| ( ( subset @ ( relation_rng @ SV96 ) @ ( relation_rng @ SV310 ) )
= $true )
| ( ( relation @ SV310 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1846,plain,
! [SV347: $i,SV336: $i,SV205: $i] :
( ( ( ( sK48_B @ SV205 )
= ( ordered_pair @ SV336 @ SV347 ) )
= $false )
| ( ( relation @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1847,plain,
! [SV348: $i,SV326: $i,SV142: $i,SV75: $i] :
( ( ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV326 @ SV348 ) )
= $false )
| ( ( in @ SV75 @ SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1848,plain,
! [SV337: $i,SV327: $i,SV142: $i,SV75: $i] :
( ( ( in @ ( ordered_pair @ SV75 @ SV142 ) @ ( cartesian_product2 @ SV327 @ SV337 ) )
= $false )
| ( ( in @ SV142 @ SV337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1849,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) ) )
= $false )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1850,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) ) )
= $false )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1851,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 )
= $true )
| ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 )
= $true )
| ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(1852,plain,
! [SV224: $i,SV79: $i,SV266: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV266 )
| ( in @ SV359 @ SV79 )
| ( in @ SV359 @ SV224 ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(1853,plain,
! [SV224: $i,SV266: $i,SV79: $i] :
( ( ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) )
= $false )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1854,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 ) )
= $true )
| ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(1855,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) )
= $false )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1856,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) ) )
= $false )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1857,plain,
! [SV268: $i,SV228: $i,SV80: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ SV80 )
| ( in @ SV360 @ SV228 )
| ( in @ SV360 @ SV268 ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(1858,plain,
! [SV228: $i,SV80: $i,SV268: $i] :
( ( ( ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) )
| ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) )
= $false )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1859,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1860,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) )
= $false )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1794]) ).
thf(1861,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) ) )
= $false )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1794]) ).
thf(1862,plain,
! [SV270: $i,SV234: $i,SV81: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ SV81 )
| ~ ( in @ SV361 @ SV234 )
| ( in @ SV361 @ SV270 ) )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(1863,plain,
! [SV234: $i,SV81: $i,SV270: $i] :
( ( ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) )
| ~ ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) )
= $false )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1864,plain,
! [SV362: $i,SV82: $i,SV349: $i] :
( ( ~ ( in @ SV349 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SV362 @ SV349 )
| ( in @ SV362 @ ( sK32_B @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(1865,plain,
! [SV350: $i,SV328: $i,SV144: $i,SV83: $i] :
( ( ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV328 @ SV350 ) )
= $false )
| ( ( in @ SV83 @ SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1866,plain,
! [SV338: $i,SV329: $i,SV144: $i,SV83: $i] :
( ( ( in @ ( ordered_pair @ SV83 @ SV144 ) @ ( cartesian_product2 @ SV329 @ SV338 ) )
= $false )
| ( ( in @ SV144 @ SV338 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1867,plain,
! [SV180: $i,SV238: $i] :
( ( ( in @ ( sK29_C @ SV238 @ SV180 ) @ SV238 )
= $false )
| ( ( ( sK29_C @ SV238 @ SV180 )
= SV180 )
= $false )
| ( ( SV238
= ( singleton @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1868,plain,
! [SV239: $i,SV181: $i,SV351: $i] :
( ( ( ( SV351 != SV181 ) )
= $true )
| ( ( in @ SV351 @ SV239 )
= $true )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(1869,plain,
! [SV181: $i,SV239: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ SV239 ) )
= $true )
| ( ( SV352 = SV181 )
= $true )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(1870,plain,
! [SV353: $i,SV182: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV353 ) )
= $true )
| ( ( ~ ( in @ SV353 @ SV182 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1871,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) ) )
= $false )
| ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1805]) ).
thf(1872,plain,
! [SV182: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 ) )
= $false )
| ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1805]) ).
thf(1873,plain,
! [SV241: $i,SV183: $i,SV354: $i] :
( ( ( ! [SY717: $i] :
( ~ ( in @ SV354 @ SY717 )
| ~ ( in @ SY717 @ SV183 ) ) )
= $true )
| ( ( in @ SV354 @ SV241 )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(1874,plain,
! [SV183: $i,SV241: $i,SV355: $i] :
( ( ( ~ ( in @ SV355 @ SV241 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV355 @ ( sK16_D @ SV355 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SV355 @ SV241 @ SV183 ) @ SV183 ) ) )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1875,plain,
! [SV84: $i,SV321: $i] :
( ( ( ! [SY698: $i] :
( ~ ( subset @ SY698 @ SV321 )
| ( in @ SY698 @ ( sK3_SY300 @ SV321 @ SV84 ) ) ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1876,plain,
! [SV84: $i,SV321: $i] :
( ( ( in @ ( sK3_SY300 @ SV321 @ SV84 ) @ ( sK2_B @ SV84 ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1877,plain,
! [SV363: $i,SV84: $i,SV356: $i] :
( ( ~ ( in @ SV356 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SV363 @ SV356 )
| ( in @ SV363 @ ( sK2_B @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(1878,plain,
! [SV272: $i,SV244: $i,SV85: $i,SV364: $i] :
( ( ( ! [SY719: $i] :
( ~ ( in @ SV364 @ SV85 )
| ~ ( in @ SY719 @ SV244 )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SV364 @ SY719 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(1879,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1880,plain,
! [SV273: $i,SV365: $i,SV245: $i,SV85: $i] :
( ( ( ! [SY720: $i,SY721: $i] :
( ~ ( in @ SY720 @ SV85 )
| ~ ( in @ SY721 @ SV245 )
| ( SV365
!= ( ordered_pair @ SY720 @ SY721 ) ) )
| ( in @ SV365 @ SV273 ) )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(1881,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV273 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SV366
!= ( ordered_pair @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) ) ) ) )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(1882,plain,
! [SV86: $i,SV291: $i] :
( ( ( ! [SY672: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SY672 ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(1883,plain,
! [SV86: $i,SV291: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ ( sK41_SY326 @ SV291 @ SV86 ) ) @ SV86 )
= $true )
| ( ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 )
= $true )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1884,plain,
! [SV292: $i,SV86: $i] :
( ( ( ! [SY673: $i] :
( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ SY673 @ SY465 ) @ SV86 )
| ( in @ SY673 @ SV292 ) ) )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1885,plain,
! [SV86: $i,SV292: $i] :
( ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV292 )
| ( in @ ( ordered_pair @ SY675 @ ( sK39_D @ SY675 @ SV292 @ SV86 ) ) @ SV86 ) ) )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1886,plain,
! [SV88: $i,SV293: $i] :
( ( ( ! [SY676: $i] :
~ ( in @ ( ordered_pair @ SY676 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) )
= $true )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(1887,plain,
! [SV88: $i,SV293: $i] :
( ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV293 @ SV88 ) @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
= $true )
| ( ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 )
= $true )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1888,plain,
! [SV294: $i,SV88: $i] :
( ( ( ! [SY677: $i] :
( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ SY471 @ SY677 ) @ SV88 )
| ( in @ SY677 @ SV294 ) ) )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1889,plain,
! [SV88: $i,SV294: $i] :
( ( ( ! [SY679: $i] :
( ~ ( in @ SY679 @ SV294 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY679 @ SV294 @ SV88 ) @ SY679 ) @ SV88 ) ) )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1890,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) )
| ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) ) )
= $false )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1891,plain,
! [SV330: $i,SV295: $i] :
( ( ( ~ ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV295 )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) ) )
= $false )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1892,plain,
! [SV296: $i,SV331: $i] :
( ( ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV331 @ SV296 ) ) )
| ( in @ SY706 @ SV331 ) )
| ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV331 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SV296 )
| ( in @ SY707 @ SY685 ) ) ) )
= $false )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1893,plain,
! [SV297: $i,SV340: $i] :
( ( ( SV340
= ( set_meet @ SV297 ) )
= $false )
| ( ( SV340 = empty_set )
= $true )
| ( ( SV297 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1894,plain,
! [SV298: $i,SV341: $i] :
( ( ( SV341 = empty_set )
= $false )
| ( ( SV341
= ( set_meet @ SV298 ) )
= $true )
| ( ( SV298 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1895,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) ) )
= $false )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1896,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) ) )
= $false )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1897,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV89 )
= $true )
| ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV250 )
= $true )
| ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1898,plain,
! [SV251: $i,SV89: $i,SV275: $i,SV367: $i] :
( ( ( ~ ( in @ SV367 @ SV275 )
| ( SV367 = SV89 )
| ( SV367 = SV251 ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1899,plain,
! [SV251: $i,SV275: $i,SV89: $i] :
( ( ( ~ ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) )
| ~ ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) )
= $false )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1900,plain,
! [SV301: $i,SV342: $i] :
( ( ( element @ SV342 @ SV301 )
= $false )
| ( ( empty @ SV342 )
= $true )
| ( ( empty @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1901,plain,
! [SV302: $i,SV343: $i] :
( ( ( empty @ SV343 )
= $false )
| ( ( element @ SV343 @ SV302 )
= $true )
| ( ( empty @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1902,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( relation @ SV344 )
= $false )
| ( ( ~ ( ~ ( ! [SY710: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SY710 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY710 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) ) )
| ( SV344
= ( relation_composition @ SV90 @ SV195 ) ) )
= $true )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1903,plain,
! [SV195: $i,SV90: $i,SV345: $i] :
( ( ( relation @ SV345 )
= $false )
| ( ( ( SV345
!= ( relation_composition @ SV90 @ SV195 ) )
| ~ ( ~ ! [SY711: $i,SY712: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY711 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY712 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY711 @ SY712 ) @ SV345 ) )
| ~ ! [SY714: $i,SY715: $i] :
( ~ ( in @ ( ordered_pair @ SY714 @ SY715 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SY714 @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) @ SY715 ) @ SV195 ) ) ) ) )
= $true )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1904,plain,
! [SV198: $i,SV254: $i] :
( ( ( subset @ ( sK28_C @ SV254 @ SV198 ) @ SV198 )
= $false )
| ( ( in @ ( sK28_C @ SV254 @ SV198 ) @ SV254 )
= $false )
| ( ( SV254
= ( powerset @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1905,plain,
! [SV199: $i,SV255: $i,SV357: $i] :
( ( ( ~ ( in @ SV357 @ SV255 ) )
= $true )
| ( ( subset @ SV357 @ SV199 )
= $true )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(1906,plain,
! [SV255: $i,SV199: $i,SV358: $i] :
( ( ( ~ ( subset @ SV358 @ SV199 ) )
= $true )
| ( ( in @ SV358 @ SV255 )
= $true )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(1907,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) ) )
= $false )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1908,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) ) )
= $false )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1909,plain,
! [SV91: $i,SV304: $i] :
( ( ( ~ ! [SY692: $i,SY693: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SV304 )
| ( in @ ( ordered_pair @ SY693 @ SY692 ) @ SV91 ) )
| ~ ! [SY694: $i,SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ SY694 ) @ SV91 )
| ( in @ ( ordered_pair @ SY694 @ SY695 ) @ SV304 ) ) )
= $false )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1910,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1911,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
| ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1912,plain,
! [SV224: $i,SV79: $i,SV266: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV266 ) )
= $true )
| ( ( ( in @ SV359 @ SV79 )
| ( in @ SV359 @ SV224 ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(1913,plain,
! [SV224: $i,SV266: $i,SV79: $i] :
( ( ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) ) )
= $false )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(1914,plain,
! [SV79: $i,SV266: $i,SV224: $i] :
( ( ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) )
= $false )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(1915,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
= $false )
| ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1916,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1917,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
| ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 ) )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1918,plain,
! [SV268: $i,SV228: $i,SV80: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ SV80 )
| ( in @ SV360 @ SV228 ) )
= $true )
| ( ( in @ SV360 @ SV268 )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(1919,plain,
! [SV228: $i,SV80: $i,SV268: $i] :
( ( ( ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) ) )
= $false )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1920,plain,
! [SV80: $i,SV228: $i,SV268: $i] :
( ( ( ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) )
= $false )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1921,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1922,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1923,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
| ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(1924,plain,
! [SV270: $i,SV234: $i,SV81: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ SV81 )
| ~ ( in @ SV361 @ SV234 ) )
= $true )
| ( ( in @ SV361 @ SV270 )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(1925,plain,
! [SV234: $i,SV81: $i,SV270: $i] :
( ( ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) ) )
= $false )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1863]) ).
thf(1926,plain,
! [SV81: $i,SV234: $i,SV270: $i] :
( ( ( ~ ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) )
= $false )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1863]) ).
thf(1927,plain,
! [SV362: $i,SV82: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ ( sK32_B @ SV82 ) )
| ~ ( subset @ SV362 @ SV349 ) )
= $true )
| ( ( in @ SV362 @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(1928,plain,
! [SV239: $i,SV181: $i,SV351: $i] :
( ( ( SV351 = SV181 )
= $false )
| ( ( in @ SV351 @ SV239 )
= $true )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1929,plain,
! [SV181: $i,SV239: $i,SV352: $i] :
( ( ( in @ SV352 @ SV239 )
= $false )
| ( ( SV352 = SV181 )
= $true )
| ( ( SV239
= ( singleton @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1930,plain,
! [SV353: $i,SV182: $i,SV240: $i] :
( ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV353 )
= $false )
| ( ( ~ ( in @ SV353 @ SV182 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1931,plain,
! [SV182: $i,SV240: $i] :
( ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ ( sK18_SY312 @ SV240 @ SV182 ) )
= $true )
| ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1932,plain,
! [SV182: $i,SV240: $i] :
( ( ( in @ ( sK18_SY312 @ SV240 @ SV182 ) @ SV182 )
= $true )
| ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1872]) ).
thf(1933,plain,
! [SV241: $i,SV183: $i,SV368: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ SV368 )
| ~ ( in @ SV368 @ SV183 ) )
= $true )
| ( ( in @ SV354 @ SV241 )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(1934,plain,
! [SV183: $i,SV241: $i,SV355: $i] :
( ( ( in @ SV355 @ SV241 )
= $false )
| ( ( ~ ( ~ ( in @ SV355 @ ( sK16_D @ SV355 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SV355 @ SV241 @ SV183 ) @ SV183 ) ) )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1935,plain,
! [SV84: $i,SV321: $i,SV369: $i] :
( ( ( ~ ( subset @ SV369 @ SV321 )
| ( in @ SV369 @ ( sK3_SY300 @ SV321 @ SV84 ) ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(1936,plain,
! [SV84: $i,SV321: $i] :
( ( ( in @ SV321 @ ( sK2_B @ SV84 ) )
= $false )
| ( ( in @ ( sK3_SY300 @ SV321 @ SV84 ) @ ( sK2_B @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1937,plain,
! [SV363: $i,SV84: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ ( sK2_B @ SV84 ) )
| ~ ( subset @ SV363 @ SV356 ) )
= $true )
| ( ( in @ SV363 @ ( sK2_B @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(1938,plain,
! [SV272: $i,SV244: $i,SV370: $i,SV85: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ SV85 )
| ~ ( in @ SV370 @ SV244 )
| ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SV364 @ SV370 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(1939,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1940,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1941,plain,
! [SV273: $i,SV365: $i,SV245: $i,SV85: $i] :
( ( ( ! [SY720: $i,SY721: $i] :
( ~ ( in @ SY720 @ SV85 )
| ~ ( in @ SY721 @ SV245 )
| ( SV365
!= ( ordered_pair @ SY720 @ SY721 ) ) ) )
= $true )
| ( ( in @ SV365 @ SV273 )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(1942,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV273 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SV366
!= ( ordered_pair @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) ) ) ) )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(1943,plain,
! [SV371: $i,SV86: $i,SV291: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SV371 ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(1944,plain,
! [SV292: $i,SV86: $i,SV372: $i] :
( ( ( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SV372 @ SY722 ) @ SV86 )
| ( in @ SV372 @ SV292 ) )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(1945,plain,
! [SV86: $i,SV292: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV292 )
| ( in @ ( ordered_pair @ SV373 @ ( sK39_D @ SV373 @ SV292 @ SV86 ) ) @ SV86 ) )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(1946,plain,
! [SV88: $i,SV293: $i,SV374: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV374 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) )
= $true )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(1947,plain,
! [SV294: $i,SV88: $i,SV375: $i] :
( ( ( ! [SY723: $i] :
~ ( in @ ( ordered_pair @ SY723 @ SV375 ) @ SV88 )
| ( in @ SV375 @ SV294 ) )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(1948,plain,
! [SV88: $i,SV294: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ SV294 )
| ( in @ ( ordered_pair @ ( sK36_D @ SV376 @ SV294 @ SV88 ) @ SV376 ) @ SV88 ) )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(1949,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) )
| ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1950,plain,
! [SV330: $i,SV295: $i] :
( ( ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV295 )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SY705 ) )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1951,plain,
! [SV296: $i,SV331: $i] :
( ( ( ~ ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV331 @ SV296 ) ) )
| ( in @ SY706 @ SV331 ) ) )
= $false )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1952,plain,
! [SV296: $i,SV331: $i] :
( ( ( ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV331 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SV296 )
| ( in @ SY707 @ SY685 ) ) ) )
= $false )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1953,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1895]) ).
thf(1954,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
| ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(1955,plain,
! [SV251: $i,SV89: $i,SV275: $i,SV367: $i] :
( ( ( ~ ( in @ SV367 @ SV275 ) )
= $true )
| ( ( ( SV367 = SV89 )
| ( SV367 = SV251 ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(1956,plain,
! [SV251: $i,SV275: $i,SV89: $i] :
( ( ( ~ ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) ) )
= $false )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1957,plain,
! [SV89: $i,SV275: $i,SV251: $i] :
( ( ( ~ ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) )
= $false )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1958,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( ~ ( ! [SY710: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SY710 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY710 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) ) ) )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(1959,plain,
! [SV195: $i,SV90: $i,SV345: $i] :
( ( ( ( SV345
!= ( relation_composition @ SV90 @ SV195 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY711: $i,SY712: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY711 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY712 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY711 @ SY712 ) @ SV345 ) )
| ~ ! [SY714: $i,SY715: $i] :
( ~ ( in @ ( ordered_pair @ SY714 @ SY715 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SY714 @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) @ SY715 ) @ SV195 ) ) ) ) )
= $true )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(1960,plain,
! [SV199: $i,SV255: $i,SV357: $i] :
( ( ( in @ SV357 @ SV255 )
= $false )
| ( ( subset @ SV357 @ SV199 )
= $true )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1961,plain,
! [SV255: $i,SV199: $i,SV358: $i] :
( ( ( subset @ SV358 @ SV199 )
= $false )
| ( ( in @ SV358 @ SV255 )
= $true )
| ( ( SV255
= ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1962,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
= $true )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1907]) ).
thf(1963,plain,
! [SV91: $i,SV303: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
= $true )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(1964,plain,
! [SV91: $i,SV304: $i] :
( ( ( ~ ! [SY692: $i,SY693: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SV304 )
| ( in @ ( ordered_pair @ SY693 @ SY692 ) @ SV91 ) ) )
= $false )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1909]) ).
thf(1965,plain,
! [SV304: $i,SV91: $i] :
( ( ( ~ ! [SY694: $i,SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ SY694 ) @ SV91 )
| ( in @ ( ordered_pair @ SY694 @ SY695 ) @ SV304 ) ) )
= $false )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1909]) ).
thf(1966,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(1967,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1968,plain,
! [SV224: $i,SV79: $i,SV266: $i,SV359: $i] :
( ( ( in @ SV359 @ SV266 )
= $false )
| ( ( ( in @ SV359 @ SV79 )
| ( in @ SV359 @ SV224 ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(1969,plain,
! [SV224: $i,SV266: $i,SV79: $i] :
( ( ( ! [SY646: $i] :
( ~ ( in @ SY646 @ SV79 )
| ( in @ SY646 @ SV266 ) ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1970,plain,
! [SV79: $i,SV266: $i,SV224: $i] :
( ( ( ! [SY647: $i] :
( ~ ( in @ SY647 @ SV224 )
| ( in @ SY647 @ SV266 ) ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(1971,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 )
= $false )
| ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
= $true )
| ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
= $false )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(1972,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV80 )
= $true )
| ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(1973,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 ) )
= $true )
| ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(1974,plain,
! [SV268: $i,SV228: $i,SV80: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ SV80 ) )
= $true )
| ( ( in @ SV360 @ SV228 )
= $true )
| ( ( in @ SV360 @ SV268 )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(1975,plain,
! [SV228: $i,SV80: $i,SV268: $i] :
( ( ( ! [SY649: $i] :
( ~ ( in @ SY649 @ SV268 )
| ( in @ SY649 @ SV80 ) ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(1976,plain,
! [SV80: $i,SV228: $i,SV268: $i] :
( ( ( ! [SY650: $i] :
( ~ ( in @ SY650 @ SV268 )
| ~ ( in @ SY650 @ SV228 ) ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(1977,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
= $false )
| ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 ) )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1978,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
= $true )
| ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(1979,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
= $true )
| ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 )
= $true )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(1980,plain,
! [SV270: $i,SV234: $i,SV81: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ SV81 ) )
= $true )
| ( ( ~ ( in @ SV361 @ SV234 ) )
= $true )
| ( ( in @ SV361 @ SV270 )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(1981,plain,
! [SV234: $i,SV81: $i,SV270: $i] :
( ( ( ! [SY652: $i] :
( ~ ( in @ SY652 @ SV270 )
| ( in @ SY652 @ SV81 ) ) )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1982,plain,
! [SV81: $i,SV234: $i,SV270: $i] :
( ( ( ! [SY653: $i] :
( ~ ( in @ SY653 @ SV270 )
| ( in @ SY653 @ SV234 ) ) )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(1983,plain,
! [SV362: $i,SV82: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ ( sK32_B @ SV82 ) ) )
= $true )
| ( ( ~ ( subset @ SV362 @ SV349 ) )
= $true )
| ( ( in @ SV362 @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(1984,plain,
! [SV240: $i,SV182: $i,SV353: $i] :
( ( ( in @ SV353 @ SV182 )
= $false )
| ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV353 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 ) )
= $true )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1985,plain,
! [SV241: $i,SV183: $i,SV368: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ SV368 ) )
= $true )
| ( ( ~ ( in @ SV368 @ SV183 ) )
= $true )
| ( ( in @ SV354 @ SV241 )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(1986,plain,
! [SV183: $i,SV241: $i,SV355: $i] :
( ( ( ~ ( in @ SV355 @ ( sK16_D @ SV355 @ SV241 @ SV183 ) )
| ~ ( in @ ( sK16_D @ SV355 @ SV241 @ SV183 ) @ SV183 ) )
= $false )
| ( ( in @ SV355 @ SV241 )
= $false )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(1987,plain,
! [SV84: $i,SV321: $i,SV369: $i] :
( ( ( ~ ( subset @ SV369 @ SV321 ) )
= $true )
| ( ( in @ SV369 @ ( sK3_SY300 @ SV321 @ SV84 ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(1988,plain,
! [SV363: $i,SV84: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ ( sK2_B @ SV84 ) ) )
= $true )
| ( ( ~ ( subset @ SV363 @ SV356 ) )
= $true )
| ( ( in @ SV363 @ ( sK2_B @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(1989,plain,
! [SV272: $i,SV244: $i,SV370: $i,SV85: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ SV85 )
| ~ ( in @ SV370 @ SV244 ) )
= $true )
| ( ( ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SV364 @ SV370 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(1990,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1939]) ).
thf(1991,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ( sK23_D @ SV272 @ SV244 @ SV85 )
= ( ordered_pair @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(1992,plain,
! [SV273: $i,SV365: $i,SV245: $i,SV85: $i,SV377: $i] :
( ( ( ! [SY724: $i] :
( ~ ( in @ SV377 @ SV85 )
| ~ ( in @ SY724 @ SV245 )
| ( SV365
!= ( ordered_pair @ SV377 @ SY724 ) ) ) )
= $true )
| ( ( in @ SV365 @ SV273 )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(1993,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( in @ SV366 @ SV273 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SV366
!= ( ordered_pair @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) ) ) ) )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(1994,plain,
! [SV371: $i,SV86: $i,SV291: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SV371 ) @ SV86 )
= $false )
| ( ( ~ ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(1995,plain,
! [SV292: $i,SV86: $i,SV372: $i] :
( ( ( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SV372 @ SY722 ) @ SV86 ) )
= $true )
| ( ( in @ SV372 @ SV292 )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(1996,plain,
! [SV86: $i,SV292: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV292 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ ( sK39_D @ SV373 @ SV292 @ SV86 ) ) @ SV86 )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(1997,plain,
! [SV88: $i,SV293: $i,SV374: $i] :
( ( ( in @ ( ordered_pair @ SV374 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
= $false )
| ( ( ~ ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 ) )
= $true )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(1998,plain,
! [SV294: $i,SV88: $i,SV375: $i] :
( ( ( ! [SY723: $i] :
~ ( in @ ( ordered_pair @ SY723 @ SV375 ) @ SV88 ) )
= $true )
| ( ( in @ SV375 @ SV294 )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(1999,plain,
! [SV88: $i,SV294: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ SV294 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK36_D @ SV376 @ SV294 @ SV88 ) @ SV376 ) @ SV88 )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2000,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2001,plain,
! [SV330: $i,SV295: $i] :
( ( ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV295 )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SY705 ) ) )
= $true )
| ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2002,plain,
! [SV296: $i,SV331: $i] :
( ( ( ! [SY706: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY706 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SY706 @ ( sK43_D @ SY706 @ SV331 @ SV296 ) ) )
| ( in @ SY706 @ SV331 ) ) )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(2003,plain,
! [SV296: $i,SV331: $i] :
( ( ( ! [SY707: $i] :
( ~ ( in @ SY707 @ SV331 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SV296 )
| ( in @ SY707 @ SY685 ) ) ) )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2004,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 ) )
= $true )
| ( ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2005,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 ) )
= $true )
| ( ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2006,plain,
! [SV251: $i,SV89: $i,SV275: $i,SV367: $i] :
( ( ( in @ SV367 @ SV275 )
= $false )
| ( ( ( SV367 = SV89 )
| ( SV367 = SV251 ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2007,plain,
! [SV251: $i,SV275: $i,SV89: $i] :
( ( ( ! [SY662: $i] :
( ( SY662 != SV89 )
| ( in @ SY662 @ SV275 ) ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(2008,plain,
! [SV89: $i,SV275: $i,SV251: $i] :
( ( ( ! [SY663: $i] :
( ( SY663 != SV251 )
| ( in @ SY663 @ SV275 ) ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1957]) ).
thf(2009,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( ! [SY710: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SY710 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY710 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) ) )
= $false )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2010,plain,
! [SV195: $i,SV90: $i,SV345: $i] :
( ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( ~ ( ~ ! [SY711: $i,SY712: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY711 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY712 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY711 @ SY712 ) @ SV345 ) )
| ~ ! [SY714: $i,SY715: $i] :
( ~ ( in @ ( ordered_pair @ SY714 @ SY715 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SY714 @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) @ SY715 ) @ SV195 ) ) ) ) )
= $true )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2011,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
= $true )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2012,plain,
! [SV91: $i,SV303: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 )
= $true )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2013,plain,
! [SV91: $i,SV304: $i] :
( ( ( ! [SY692: $i,SY693: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SV304 )
| ( in @ ( ordered_pair @ SY693 @ SY692 ) @ SV91 ) ) )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1964]) ).
thf(2014,plain,
! [SV304: $i,SV91: $i] :
( ( ( ! [SY694: $i,SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ SY694 ) @ SV91 )
| ( in @ ( ordered_pair @ SY694 @ SY695 ) @ SV304 ) ) )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2015,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2016,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 ) )
= $true )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2017,plain,
! [SV266: $i,SV224: $i,SV79: $i,SV359: $i] :
( ( ( in @ SV359 @ SV79 )
= $true )
| ( ( in @ SV359 @ SV224 )
= $true )
| ( ( in @ SV359 @ SV266 )
= $false )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2018,plain,
! [SV224: $i,SV266: $i,SV79: $i,SV378: $i] :
( ( ( ~ ( in @ SV378 @ SV79 )
| ( in @ SV378 @ SV266 ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2019,plain,
! [SV79: $i,SV266: $i,SV224: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV224 )
| ( in @ SV379 @ SV266 ) )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2020,plain,
! [SV80: $i,SV227: $i,SV267: $i] :
( ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV227 )
= $false )
| ( ( in @ ( sK15_D @ SV267 @ SV227 @ SV80 ) @ SV267 )
= $true )
| ( ( SV267
= ( set_difference @ SV80 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2021,plain,
! [SV268: $i,SV228: $i,SV80: $i,SV360: $i] :
( ( ( in @ SV360 @ SV80 )
= $false )
| ( ( in @ SV360 @ SV228 )
= $true )
| ( ( in @ SV360 @ SV268 )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2022,plain,
! [SV228: $i,SV80: $i,SV268: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ SV268 )
| ( in @ SV380 @ SV80 ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2023,plain,
! [SV80: $i,SV228: $i,SV268: $i,SV381: $i] :
( ( ( ~ ( in @ SV381 @ SV268 )
| ~ ( in @ SV381 @ SV228 ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2024,plain,
! [SV81: $i,SV233: $i,SV269: $i] :
( ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV269 )
= $false )
| ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV81 )
= $false )
| ( ( in @ ( sK19_D @ SV269 @ SV233 @ SV81 ) @ SV233 )
= $false )
| ( ( SV269
= ( set_intersection2 @ SV81 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2025,plain,
! [SV270: $i,SV234: $i,SV81: $i,SV361: $i] :
( ( ( in @ SV361 @ SV81 )
= $false )
| ( ( ~ ( in @ SV361 @ SV234 ) )
= $true )
| ( ( in @ SV361 @ SV270 )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2026,plain,
! [SV234: $i,SV81: $i,SV270: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ SV270 )
| ( in @ SV382 @ SV81 ) )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2027,plain,
! [SV81: $i,SV234: $i,SV270: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ SV270 )
| ( in @ SV383 @ SV234 ) )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2028,plain,
! [SV362: $i,SV82: $i,SV349: $i] :
( ( ( in @ SV349 @ ( sK32_B @ SV82 ) )
= $false )
| ( ( ~ ( subset @ SV362 @ SV349 ) )
= $true )
| ( ( in @ SV362 @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2029,plain,
! [SV353: $i,SV182: $i,SV240: $i] :
( ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV240 )
= $false )
| ( ( in @ ( sK17_C @ SV240 @ SV182 ) @ SV353 )
= $false )
| ( ( in @ SV353 @ SV182 )
= $false )
| ( ( SV240
= ( union @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2030,plain,
! [SV241: $i,SV183: $i,SV368: $i,SV354: $i] :
( ( ( in @ SV354 @ SV368 )
= $false )
| ( ( ~ ( in @ SV368 @ SV183 ) )
= $true )
| ( ( in @ SV354 @ SV241 )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2031,plain,
! [SV183: $i,SV241: $i,SV355: $i] :
( ( ( ~ ( in @ SV355 @ ( sK16_D @ SV355 @ SV241 @ SV183 ) ) )
= $false )
| ( ( in @ SV355 @ SV241 )
= $false )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2032,plain,
! [SV183: $i,SV241: $i,SV355: $i] :
( ( ( ~ ( in @ ( sK16_D @ SV355 @ SV241 @ SV183 ) @ SV183 ) )
= $false )
| ( ( in @ SV355 @ SV241 )
= $false )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2033,plain,
! [SV84: $i,SV321: $i,SV369: $i] :
( ( ( subset @ SV369 @ SV321 )
= $false )
| ( ( in @ SV369 @ ( sK3_SY300 @ SV321 @ SV84 ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( sK2_B @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2034,plain,
! [SV363: $i,SV84: $i,SV356: $i] :
( ( ( in @ SV356 @ ( sK2_B @ SV84 ) )
= $false )
| ( ( ~ ( subset @ SV363 @ SV356 ) )
= $true )
| ( ( in @ SV363 @ ( sK2_B @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2035,plain,
! [SV272: $i,SV244: $i,SV370: $i,SV85: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV370 @ SV244 ) )
= $true )
| ( ( ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SV364 @ SV370 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2036,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
= $false )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2037,plain,
! [SV273: $i,SV365: $i,SV245: $i,SV384: $i,SV85: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV85 )
| ~ ( in @ SV384 @ SV245 )
| ( SV365
!= ( ordered_pair @ SV377 @ SV384 ) ) )
= $true )
| ( ( in @ SV365 @ SV273 )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2038,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
| ( SV366
!= ( ordered_pair @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) ) ) )
= $false )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2039,plain,
! [SV371: $i,SV86: $i,SV291: $i] :
( ( ( in @ ( sK40_C @ SV291 @ SV86 ) @ SV291 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK40_C @ SV291 @ SV86 ) @ SV371 ) @ SV86 )
= $false )
| ( ( SV291
= ( relation_dom @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2040,plain,
! [SV292: $i,SV86: $i,SV385: $i,SV372: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV372 @ SV385 ) @ SV86 ) )
= $true )
| ( ( in @ SV372 @ SV292 )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2041,plain,
! [SV86: $i,SV292: $i,SV373: $i] :
( ( ( in @ SV373 @ SV292 )
= $false )
| ( ( in @ ( ordered_pair @ SV373 @ ( sK39_D @ SV373 @ SV292 @ SV86 ) ) @ SV86 )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2042,plain,
! [SV374: $i,SV88: $i,SV293: $i] :
( ( ( in @ ( sK37_C @ SV293 @ SV88 ) @ SV293 )
= $false )
| ( ( in @ ( ordered_pair @ SV374 @ ( sK37_C @ SV293 @ SV88 ) ) @ SV88 )
= $false )
| ( ( SV293
= ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2043,plain,
! [SV294: $i,SV88: $i,SV375: $i,SV386: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV386 @ SV375 ) @ SV88 ) )
= $true )
| ( ( in @ SV375 @ SV294 )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2044,plain,
! [SV88: $i,SV294: $i,SV376: $i] :
( ( ( in @ SV376 @ SV294 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK36_D @ SV376 @ SV294 @ SV88 ) @ SV376 ) @ SV88 )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2045,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
| ~ ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2046,plain,
! [SV330: $i,SV295: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV295 )
| ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV387 ) )
= $true )
| ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2047,plain,
! [SV296: $i,SV331: $i,SV388: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_D @ SV388 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SV388 @ ( sK43_D @ SV388 @ SV331 @ SV296 ) ) )
| ( in @ SV388 @ SV331 ) )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2048,plain,
! [SV296: $i,SV331: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV331 )
| ! [SY725: $i] :
( ~ ( in @ SY725 @ SV296 )
| ( in @ SV389 @ SY725 ) ) )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2049,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
= $false )
| ( ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV89 ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2050,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
= $false )
| ( ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
!= SV250 ) )
= $true )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2051,plain,
! [SV275: $i,SV251: $i,SV89: $i,SV367: $i] :
( ( ( SV367 = SV89 )
= $true )
| ( ( SV367 = SV251 )
= $true )
| ( ( in @ SV367 @ SV275 )
= $false )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2006]) ).
thf(2052,plain,
! [SV251: $i,SV275: $i,SV89: $i,SV390: $i] :
( ( ( ( SV390 != SV89 )
| ( in @ SV390 @ SV275 ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2053,plain,
! [SV89: $i,SV275: $i,SV251: $i,SV391: $i] :
( ( ( ( SV391 != SV251 )
| ( in @ SV391 @ SV275 ) )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2054,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( ! [SY710: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SY710 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY710 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) ) )
= $false )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2055,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) ) )
= $false )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2056,plain,
! [SV345: $i,SV195: $i,SV90: $i] :
( ( ( ~ ! [SY711: $i,SY712: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY711 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY712 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY711 @ SY712 ) @ SV345 ) )
| ~ ! [SY714: $i,SY715: $i] :
( ~ ( in @ ( ordered_pair @ SY714 @ SY715 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SY714 @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) @ SY715 ) @ SV195 ) ) ) )
= $false )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2057,plain,
! [SV91: $i,SV303: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 ) )
= $true )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2058,plain,
! [SV91: $i,SV304: $i,SV392: $i] :
( ( ( ! [SY726: $i] :
( ~ ( in @ ( ordered_pair @ SV392 @ SY726 ) @ SV304 )
| ( in @ ( ordered_pair @ SY726 @ SV392 ) @ SV91 ) ) )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2059,plain,
! [SV304: $i,SV91: $i,SV393: $i] :
( ( ( ! [SY727: $i] :
( ~ ( in @ ( ordered_pair @ SY727 @ SV393 ) @ SV91 )
| ( in @ ( ordered_pair @ SV393 @ SY727 ) @ SV304 ) ) )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2060,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV79 )
= $false )
| ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
= $false )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2061,plain,
! [SV79: $i,SV223: $i,SV265: $i] :
( ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV223 )
= $false )
| ( ( in @ ( sK26_D @ SV265 @ SV223 @ SV79 ) @ SV265 )
= $false )
| ( ( SV265
= ( set_union2 @ SV79 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2062,plain,
! [SV224: $i,SV266: $i,SV79: $i,SV378: $i] :
( ( ( ~ ( in @ SV378 @ SV79 ) )
= $true )
| ( ( in @ SV378 @ SV266 )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2063,plain,
! [SV79: $i,SV266: $i,SV224: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV224 ) )
= $true )
| ( ( in @ SV379 @ SV266 )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2064,plain,
! [SV228: $i,SV80: $i,SV268: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ SV268 ) )
= $true )
| ( ( in @ SV380 @ SV80 )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2065,plain,
! [SV80: $i,SV228: $i,SV268: $i,SV381: $i] :
( ( ( ~ ( in @ SV381 @ SV268 ) )
= $true )
| ( ( ~ ( in @ SV381 @ SV228 ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2023]) ).
thf(2066,plain,
! [SV270: $i,SV81: $i,SV234: $i,SV361: $i] :
( ( ( in @ SV361 @ SV234 )
= $false )
| ( ( in @ SV361 @ SV81 )
= $false )
| ( ( in @ SV361 @ SV270 )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2067,plain,
! [SV234: $i,SV81: $i,SV270: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ SV270 ) )
= $true )
| ( ( in @ SV382 @ SV81 )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2068,plain,
! [SV81: $i,SV234: $i,SV270: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ SV270 ) )
= $true )
| ( ( in @ SV383 @ SV234 )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2069,plain,
! [SV82: $i,SV349: $i,SV362: $i] :
( ( ( subset @ SV362 @ SV349 )
= $false )
| ( ( in @ SV349 @ ( sK32_B @ SV82 ) )
= $false )
| ( ( in @ SV362 @ ( sK32_B @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2070,plain,
! [SV241: $i,SV354: $i,SV183: $i,SV368: $i] :
( ( ( in @ SV368 @ SV183 )
= $false )
| ( ( in @ SV354 @ SV368 )
= $false )
| ( ( in @ SV354 @ SV241 )
= $true )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2071,plain,
! [SV183: $i,SV241: $i,SV355: $i] :
( ( ( in @ SV355 @ ( sK16_D @ SV355 @ SV241 @ SV183 ) )
= $true )
| ( ( in @ SV355 @ SV241 )
= $false )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2072,plain,
! [SV183: $i,SV241: $i,SV355: $i] :
( ( ( in @ ( sK16_D @ SV355 @ SV241 @ SV183 ) @ SV183 )
= $true )
| ( ( in @ SV355 @ SV241 )
= $false )
| ( ( SV241
= ( union @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2073,plain,
! [SV369: $i,SV84: $i,SV321: $i] :
( ( ( in @ SV321 @ ( sK2_B @ SV84 ) )
= $false )
| ( ( in @ SV369 @ ( sK3_SY300 @ SV321 @ SV84 ) )
= $true )
| ( ( subset @ SV369 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2074,plain,
! [SV84: $i,SV356: $i,SV363: $i] :
( ( ( subset @ SV363 @ SV356 )
= $false )
| ( ( in @ SV356 @ ( sK2_B @ SV84 ) )
= $false )
| ( ( in @ SV363 @ ( sK2_B @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2075,plain,
! [SV272: $i,SV244: $i,SV370: $i,SV85: $i,SV364: $i] :
( ( ( in @ SV364 @ SV85 )
= $false )
| ( ( ~ ( in @ SV370 @ SV244 ) )
= $true )
| ( ( ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SV364 @ SV370 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2076,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2077,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( ~ ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 ) )
= $false )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2078,plain,
! [SV273: $i,SV365: $i,SV245: $i,SV384: $i,SV85: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV85 )
| ~ ( in @ SV384 @ SV245 ) )
= $true )
| ( ( ( SV365
!= ( ordered_pair @ SV377 @ SV384 ) ) )
= $true )
| ( ( in @ SV365 @ SV273 )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2079,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 ) ) )
= $false )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2038]) ).
thf(2080,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ( SV366
!= ( ordered_pair @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) ) ) )
= $false )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2038]) ).
thf(2081,plain,
! [SV292: $i,SV86: $i,SV385: $i,SV372: $i] :
( ( ( in @ ( ordered_pair @ SV372 @ SV385 ) @ SV86 )
= $false )
| ( ( in @ SV372 @ SV292 )
= $true )
| ( ( SV292
= ( relation_dom @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2082,plain,
! [SV294: $i,SV88: $i,SV375: $i,SV386: $i] :
( ( ( in @ ( ordered_pair @ SV386 @ SV375 ) @ SV88 )
= $false )
| ( ( in @ SV375 @ SV294 )
= $true )
| ( ( SV294
= ( relation_rng @ SV88 ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2083,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2084,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2085,plain,
! [SV330: $i,SV295: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV295 ) )
= $true )
| ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV387 )
= $true )
| ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2086,plain,
! [SV296: $i,SV331: $i,SV388: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_D @ SV388 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SV388 @ ( sK43_D @ SV388 @ SV331 @ SV296 ) ) ) )
= $true )
| ( ( in @ SV388 @ SV331 )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2087,plain,
! [SV296: $i,SV331: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV331 ) )
= $true )
| ( ( ! [SY725: $i] :
( ~ ( in @ SY725 @ SV296 )
| ( in @ SV389 @ SY725 ) ) )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2088,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV89 )
= $false )
| ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
= $false )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2089,plain,
! [SV89: $i,SV250: $i,SV274: $i] :
( ( ( ( sK27_D @ SV274 @ SV250 @ SV89 )
= SV250 )
= $false )
| ( ( in @ ( sK27_D @ SV274 @ SV250 @ SV89 ) @ SV274 )
= $false )
| ( ( SV274
= ( unordered_pair @ SV89 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2090,plain,
! [SV251: $i,SV275: $i,SV89: $i,SV390: $i] :
( ( ( ( SV390 != SV89 ) )
= $true )
| ( ( in @ SV390 @ SV275 )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2091,plain,
! [SV89: $i,SV275: $i,SV251: $i,SV391: $i] :
( ( ( ( SV391 != SV251 ) )
= $true )
| ( ( in @ SV391 @ SV275 )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2092,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ! [SY710: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SY710 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY710 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2093,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2094,plain,
! [SV345: $i,SV195: $i,SV90: $i] :
( ( ( ~ ! [SY711: $i,SY712: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY711 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY712 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY711 @ SY712 ) @ SV345 ) ) )
= $false )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2056]) ).
thf(2095,plain,
! [SV90: $i,SV195: $i,SV345: $i] :
( ( ( ~ ! [SY714: $i,SY715: $i] :
( ~ ( in @ ( ordered_pair @ SY714 @ SY715 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SY714 @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) @ SY715 ) @ SV195 ) ) ) )
= $false )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2056]) ).
thf(2096,plain,
! [SV91: $i,SV303: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY310 @ SV303 @ SV91 ) @ ( sK13_C @ SV303 @ SV91 ) ) @ SV91 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_C @ SV303 @ SV91 ) @ ( sK14_SY310 @ SV303 @ SV91 ) ) @ SV303 )
= $false )
| ( ( SV303
= ( relation_inverse @ SV91 ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2097,plain,
! [SV91: $i,SV304: $i,SV394: $i,SV392: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV392 @ SV394 ) @ SV304 )
| ( in @ ( ordered_pair @ SV394 @ SV392 ) @ SV91 ) )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2098,plain,
! [SV304: $i,SV91: $i,SV393: $i,SV395: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV395 @ SV393 ) @ SV91 )
| ( in @ ( ordered_pair @ SV393 @ SV395 ) @ SV304 ) )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2099,plain,
! [SV224: $i,SV266: $i,SV79: $i,SV378: $i] :
( ( ( in @ SV378 @ SV79 )
= $false )
| ( ( in @ SV378 @ SV266 )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2100,plain,
! [SV79: $i,SV266: $i,SV224: $i,SV379: $i] :
( ( ( in @ SV379 @ SV224 )
= $false )
| ( ( in @ SV379 @ SV266 )
= $true )
| ( ( SV266
= ( set_union2 @ SV79 @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2101,plain,
! [SV228: $i,SV80: $i,SV268: $i,SV380: $i] :
( ( ( in @ SV380 @ SV268 )
= $false )
| ( ( in @ SV380 @ SV80 )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2102,plain,
! [SV80: $i,SV228: $i,SV268: $i,SV381: $i] :
( ( ( in @ SV381 @ SV268 )
= $false )
| ( ( ~ ( in @ SV381 @ SV228 ) )
= $true )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2103,plain,
! [SV234: $i,SV81: $i,SV270: $i,SV382: $i] :
( ( ( in @ SV382 @ SV270 )
= $false )
| ( ( in @ SV382 @ SV81 )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2104,plain,
! [SV81: $i,SV234: $i,SV270: $i,SV383: $i] :
( ( ( in @ SV383 @ SV270 )
= $false )
| ( ( in @ SV383 @ SV234 )
= $true )
| ( ( SV270
= ( set_intersection2 @ SV81 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2105,plain,
! [SV272: $i,SV85: $i,SV364: $i,SV244: $i,SV370: $i] :
( ( ( in @ SV370 @ SV244 )
= $false )
| ( ( in @ SV364 @ SV85 )
= $false )
| ( ( ( ( sK23_D @ SV272 @ SV244 @ SV85 )
!= ( ordered_pair @ SV364 @ SV370 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2106,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( in @ ( sK24_SY316 @ SV272 @ SV244 @ SV85 ) @ SV85 )
= $true )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2107,plain,
! [SV85: $i,SV244: $i,SV272: $i] :
( ( ( in @ ( sK25_SY318 @ SV272 @ SV244 @ SV85 ) @ SV244 )
= $true )
| ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2108,plain,
! [SV273: $i,SV365: $i,SV245: $i,SV384: $i,SV85: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV384 @ SV245 ) )
= $true )
| ( ( ( SV365
!= ( ordered_pair @ SV377 @ SV384 ) ) )
= $true )
| ( ( in @ SV365 @ SV273 )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2109,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 ) ) )
= $true )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2110,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( SV366
= ( ordered_pair @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) ) )
= $true )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2111,plain,
! [SV295: $i,SV330: $i] :
( ( ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2112,plain,
! [SV295: $i,SV330: $i] :
( ( ( ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2113,plain,
! [SV330: $i,SV295: $i,SV387: $i] :
( ( ( in @ SV387 @ SV295 )
= $false )
| ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV387 )
= $true )
| ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2114,plain,
! [SV296: $i,SV331: $i,SV388: $i] :
( ( ( ~ ( in @ ( sK43_D @ SV388 @ SV331 @ SV296 ) @ SV296 )
| ~ ~ ( in @ SV388 @ ( sK43_D @ SV388 @ SV331 @ SV296 ) ) )
= $false )
| ( ( in @ SV388 @ SV331 )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2115,plain,
! [SV296: $i,SV331: $i,SV389: $i] :
( ( ( in @ SV389 @ SV331 )
= $false )
| ( ( ! [SY725: $i] :
( ~ ( in @ SY725 @ SV296 )
| ( in @ SV389 @ SY725 ) ) )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2116,plain,
! [SV251: $i,SV275: $i,SV89: $i,SV390: $i] :
( ( ( SV390 = SV89 )
= $false )
| ( ( in @ SV390 @ SV275 )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2117,plain,
! [SV89: $i,SV275: $i,SV251: $i,SV391: $i] :
( ( ( SV391 = SV251 )
= $false )
| ( ( in @ SV391 @ SV275 )
= $true )
| ( ( SV275
= ( unordered_pair @ SV89 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2118,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ! [SY710: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SY710 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY710 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2119,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2120,plain,
! [SV345: $i,SV195: $i,SV90: $i] :
( ( ( ! [SY711: $i,SY712: $i] :
( ! [SY584: $i] :
( ~ ( in @ ( ordered_pair @ SY711 @ SY584 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY584 @ SY712 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SY711 @ SY712 ) @ SV345 ) ) )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2094]) ).
thf(2121,plain,
! [SV90: $i,SV195: $i,SV345: $i] :
( ( ( ! [SY714: $i,SY715: $i] :
( ~ ( in @ ( ordered_pair @ SY714 @ SY715 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SY714 @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY715 @ SY714 @ SV345 @ SV195 @ SV90 ) @ SY715 ) @ SV195 ) ) ) )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2122,plain,
! [SV91: $i,SV304: $i,SV394: $i,SV392: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV392 @ SV394 ) @ SV304 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV394 @ SV392 ) @ SV91 )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2123,plain,
! [SV304: $i,SV91: $i,SV393: $i,SV395: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV395 @ SV393 ) @ SV91 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV393 @ SV395 ) @ SV304 )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2124,plain,
! [SV80: $i,SV268: $i,SV228: $i,SV381: $i] :
( ( ( in @ SV381 @ SV228 )
= $false )
| ( ( in @ SV381 @ SV268 )
= $false )
| ( ( SV268
= ( set_difference @ SV80 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2125,plain,
! [SV370: $i,SV364: $i,SV85: $i,SV244: $i,SV272: $i] :
( ( ( ( sK23_D @ SV272 @ SV244 @ SV85 )
= ( ordered_pair @ SV364 @ SV370 ) )
= $false )
| ( ( in @ SV364 @ SV85 )
= $false )
| ( ( in @ SV370 @ SV244 )
= $false )
| ( ( ~ ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 ) )
= $true )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2126,plain,
! [SV273: $i,SV365: $i,SV245: $i,SV384: $i,SV85: $i,SV377: $i] :
( ( ( in @ SV377 @ SV85 )
= $false )
| ( ( ~ ( in @ SV384 @ SV245 ) )
= $true )
| ( ( ( SV365
!= ( ordered_pair @ SV377 @ SV384 ) ) )
= $true )
| ( ( in @ SV365 @ SV273 )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2127,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 )
| ~ ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
= $false )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2128,plain,
! [SV295: $i,SV330: $i] :
( ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 )
= $false )
| ( ( in @ ( sK45_SY327 @ SV330 @ SV295 ) @ SV295 )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2129,plain,
! [SV295: $i,SV330: $i] :
( ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2130,plain,
! [SV296: $i,SV331: $i,SV388: $i] :
( ( ( ~ ( in @ ( sK43_D @ SV388 @ SV331 @ SV296 ) @ SV296 ) )
= $false )
| ( ( in @ SV388 @ SV331 )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2131,plain,
! [SV296: $i,SV331: $i,SV388: $i] :
( ( ( ~ ~ ( in @ SV388 @ ( sK43_D @ SV388 @ SV331 @ SV296 ) ) )
= $false )
| ( ( in @ SV388 @ SV331 )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2132,plain,
! [SV331: $i,SV389: $i,SV296: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV296 )
| ( in @ SV389 @ SV396 ) )
= $true )
| ( ( in @ SV389 @ SV331 )
= $false )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2133,plain,
! [SV397: $i,SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SV397 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SV397 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2134,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2135,plain,
! [SV345: $i,SV195: $i,SV90: $i,SV398: $i] :
( ( ( ! [SY728: $i] :
( ! [SY729: $i] :
( ~ ( in @ ( ordered_pair @ SV398 @ SY729 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY729 @ SY728 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SV398 @ SY728 ) @ SV345 ) ) )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2136,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV399: $i] :
( ( ( ! [SY730: $i] :
( ~ ( in @ ( ordered_pair @ SV399 @ SY730 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SV399 @ ( sK9_F @ SY730 @ SV399 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY730 @ SV399 @ SV345 @ SV195 @ SV90 ) @ SY730 ) @ SV195 ) ) ) )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2137,plain,
! [SV91: $i,SV304: $i,SV394: $i,SV392: $i] :
( ( ( in @ ( ordered_pair @ SV392 @ SV394 ) @ SV304 )
= $false )
| ( ( in @ ( ordered_pair @ SV394 @ SV392 ) @ SV91 )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2138,plain,
! [SV304: $i,SV91: $i,SV393: $i,SV395: $i] :
( ( ( in @ ( ordered_pair @ SV395 @ SV393 ) @ SV91 )
= $false )
| ( ( in @ ( ordered_pair @ SV393 @ SV395 ) @ SV304 )
= $true )
| ( ( SV304
= ( relation_inverse @ SV91 ) )
= $false )
| ( ( relation @ SV304 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2139,plain,
! [SV364: $i,SV370: $i,SV85: $i,SV244: $i,SV272: $i] :
( ( ( in @ ( sK23_D @ SV272 @ SV244 @ SV85 ) @ SV272 )
= $false )
| ( ( in @ SV370 @ SV244 )
= $false )
| ( ( in @ SV364 @ SV85 )
= $false )
| ( ( ( sK23_D @ SV272 @ SV244 @ SV85 )
= ( ordered_pair @ SV364 @ SV370 ) )
= $false )
| ( ( SV272
= ( cartesian_product2 @ SV85 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2140,plain,
! [SV273: $i,SV365: $i,SV85: $i,SV377: $i,SV245: $i,SV384: $i] :
( ( ( in @ SV384 @ SV245 )
= $false )
| ( ( in @ SV377 @ SV85 )
= $false )
| ( ( ( SV365
!= ( ordered_pair @ SV377 @ SV384 ) ) )
= $true )
| ( ( in @ SV365 @ SV273 )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2141,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2142,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( ~ ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 ) )
= $false )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2143,plain,
! [SV295: $i,SV330: $i] :
( ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ SV330 )
= $false )
| ( ( in @ ( sK44_C @ SV330 @ SV295 ) @ ( sK45_SY327 @ SV330 @ SV295 ) )
= $false )
| ( ( SV330
= ( set_meet @ SV295 ) )
= $true )
| ( ( SV295 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2144,plain,
! [SV296: $i,SV331: $i,SV388: $i] :
( ( ( in @ ( sK43_D @ SV388 @ SV331 @ SV296 ) @ SV296 )
= $true )
| ( ( in @ SV388 @ SV331 )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2130]) ).
thf(2145,plain,
! [SV296: $i,SV331: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ ( sK43_D @ SV388 @ SV331 @ SV296 ) ) )
= $true )
| ( ( in @ SV388 @ SV331 )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2131]) ).
thf(2146,plain,
! [SV331: $i,SV389: $i,SV296: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV296 ) )
= $true )
| ( ( in @ SV389 @ SV396 )
= $true )
| ( ( in @ SV389 @ SV331 )
= $false )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2147,plain,
! [SV397: $i,SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SV397 ) @ SV90 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV397 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2148,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2134]) ).
thf(2149,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2134]) ).
thf(2150,plain,
! [SV345: $i,SV195: $i,SV400: $i,SV90: $i,SV398: $i] :
( ( ( ! [SY731: $i] :
( ~ ( in @ ( ordered_pair @ SV398 @ SY731 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY731 @ SV400 ) @ SV195 ) )
| ( in @ ( ordered_pair @ SV398 @ SV400 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2151,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV401: $i,SV399: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV399 @ SV401 ) @ SV345 )
| ~ ( ~ ( in @ ( ordered_pair @ SV399 @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) @ SV401 ) @ SV195 ) ) )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2152,plain,
! [SV273: $i,SV245: $i,SV85: $i,SV384: $i,SV377: $i,SV365: $i] :
( ( ( SV365
= ( ordered_pair @ SV377 @ SV384 ) )
= $false )
| ( ( in @ SV377 @ SV85 )
= $false )
| ( ( in @ SV384 @ SV245 )
= $false )
| ( ( in @ SV365 @ SV273 )
= $true )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2153,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( in @ ( sK21_E @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV85 )
= $true )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2154,plain,
! [SV85: $i,SV245: $i,SV273: $i,SV366: $i] :
( ( ( in @ ( sK22_SY313 @ SV366 @ SV273 @ SV245 @ SV85 ) @ SV245 )
= $true )
| ( ( in @ SV366 @ SV273 )
= $false )
| ( ( SV273
= ( cartesian_product2 @ SV85 @ SV245 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2142]) ).
thf(2155,plain,
! [SV296: $i,SV331: $i,SV388: $i] :
( ( ( in @ SV388 @ ( sK43_D @ SV388 @ SV331 @ SV296 ) )
= $false )
| ( ( in @ SV388 @ SV331 )
= $true )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2156,plain,
! [SV331: $i,SV389: $i,SV296: $i,SV396: $i] :
( ( ( in @ SV396 @ SV296 )
= $false )
| ( ( in @ SV389 @ SV396 )
= $true )
| ( ( in @ SV389 @ SV331 )
= $false )
| ( ( SV331
= ( set_meet @ SV296 ) )
= $false )
| ( ( SV296 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2157,plain,
! [SV397: $i,SV90: $i,SV195: $i,SV344: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SV397 ) @ SV90 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV397 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2158,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) ) @ SV90 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2159,plain,
! [SV90: $i,SV195: $i,SV344: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY309 @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2160,plain,
! [SV345: $i,SV195: $i,SV400: $i,SV90: $i,SV398: $i] :
( ( ( ! [SY731: $i] :
( ~ ( in @ ( ordered_pair @ SV398 @ SY731 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY731 @ SV400 ) @ SV195 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV398 @ SV400 ) @ SV345 )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2161,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV401: $i,SV399: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV399 @ SV401 ) @ SV345 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV399 @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) @ SV401 ) @ SV195 ) ) )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2162,plain,
! [SV90: $i,SV195: $i,SV344: $i,SV397: $i] :
( ( ( in @ ( ordered_pair @ SV397 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SV397 ) @ SV90 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 ) )
= $true )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2163,plain,
! [SV345: $i,SV195: $i,SV400: $i,SV90: $i,SV402: $i,SV398: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV398 @ SV402 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SV402 @ SV400 ) @ SV195 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV398 @ SV400 ) @ SV345 )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2164,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV401: $i,SV399: $i] :
( ( ( in @ ( ordered_pair @ SV399 @ SV401 ) @ SV345 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV399 @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) @ SV401 ) @ SV195 ) ) )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2165,plain,
! [SV397: $i,SV90: $i,SV195: $i,SV344: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV344 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV344 @ SV195 @ SV90 ) @ SV397 ) @ SV90 )
= $false )
| ( ( in @ ( ordered_pair @ SV397 @ ( sK11_SY305 @ SV344 @ SV195 @ SV90 ) ) @ SV195 )
= $false )
| ( ( SV344
= ( relation_composition @ SV90 @ SV195 ) )
= $true )
| ( ( relation @ SV344 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2166,plain,
! [SV345: $i,SV195: $i,SV400: $i,SV90: $i,SV402: $i,SV398: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV398 @ SV402 ) @ SV90 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV402 @ SV400 ) @ SV195 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV398 @ SV400 ) @ SV345 )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2167,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV401: $i,SV399: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV399 @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) @ SV401 ) @ SV195 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV399 @ SV401 ) @ SV345 )
= $false )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2168,plain,
! [SV345: $i,SV195: $i,SV400: $i,SV90: $i,SV402: $i,SV398: $i] :
( ( ( in @ ( ordered_pair @ SV398 @ SV402 ) @ SV90 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV402 @ SV400 ) @ SV195 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV398 @ SV400 ) @ SV345 )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2169,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV401: $i,SV399: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV399 @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) ) @ SV90 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV399 @ SV401 ) @ SV345 )
= $false )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2167]) ).
thf(2170,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV399: $i,SV401: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) @ SV401 ) @ SV195 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV399 @ SV401 ) @ SV345 )
= $false )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2167]) ).
thf(2171,plain,
! [SV345: $i,SV90: $i,SV398: $i,SV195: $i,SV400: $i,SV402: $i] :
( ( ( in @ ( ordered_pair @ SV402 @ SV400 ) @ SV195 )
= $false )
| ( ( in @ ( ordered_pair @ SV398 @ SV402 ) @ SV90 )
= $false )
| ( ( in @ ( ordered_pair @ SV398 @ SV400 ) @ SV345 )
= $true )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2172,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV401: $i,SV399: $i] :
( ( ( in @ ( ordered_pair @ SV399 @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) ) @ SV90 )
= $true )
| ( ( in @ ( ordered_pair @ SV399 @ SV401 ) @ SV345 )
= $false )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2169]) ).
thf(2173,plain,
! [SV90: $i,SV195: $i,SV345: $i,SV399: $i,SV401: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_F @ SV401 @ SV399 @ SV345 @ SV195 @ SV90 ) @ SV401 ) @ SV195 )
= $true )
| ( ( in @ ( ordered_pair @ SV399 @ SV401 ) @ SV345 )
= $false )
| ( ( SV345
= ( relation_composition @ SV90 @ SV195 ) )
= $false )
| ( ( relation @ SV345 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2170]) ).
thf(2174,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[422,2173,2172,2171,2165,2159,2158,2156,2155,2154,2153,2152,2144,2143,2139,2138,2137,2128,2124,2117,2116,2113,2110,2107,2106,2104,2103,2101,2100,2099,2096,2089,2088,2082,2081,2074,2073,2072,2071,2070,2069,2066,2061,2060,2051,2044,2042,2041,2039,2029,2024,2021,2020,2017,2012,1991,1979,1978,1972,1971,1961,1960,1936,1932,1931,1929,1928,1904,1901,1900,1897,1894,1893,1887,1883,1867,1866,1865,1851,1848,1847,1846,1845,1844,1843,1842,1832,1831,1798,1788,1781,1780,1776,1775,1772,1771,1770,1765,1739,1736,1735,1728,1723,1721,1716,1715,1705,1704,1700,1698,1697,1696,1692,1691,1633,1628,1627,1623,1617,1612,1610,1604,1596,1584,1569,1566,1565,1564,1552,1536,1535,1528,1524,1523,1522,1521,1507,1506,1484,1483,1482,1481,1458,1457,1452,1451,1444,1440,1439,1433,1425,1424,1422,1421,1420,1419,1418,1416,1401,1391,1390,1384,1366,1365,1331,1330,1320,1318,1309,1301,1299,1298,1295,1294,1286,1280,1189,1186,1185,1184,1183,1182,1179,1178,1177,1171,1170,1169,1157,1125,1124,1098,1064,1063,1061,1060,1057,1054,1051,1050,1048,1044,1042,1038,1033,1023,997,996,964,947,946,945,944,922,920,899,896,895,890,889,888,882,881,784,782,781,780,779,773,769,766,765,764,758,733,671,670,669,668,655,649,625,624,623,622,607,549,535,448]) ).
thf(2175,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(2176,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)],[417]) ).
thf(2177,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)],[416]) ).
thf(2178,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(2179,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)],[415]) ).
thf(2180,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(2181,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)],[413]) ).
thf(2182,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(2183,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)],[412]) ).
thf(2184,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)],[411]) ).
thf(2185,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)],[410]) ).
thf(2186,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(2187,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(2188,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(2189,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)],[406]) ).
thf(2190,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)],[405]) ).
thf(2191,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK49_B @ A ) @ ( sK50_SY332 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(2192,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(2193,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( A = empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(2194,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(2195,plain,
( ( ! [A: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ( sK48_B @ A )
!= ( ordered_pair @ SY330 @ SY331 ) )
& ( in @ ( sK48_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK46_C @ B @ A ) @ ( sK47_SY329 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(2196,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK45_SY327 @ B @ A ) @ A )
& ~ ( in @ ( sK44_C @ B @ A ) @ ( sK45_SY327 @ B @ A ) ) )
| ~ ( in @ ( sK44_C @ B @ A ) @ B ) )
& ( ! [SY328: $i] :
( ~ ( in @ SY328 @ A )
| ( in @ ( sK44_C @ B @ A ) @ SY328 ) )
| ( 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)],[400]) ).
thf(2197,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)],[399]) ).
thf(2198,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY325: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ SY325 ) @ A )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY326 @ 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)],[398]) ).
thf(2199,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY323: $i] :
~ ( in @ ( ordered_pair @ SY323 @ ( sK37_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK37_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK38_SY324 @ 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)],[397]) ).
thf(2200,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(2201,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)],[395]) ).
thf(2202,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(2203,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(2204,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(2205,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(2206,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(2207,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(2208,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(2209,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(2210,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(2211,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(2212,plain,
( ( ( empty @ sK35_A )
& ( relation @ sK35_A ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(2213,plain,
( ( ~ ( empty @ sK34_A )
& ( relation @ sK34_A ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(2214,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(2215,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(2216,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(2217,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(2218,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(2219,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(2220,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(2221,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(2222,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)],[380]) ).
thf(2223,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(2224,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)],[378]) ).
thf(2225,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(2226,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)],[376]) ).
thf(2227,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)],[375]) ).
thf(2228,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)],[374]) ).
thf(2229,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)],[373]) ).
thf(2230,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)],[372]) ).
thf(2231,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(2232,plain,
( ( ! [A: $i] :
( ! [SY319: $i] :
( ~ ( subset @ SY319 @ ( sK32_B @ A ) )
| ( are_equipotent @ SY319 @ ( sK32_B @ A ) )
| ( in @ SY319 @ ( sK32_B @ A ) ) )
& ! [SY320: $i] :
( ~ ( in @ SY320 @ ( sK32_B @ A ) )
| ( in @ ( powerset @ SY320 ) @ ( sK32_B @ A ) ) )
& ! [SY321: $i,SY322: $i] :
( ~ ( in @ SY321 @ ( sK32_B @ A ) )
| ~ ( subset @ SY322 @ SY321 )
| ( in @ SY322 @ ( sK32_B @ A ) ) )
& ( in @ A @ ( sK32_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(2233,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(2234,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(2235,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(2236,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(2237,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(2238,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)],[365]) ).
thf(2239,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(2240,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)],[363]) ).
thf(2241,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(2242,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)],[362]) ).
thf(2243,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)],[361]) ).
thf(2244,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(2245,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)],[360]) ).
thf(2246,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(2247,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(2248,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(2249,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(2250,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)],[357]) ).
thf(2251,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(2252,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(2253,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)],[354]) ).
thf(2254,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(2255,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(2256,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(2257,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)],[352]) ).
thf(2258,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(2259,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(2260,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(2261,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(2262,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(2263,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(2264,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(2265,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(2266,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)],[346]) ).
thf(2267,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)],[345]) ).
thf(2268,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)],[344]) ).
thf(2269,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)],[343]) ).
thf(2270,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)],[342]) ).
thf(2271,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)],[341]) ).
thf(2272,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY314: $i,SY315: $i] :
( ~ ( in @ SY314 @ A )
| ~ ( in @ SY315 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY314 @ SY315 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY316 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY318 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY316 @ C @ B @ A ) @ ( sK25_SY318 @ 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_SY313 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY313 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(2273,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)],[339]) ).
thf(2274,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)],[338]) ).
thf(2275,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY311: $i] :
( ~ ( in @ ( sK17_C @ B @ A ) @ SY311 )
| ~ ( in @ SY311 @ A ) )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK17_C @ B @ A ) @ ( sK18_SY312 @ B @ A ) )
& ( in @ ( sK18_SY312 @ 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)],[337]) ).
thf(2276,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)],[336]) ).
thf(2277,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(2278,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY310 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY310 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ 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)],[335]) ).
thf(2279,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY308: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ SY308 ) @ A )
| ~ ( in @ ( ordered_pair @ SY308 @ ( sK11_SY305 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY305 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK12_SY309 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_SY309 @ C @ B @ A ) @ ( sK11_SY305 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY305 @ 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)],[334]) ).
thf(2280,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)],[333]) ).
thf(2281,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(2282,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(2283,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(2284,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(2285,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(2286,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(2287,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(2288,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(2289,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(2290,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(2291,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(2292,plain,
( ( ! [A: $i] :
( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK6_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(2293,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(2294,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(2295,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(2296,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(2297,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(2298,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)],[319]) ).
thf(2299,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)],[318]) ).
thf(2300,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(2301,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(2302,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(2303,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(2304,plain,
( ( ! [A: $i] :
( ! [SY298: $i] :
( ~ ( subset @ SY298 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY298 @ ( sK2_B @ A ) )
| ( in @ SY298 @ ( sK2_B @ A ) ) )
& ! [SY299: $i] :
( ( ! [SY304: $i] :
( ~ ( subset @ SY304 @ SY299 )
| ( in @ SY304 @ ( sK3_SY300 @ SY299 @ A ) ) )
& ( in @ ( sK3_SY300 @ SY299 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY299 @ ( sK2_B @ A ) ) )
& ! [SY302: $i,SY303: $i] :
( ~ ( in @ SY302 @ ( sK2_B @ A ) )
| ~ ( subset @ SY303 @ SY302 )
| ( in @ SY303 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(2305,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(2306,plain,
( ( ( ( relation_rng @ sK1_A )
= empty_set )
& ( ( relation_dom @ sK1_A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(2307,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)],[2238]) ).
thf(2308,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_SY305 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY305 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY309 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY305 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY305 @ 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)],[2279]) ).
thf(2309,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_SY300 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK3_SY300 @ 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)],[2304]) ).
thf(2310,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)],[2229]) ).
thf(2311,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)],[2185]) ).
thf(2312,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)],[2240]) ).
thf(2313,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)],[2184]) ).
thf(2314,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY310 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY310 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ 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)],[2278]) ).
thf(2315,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)],[2228]) ).
thf(2316,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)],[2201]) ).
thf(2317,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)],[2266]) ).
thf(2318,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)],[2253]) ).
thf(2319,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)],[2227]) ).
thf(2320,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)],[2181]) ).
thf(2321,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)],[2273]) ).
thf(2322,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)],[2271]) ).
thf(2323,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)],[2242]) ).
thf(2324,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[2196]) ).
thf(2325,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_SY312 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY312 @ 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)],[2275]) ).
thf(2326,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)],[2274]) ).
thf(2327,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2206]) ).
thf(2328,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2209]) ).
thf(2329,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)],[2232]) ).
thf(2330,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2210]) ).
thf(2331,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)],[2268]) ).
thf(2332,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)],[2245]) ).
thf(2333,plain,
( ( ~ ( ( ( relation_rng @ sK1_A )
!= empty_set )
| ~ ( ( ( relation_dom @ sK1_A )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2306]) ).
thf(2334,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_SY324 @ 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)],[2199]) ).
thf(2335,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)],[2269]) ).
thf(2336,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK6_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK6_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2292]) ).
thf(2337,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)],[2222]) ).
thf(2338,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)],[2177]) ).
thf(2339,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)],[2197]) ).
thf(2340,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2193]) ).
thf(2341,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)],[2183]) ).
thf(2342,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)],[2176]) ).
thf(2343,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)],[2298]) ).
thf(2344,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)],[2299]) ).
thf(2345,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_SY329 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2195]) ).
thf(2346,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)],[2243]) ).
thf(2347,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)],[2270]) ).
thf(2348,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)],[2226]) ).
thf(2349,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)],[2179]) ).
thf(2350,plain,
( ( ~ ( ~ ( empty @ sK35_A )
| ~ ( relation @ sK35_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2212]) ).
thf(2351,plain,
( ( ~ ( ~ ~ ( empty @ sK34_A )
| ~ ( relation @ sK34_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2213]) ).
thf(2352,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)],[2250]) ).
thf(2353,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)],[2267]) ).
thf(2354,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)],[2280]) ).
thf(2355,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_SY316 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_SY318 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK24_SY316 @ SX2 @ SX1 @ SX0 ) @ ( sK25_SY318 @ 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_SY313 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY313 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2272]) ).
thf(2356,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2290]) ).
thf(2357,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)],[2257]) ).
thf(2358,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)],[2276]) ).
thf(2359,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_SY326 @ 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)],[2198]) ).
thf(2360,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2192]) ).
thf(2361,plain,
! [SV403: $i] :
( ( ( ( singleton @ SV403 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2362,plain,
! [SV404: $i] :
( ( ~ ( relation @ SV404 )
| ( subset @ SV404 @ ( cartesian_product2 @ ( relation_dom @ SV404 ) @ ( relation_rng @ SV404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2363,plain,
! [SV405: $i] :
( ( subset @ empty_set @ SV405 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2364,plain,
! [SV406: $i] :
( ( ~ ( subset @ SV406 @ empty_set )
| ( SV406 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2365,plain,
! [SV407: $i] :
( ( ~ ( relation @ SV407 )
| ! [SY732: $i] :
( ~ ( relation @ SY732 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV407 @ SY732 ) ) @ ( relation_dom @ SV407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2366,plain,
! [SV408: $i] :
( ( ~ ( relation @ SV408 )
| ! [SY733: $i] :
( ~ ( relation @ SY733 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV408 @ SY733 ) ) @ ( relation_rng @ SY733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2367,plain,
! [SV409: $i] :
( ( ~ ( relation @ SV409 )
| ! [SY734: $i] :
( ~ ( relation @ SY734 )
| ~ ( subset @ ( relation_rng @ SV409 ) @ ( relation_dom @ SY734 ) )
| ( ( relation_dom @ ( relation_composition @ SV409 @ SY734 ) )
= ( relation_dom @ SV409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2368,plain,
! [SV410: $i] :
( ( ~ ( relation @ SV410 )
| ! [SY735: $i] :
( ~ ( relation @ SY735 )
| ~ ( subset @ ( relation_dom @ SV410 ) @ ( relation_rng @ SY735 ) )
| ( ( relation_rng @ ( relation_composition @ SY735 @ SV410 ) )
= ( relation_rng @ SV410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2369,plain,
! [SV411: $i] :
( ( ~ ( relation @ SV411 )
| ( in @ ( ordered_pair @ ( sK49_B @ SV411 ) @ ( sK50_SY332 @ SV411 ) ) @ SV411 )
| ( SV411 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2370,plain,
! [SV412: $i] :
( ( ~ ( empty @ SV412 )
| ( relation @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2371,plain,
! [SV413: $i] :
( ( ~ ( relation @ SV413 )
| ( ( relation_field @ SV413 )
= ( set_union2 @ ( relation_dom @ SV413 ) @ ( relation_rng @ SV413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2372,plain,
! [SV414: $i] :
( ( ~ ( relation @ SV414 )
| ( relation @ ( relation_inverse @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2373,plain,
! [SV415: $i] :
( ( ! [SY736: $i] :
( ~ ( relation @ SV415 )
| ~ ( relation @ SY736 )
| ( relation @ ( relation_composition @ SV415 @ SY736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2374,plain,
! [SV416: $i] :
( ( ! [SY737: $i] :
( ~ ( relation @ SV416 )
| ~ ( relation @ SY737 )
| ( relation @ ( set_union2 @ SV416 @ SY737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2375,plain,
! [SV417: $i] :
( ( ( empty @ SV417 )
| ~ ( relation @ SV417 )
| ~ ( empty @ ( relation_dom @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2376,plain,
! [SV418: $i] :
( ( ( empty @ SV418 )
| ~ ( relation @ SV418 )
| ~ ( empty @ ( relation_rng @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2377,plain,
! [SV419: $i] :
( ( ~ ( relation @ SV419 )
| ( ( relation_inverse @ ( relation_inverse @ SV419 ) )
= SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2378,plain,
! [SV420: $i] :
( ( ( set_union2 @ SV420 @ empty_set )
= SV420 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2379,plain,
! [SV421: $i] :
( ( ( set_intersection2 @ SV421 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2380,plain,
! [SV422: $i] :
( ( ( set_difference @ SV422 @ empty_set )
= SV422 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2381,plain,
! [SV423: $i] :
( ( ( set_difference @ empty_set @ SV423 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2382,plain,
! [SV424: $i] :
( ( ~ ( empty @ SV424 )
| ( SV424 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2383,plain,
! [SV425: $i] :
( ( ! [SY738: $i] :
( ~ ( in @ SV425 @ SY738 )
| ( ( set_union2 @ ( singleton @ SV425 ) @ SY738 )
= SY738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2384,plain,
! [SV426: $i] :
( ( ! [SY739: $i] :
( ~ ( disjoint @ ( singleton @ SV426 ) @ SY739 )
| ~ ( in @ SV426 @ SY739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2385,plain,
! [SV427: $i] :
( ( ! [SY740: $i] :
( ( in @ SV427 @ SY740 )
| ( disjoint @ ( singleton @ SV427 ) @ SY740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2386,plain,
! [SV428: $i] :
( ( ! [SY741: $i] :
( ~ ( element @ SY741 @ ( powerset @ SV428 ) )
| ! [SY742: $i] :
( ~ ( in @ SY742 @ SY741 )
| ( in @ SY742 @ SV428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2387,plain,
! [SV429: $i] :
( ( ! [SY743: $i] :
( ~ ( subset @ SV429 @ SY743 )
| ! [SY744: $i] :
( ( in @ SY744 @ SV429 )
| ( subset @ SV429 @ ( set_difference @ SY743 @ ( singleton @ SY744 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2388,plain,
! [SV430: $i] :
( ( ! [SY745: $i] :
( ~ ( in @ SV430 @ SY745 )
| ( subset @ SV430 @ ( union @ SY745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2389,plain,
! [SV431: $i] :
( ( ! [SY746: $i,SY747: $i,SY748: $i] :
( ~ ( subset @ SV431 @ SY746 )
| ~ ( subset @ SY747 @ SY748 )
| ( subset @ ( cartesian_product2 @ SV431 @ SY747 ) @ ( cartesian_product2 @ SY746 @ SY748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2390,plain,
! [SV432: $i] :
( ( ! [SY749: $i] :
( ~ ( subset @ SV432 @ SY749 )
| ( ( set_union2 @ SV432 @ SY749 )
= SY749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2391,plain,
! [SV433: $i] :
( ( ! [SY750: $i] : ( subset @ ( set_intersection2 @ SV433 @ SY750 ) @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2392,plain,
! [SV434: $i] :
( ( ! [SY751: $i,SY752: $i] :
( ~ ( subset @ SV434 @ SY751 )
| ~ ( subset @ SV434 @ SY752 )
| ( subset @ SV434 @ ( set_intersection2 @ SY751 @ SY752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2393,plain,
! [SV435: $i] :
( ( ! [SY753: $i,SY754: $i] :
( ~ ( subset @ SV435 @ SY753 )
| ~ ( subset @ SY753 @ SY754 )
| ( subset @ SV435 @ SY754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2394,plain,
! [SV436: $i] :
( ( ! [SY755: $i] :
( ~ ( subset @ SV436 @ SY755 )
| ! [SY756: $i] : ( subset @ ( set_intersection2 @ SV436 @ SY756 ) @ ( set_intersection2 @ SY755 @ SY756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2395,plain,
! [SV437: $i] :
( ( ! [SY757: $i] :
( ~ ( subset @ SV437 @ SY757 )
| ( ( set_intersection2 @ SV437 @ SY757 )
= SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2396,plain,
! [SV438: $i] :
( ( ! [SY758: $i] :
( ~ ( subset @ SV438 @ SY758 )
| ! [SY759: $i] : ( subset @ ( set_difference @ SV438 @ SY759 ) @ ( set_difference @ SY758 @ SY759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2397,plain,
! [SV439: $i] :
( ( ! [SY760: $i] : ( subset @ ( set_difference @ SV439 @ SY760 ) @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2398,plain,
! [SV440: $i] :
( ( ! [SY761: $i] :
( ( set_union2 @ SV440 @ ( set_difference @ SY761 @ SV440 ) )
= ( set_union2 @ SV440 @ SY761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2399,plain,
! [SV441: $i] :
( ( ! [SY762: $i] :
( ( set_difference @ ( set_union2 @ SV441 @ SY762 ) @ SY762 )
= ( set_difference @ SV441 @ SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2400,plain,
! [SV442: $i] :
( ( ! [SY763: $i] :
( ~ ( subset @ SV442 @ SY763 )
| ( SY763
= ( set_union2 @ SV442 @ ( set_difference @ SY763 @ SV442 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2401,plain,
! [SV443: $i] :
( ( ! [SY764: $i] :
( ~ ( in @ SV443 @ SY764 )
| ( ( set_union2 @ ( singleton @ SV443 ) @ SY764 )
= SY764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2402,plain,
! [SV444: $i] :
( ( ! [SY765: $i] :
( ( set_difference @ SV444 @ ( set_difference @ SV444 @ SY765 ) )
= ( set_intersection2 @ SV444 @ SY765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2403,plain,
! [SV445: $i] :
( ( ! [SY766: $i] :
( ~ ( proper_subset @ SY766 @ SV445 )
| ~ ( subset @ SV445 @ SY766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2404,plain,
! [SV446: $i] :
( ( ! [SY767: $i,SY768: $i] :
( ~ ( disjoint @ SY767 @ SY768 )
| ~ ( subset @ SV446 @ SY767 )
| ( disjoint @ SV446 @ SY768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2405,plain,
! [SV447: $i] :
( ( ( unordered_pair @ SV447 @ SV447 )
= ( singleton @ SV447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2406,plain,
! [SV448: $i] :
( ( ! [SY769: $i] :
( ~ ( subset @ ( singleton @ SV448 ) @ ( singleton @ SY769 ) )
| ( SV448 = SY769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2407,plain,
! [SV449: $i] :
( ( ! [SY770: $i] : ( subset @ SV449 @ ( set_union2 @ SV449 @ SY770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2408,plain,
! [SV450: $i] :
( ( ! [SY771: $i,SY772: $i] :
( ~ ( subset @ SV450 @ SY771 )
| ~ ( subset @ SY772 @ SY771 )
| ( subset @ ( set_union2 @ SV450 @ SY772 ) @ SY771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2409,plain,
! [SV451: $i] :
( ( ! [SY773: $i] :
( ! [SY774: $i] :
( ( singleton @ SV451 )
!= ( unordered_pair @ SY773 @ SY774 ) )
| ( SV451 = SY773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2410,plain,
! [SV452: $i] :
( ( ! [SY775: $i] :
( ~ ( in @ SV452 @ SY775 )
| ( subset @ SV452 @ ( union @ SY775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2411,plain,
! [SV453: $i] :
( ( ( union @ ( powerset @ SV453 ) )
= SV453 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2412,plain,
! [SV454: $i] :
( ( ! [SY776: $i,SY777: $i] :
( ( ( singleton @ SV454 )
!= ( unordered_pair @ SY776 @ SY777 ) )
| ( SY776 = SY777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2413,plain,
! [SV455: $i] :
( ( ! [SY778: $i] :
( ~ ( in @ SV455 @ SY778 )
| ~ ( in @ SY778 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2414,plain,
! [SV456: $i] :
( ( ! [SY779: $i] :
( ( set_union2 @ SV456 @ SY779 )
= ( set_union2 @ SY779 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2415,plain,
! [SV457: $i] :
( ( ! [SY780: $i] :
( ( set_intersection2 @ SV457 @ SY780 )
= ( set_intersection2 @ SY780 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2416,plain,
! [SV458: $i] :
( ( ! [SY781: $i] :
( ( ordered_pair @ SV458 @ SY781 )
= ( unordered_pair @ ( unordered_pair @ SV458 @ SY781 ) @ ( singleton @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2417,plain,
! [SV459: $i] :
( ( ~ ( empty @ ( powerset @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2418,plain,
! [SV460: $i] :
( ( ! [SY782: $i] :
~ ( empty @ ( ordered_pair @ SV460 @ SY782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2419,plain,
! [SV461: $i] :
( ( ~ ( empty @ ( singleton @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2420,plain,
! [SV462: $i] :
( ( ( empty @ SV462 )
| ! [SY783: $i] :
~ ( empty @ ( set_union2 @ SV462 @ SY783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2421,plain,
! [SV463: $i] :
( ( ! [SY784: $i] :
~ ( empty @ ( unordered_pair @ SV463 @ SY784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2422,plain,
! [SV464: $i] :
( ( ( empty @ SV464 )
| ! [SY785: $i] :
~ ( empty @ ( set_union2 @ SY785 @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2423,plain,
! [SV465: $i] :
( ( ! [SY786: $i] :
( ( empty @ SV465 )
| ( empty @ SY786 )
| ~ ( empty @ ( cartesian_product2 @ SV465 @ SY786 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2424,plain,
! [SV466: $i] :
( ( ( set_union2 @ SV466 @ SV466 )
= SV466 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2425,plain,
! [SV467: $i] :
( ( ( set_intersection2 @ SV467 @ SV467 )
= SV467 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2426,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2427,plain,
! [SV468: $i] :
( ( subset @ SV468 @ SV468 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2428,plain,
! [SV469: $i] :
( ( ! [SY787: $i] :
( ~ ( disjoint @ SV469 @ SY787 )
| ( disjoint @ SY787 @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2429,plain,
! [SV470: $i] :
( ( ! [SY788: $i] :
( ~ ( in @ SV470 @ SY788 )
| ( element @ SV470 @ SY788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2430,plain,
! [SV471: $i] :
( ( ! [SY789: $i] :
( ~ ( element @ SV471 @ SY789 )
| ( empty @ SY789 )
| ( in @ SV471 @ SY789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2431,plain,
! [SV472: $i] :
( ( ! [SY790: $i,SY791: $i] :
( ~ ( element @ SY790 @ ( powerset @ SY791 ) )
| ~ ( in @ SV472 @ SY790 )
| ( element @ SV472 @ SY791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2432,plain,
! [SV473: $i] :
( ( ! [SY792: $i,SY793: $i] :
( ~ ( element @ SY792 @ ( powerset @ SY793 ) )
| ~ ( in @ SV473 @ SY792 )
| ~ ( empty @ SY793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2433,plain,
! [SV474: $i] :
( ( ! [SY794: $i] :
( ~ ( empty @ SY794 )
| ~ ( in @ SV474 @ SY794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2434,plain,
! [SV475: $i] :
( ( ! [SY795: $i] :
( ( SV475 = SY795 )
| ~ ( empty @ SV475 )
| ~ ( empty @ SY795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2435,plain,
! [SV476: $i] :
( ( ~ ( ~ ! [SY796: $i,SY797: $i] :
( ~ ( relation @ SY797 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY796 ) @ SY797 )
| ( in @ SV476 @ ( relation_field @ SY797 ) ) )
| ~ ! [SY798: $i,SY799: $i] :
( ~ ( relation @ SY799 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY798 ) @ SY799 )
| ( in @ SY798 @ ( relation_field @ SY799 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2436,plain,
! [SV477: $i] :
( ( ~ ( relation @ SV477 )
| ! [SY800: $i] :
( ~ ( relation @ SY800 )
| ~ ( ~ ! [SY801: $i] :
( ~ ( relation @ SY801 )
| ~ ( ~ ( ! [SY802: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ SY802 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY802 @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY800 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY801 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK12_SY309 @ SY801 @ SY800 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY800 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY801 ) ) )
| ( SY801
= ( relation_composition @ SV477 @ SY800 ) ) )
| ~ ! [SY803: $i] :
( ~ ( relation @ SY803 )
| ( SY803
!= ( relation_composition @ SV477 @ SY800 ) )
| ~ ( ~ ! [SY804: $i,SY805: $i] :
( ! [SY806: $i] :
( ~ ( in @ ( ordered_pair @ SY804 @ SY806 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY806 @ SY805 ) @ SY800 ) )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SY803 ) )
| ~ ! [SY807: $i,SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY807 @ SY808 ) @ SY803 )
| ~ ( ~ ( in @ ( ordered_pair @ SY807 @ ( sK9_F @ SY808 @ SY807 @ SY803 @ SY800 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY808 @ SY807 @ SY803 @ SY800 @ SV477 ) @ SY808 ) @ SY800 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2437,plain,
! [SV478: $i] :
( ( ~ ( ~ ! [SY809: $i] :
( ~ ( subset @ SY809 @ ( sK2_B @ SV478 ) )
| ( are_equipotent @ SY809 @ ( sK2_B @ SV478 ) )
| ( in @ SY809 @ ( sK2_B @ SV478 ) ) )
| ~ ~ ( ~ ! [SY810: $i] :
( ~ ( ~ ! [SY811: $i] :
( ~ ( subset @ SY811 @ SY810 )
| ( in @ SY811 @ ( sK3_SY300 @ SY810 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY810 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SY810 @ ( sK2_B @ SV478 ) ) )
| ~ ~ ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2438,plain,
! [SV479: $i] :
( ( ~ ( ~ ! [SY814: $i] :
( ~ ( subset @ SV479 @ SY814 )
| ! [SY815: $i] : ( subset @ ( cartesian_product2 @ SV479 @ SY815 ) @ ( cartesian_product2 @ SY814 @ SY815 ) ) )
| ~ ! [SY816: $i] :
( ~ ( subset @ SV479 @ SY816 )
| ! [SY817: $i] : ( subset @ ( cartesian_product2 @ SY817 @ SV479 ) @ ( cartesian_product2 @ SY817 @ SY816 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2439,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)],[2311]) ).
thf(2440,plain,
! [SV480: $i] :
( ( ! [SY818: $i] :
~ ( ~ ! [SY819: $i] :
( ! [SY820: $i] :
( ( ordered_pair @ SV480 @ SY818 )
!= ( ordered_pair @ SY819 @ SY820 ) )
| ( SV480 = SY819 ) )
| ~ ! [SY821: $i,SY822: $i] :
( ( ( ordered_pair @ SV480 @ SY818 )
!= ( ordered_pair @ SY821 @ SY822 ) )
| ( SY818 = SY822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2441,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)],[2313]) ).
thf(2442,plain,
! [SV481: $i] :
( ( ~ ( relation @ SV481 )
| ~ ( ~ ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) ) )
| ( SY823
= ( relation_inverse @ SV481 ) ) )
| ~ ! [SY824: $i] :
( ~ ( relation @ SY824 )
| ( SY824
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY825: $i,SY826: $i] :
( ~ ( in @ ( ordered_pair @ SY825 @ SY826 ) @ SY824 )
| ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV481 ) )
| ~ ! [SY827: $i,SY828: $i] :
( ~ ( in @ ( ordered_pair @ SY828 @ SY827 ) @ SV481 )
| ( in @ ( ordered_pair @ SY827 @ SY828 ) @ SY824 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2443,plain,
! [SV482: $i] :
( ( ! [SY829: $i] :
~ ( ~ ! [SY830: $i,SY831: $i] :
( ~ ( in @ SV482 @ SY830 )
| ~ ( in @ SY829 @ SY831 )
| ( in @ ( ordered_pair @ SV482 @ SY829 ) @ ( cartesian_product2 @ SY830 @ SY831 ) ) )
| ~ ~ ( ~ ! [SY832: $i] :
( ! [SY833: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SY829 ) @ ( cartesian_product2 @ SY832 @ SY833 ) )
| ( in @ SV482 @ SY832 ) )
| ~ ! [SY834: $i,SY835: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SY829 ) @ ( cartesian_product2 @ SY834 @ SY835 ) )
| ( in @ SY829 @ SY835 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2444,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)],[2316]) ).
thf(2445,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)],[2317]) ).
thf(2446,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)],[2318]) ).
thf(2447,plain,
! [SV483: $i] :
( ( ! [SY836: $i] :
( ~ ( ~ ( in @ ( sK33_C @ SY836 @ SV483 ) @ SV483 )
| ~ ~ ( in @ ( sK33_C @ SY836 @ SV483 ) @ SY836 ) )
| ( element @ SV483 @ ( powerset @ SY836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2448,plain,
! [SV484: $i] :
( ( ~ ( relation @ SV484 )
| ~ ( ~ ! [SY837: $i] :
( ~ ( relation @ SY837 )
| ~ ( subset @ SV484 @ SY837 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SY837 ) ) )
| ~ ! [SY838: $i] :
( ~ ( relation @ SY838 )
| ~ ( subset @ SV484 @ SY838 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SY838 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2449,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)],[2321]) ).
thf(2450,plain,
! [SV485: $i] :
( ( ~ ( ~ ! [SY839: $i,SY840: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY839 ) ) )
| ~ ( ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY839 ) ) )
| ( SY840
= ( set_union2 @ SV485 @ SY839 ) ) )
| ~ ! [SY841: $i,SY842: $i] :
( ( SY842
!= ( set_union2 @ SV485 @ SY841 ) )
| ~ ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SY842 )
| ( in @ SY843 @ SV485 )
| ( in @ SY843 @ SY841 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV485 )
| ( in @ SY844 @ SY842 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY841 )
| ( in @ SX3 @ SY842 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2451,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)],[2323]) ).
thf(2452,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[2324]) ).
thf(2453,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_SY312 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY312 @ 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)],[2325]) ).
thf(2454,plain,
! [SV486: $i] :
( ( ~ ( ~ ! [SY846: $i,SY847: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY846 )
| ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) )
| ~ ( ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY846 )
| ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) ) ) )
| ( SY847
= ( set_intersection2 @ SV486 @ SY846 ) ) )
| ~ ! [SY848: $i,SY849: $i] :
( ( SY849
!= ( set_intersection2 @ SV486 @ SY848 ) )
| ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ SV486 )
| ~ ( in @ SY850 @ SY848 )
| ( in @ SY850 @ SY849 ) )
| ~ ~ ( ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY849 )
| ( in @ SY851 @ SV486 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY849 )
| ( in @ SX3 @ SY848 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2455,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2456,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2457,plain,
! [SV487: $i] :
( ( ~ ( ~ ! [SY853: $i] :
( ~ ( subset @ SY853 @ ( sK32_B @ SV487 ) )
| ( are_equipotent @ SY853 @ ( sK32_B @ SV487 ) )
| ( in @ SY853 @ ( sK32_B @ SV487 ) ) )
| ~ ~ ( ~ ! [SY854: $i] :
( ~ ( in @ SY854 @ ( sK32_B @ SV487 ) )
| ( in @ ( powerset @ SY854 ) @ ( sK32_B @ SV487 ) ) )
| ~ ~ ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) )
| ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2458,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2459,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)],[2331]) ).
thf(2460,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)],[2332]) ).
thf(2461,plain,
( ( ( ( relation_rng @ sK1_A )
!= empty_set )
| ~ ( ( ( relation_dom @ sK1_A )
!= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2462,plain,
! [SV488: $i] :
( ( ~ ( relation @ SV488 )
| ~ ( ~ ! [SY857: $i] :
( ~ ( ~ ( ! [SY858: $i] :
~ ( in @ ( ordered_pair @ SY858 @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY857 @ SV488 ) @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) ) )
| ( SY857
= ( relation_rng @ SV488 ) ) )
| ~ ! [SY859: $i] :
( ( SY859
!= ( relation_rng @ SV488 ) )
| ~ ( ~ ! [SY860: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY860 ) @ SV488 )
| ( in @ SY860 @ SY859 ) )
| ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY859 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY862 @ SY859 @ SV488 ) @ SY862 ) @ SV488 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2463,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)],[2335]) ).
thf(2464,plain,
! [SV489: $i] :
( ( ~ ( ~ ( element @ ( sK6_B @ SV489 ) @ ( powerset @ SV489 ) )
| ~ ( empty @ ( sK6_B @ SV489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2465,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)],[2337]) ).
thf(2466,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)],[2338]) ).
thf(2467,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)],[2339]) ).
thf(2468,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2469,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)],[2341]) ).
thf(2470,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)],[2342]) ).
thf(2471,plain,
! [SV490: $i] :
( ( ! [SY863: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_C @ SY863 @ SV490 ) @ SV490 )
| ~ ( in @ ( sK4_C @ SY863 @ SV490 ) @ SY863 ) )
| ~ ( ( in @ ( sK4_C @ SY863 @ SV490 ) @ SV490 )
| ( in @ ( sK4_C @ SY863 @ SV490 ) @ SY863 ) ) )
| ( SV490 = SY863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2472,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)],[2344]) ).
thf(2473,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_SY329 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2474,plain,
! [SV491: $i] :
( ( ~ ( ~ ! [SY864: $i,SY865: $i] :
( ~ ( in @ SV491 @ SY865 )
| ~ ( in @ SY864 @ SY865 )
| ( subset @ ( unordered_pair @ SV491 @ SY864 ) @ SY865 ) )
| ~ ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY866 ) @ SY867 )
| ( in @ SV491 @ SY867 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY868 ) @ SY869 )
| ( in @ SY868 @ SY869 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2475,plain,
! [SV492: $i] :
( ( ~ ( ~ ! [SY870: $i,SY871: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
!= SY870 ) ) )
| ~ ( ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
= SV492 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
= SY870 ) ) )
| ( SY871
= ( unordered_pair @ SV492 @ SY870 ) ) )
| ~ ! [SY872: $i,SY873: $i] :
( ( SY873
!= ( unordered_pair @ SV492 @ SY872 ) )
| ~ ( ~ ! [SY874: $i] :
( ~ ( in @ SY874 @ SY873 )
| ( SY874 = SV492 )
| ( SY874 = SY872 ) )
| ~ ~ ( ~ ! [SY875: $i] :
( ( SY875 != SV492 )
| ( in @ SY875 @ SY873 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY872 )
| ( in @ SX3 @ SY873 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2476,plain,
! [SV493: $i] :
( ( ! [SY877: $i] :
~ ( ~ ! [SY878: $i,SY879: $i] :
( ~ ( in @ SV493 @ SY878 )
| ~ ( in @ SY877 @ SY879 )
| ( in @ ( ordered_pair @ SV493 @ SY877 ) @ ( cartesian_product2 @ SY878 @ SY879 ) ) )
| ~ ~ ( ~ ! [SY880: $i] :
( ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SY877 ) @ ( cartesian_product2 @ SY880 @ SY881 ) )
| ( in @ SV493 @ SY880 ) )
| ~ ! [SY882: $i,SY883: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SY877 ) @ ( cartesian_product2 @ SY882 @ SY883 ) )
| ( in @ SY877 @ SY883 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2477,plain,
! [SV494: $i] :
( ( ~ ( ~ ! [SY884: $i,SY885: $i] :
( ~ ( relation @ SY885 )
| ~ ( in @ ( ordered_pair @ SV494 @ SY884 ) @ SY885 )
| ( in @ SV494 @ ( relation_dom @ SY885 ) ) )
| ~ ! [SY886: $i,SY887: $i] :
( ~ ( relation @ SY887 )
| ~ ( in @ ( ordered_pair @ SV494 @ SY886 ) @ SY887 )
| ( in @ SY886 @ ( relation_rng @ SY887 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2478,plain,
( ( ~ ( empty @ sK35_A )
| ~ ( relation @ sK35_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2479,plain,
( ( ~ ~ ( empty @ sK34_A )
| ~ ( relation @ sK34_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2480,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)],[2352]) ).
thf(2481,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)],[2353]) ).
thf(2482,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)],[2354]) ).
thf(2483,plain,
! [SV495: $i] :
( ( ~ ( ~ ! [SY888: $i,SY889: $i] :
( ~ ( ~ ( ! [SY890: $i,SY891: $i] :
( ~ ( in @ SY890 @ SV495 )
| ~ ( in @ SY891 @ SY888 )
| ( ( sK23_D @ SY889 @ SY888 @ SV495 )
!= ( ordered_pair @ SY890 @ SY891 ) ) )
| ~ ( in @ ( sK23_D @ SY889 @ SY888 @ SV495 ) @ SY889 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY889 @ SY888 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SY889 @ SY888 @ SV495 ) @ SY888 ) )
| ( ( sK23_D @ SY889 @ SY888 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SY889 @ SY888 @ SV495 ) @ ( sK25_SY318 @ SY889 @ SY888 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SY889 @ SY888 @ SV495 ) @ SY889 ) ) )
| ( SY889
= ( cartesian_product2 @ SV495 @ SY888 ) ) )
| ~ ! [SY892: $i,SY893: $i] :
( ( SY893
!= ( cartesian_product2 @ SV495 @ SY892 ) )
| ~ ( ~ ! [SY894: $i] :
( ! [SY895: $i,SY896: $i] :
( ~ ( in @ SY895 @ SV495 )
| ~ ( in @ SY896 @ SY892 )
| ( SY894
!= ( ordered_pair @ SY895 @ SY896 ) ) )
| ( in @ SY894 @ SY893 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SY893 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY897 @ SY893 @ SY892 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY897 @ SY893 @ SY892 @ SV495 ) @ SY892 ) )
| ( SY897
!= ( ordered_pair @ ( sK21_E @ SY897 @ SY893 @ SY892 @ SV495 ) @ ( sK22_SY313 @ SY897 @ SY893 @ SY892 @ SV495 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2484,plain,
! [SV496: $i] :
( ( ( empty @ SV496 )
| ~ ( ~ ( element @ ( sK8_B @ SV496 ) @ ( powerset @ SV496 ) )
| ~ ~ ( empty @ ( sK8_B @ SV496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2485,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)],[2357]) ).
thf(2486,plain,
! [SV497: $i] :
( ( ~ ( ~ ! [SY898: $i,SY899: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY898 )
| ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY898 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) ) ) )
| ( SY899
= ( set_difference @ SV497 @ SY898 ) ) )
| ~ ! [SY900: $i,SY901: $i] :
( ( SY901
!= ( set_difference @ SV497 @ SY900 ) )
| ~ ( ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV497 )
| ( in @ SY902 @ SY900 )
| ( in @ SY902 @ SY901 ) )
| ~ ~ ( ~ ! [SY903: $i] :
( ~ ( in @ SY903 @ SY901 )
| ( in @ SY903 @ SV497 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY901 )
| ~ ( in @ SX3 @ SY900 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2487,plain,
! [SV498: $i] :
( ( ~ ( relation @ SV498 )
| ~ ( ~ ! [SY905: $i] :
( ~ ( ~ ( ! [SY906: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ SY906 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ ( sK41_SY326 @ SY905 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) ) )
| ( SY905
= ( relation_dom @ SV498 ) ) )
| ~ ! [SY907: $i] :
( ( SY907
!= ( relation_dom @ SV498 ) )
| ~ ( ~ ! [SY908: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY908 @ SY909 ) @ SV498 )
| ( in @ SY908 @ SY907 ) )
| ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SY907 )
| ( in @ ( ordered_pair @ SY910 @ ( sK39_D @ SY910 @ SY907 @ SV498 ) ) @ SV498 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2488,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2489,plain,
! [SV403: $i] :
( ( ( singleton @ SV403 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2490,plain,
! [SV404: $i] :
( ( ( ~ ( relation @ SV404 ) )
= $true )
| ( ( subset @ SV404 @ ( cartesian_product2 @ ( relation_dom @ SV404 ) @ ( relation_rng @ SV404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2491,plain,
! [SV406: $i] :
( ( ( ~ ( subset @ SV406 @ empty_set ) )
= $true )
| ( ( SV406 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2492,plain,
! [SV407: $i] :
( ( ( ~ ( relation @ SV407 ) )
= $true )
| ( ( ! [SY732: $i] :
( ~ ( relation @ SY732 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV407 @ SY732 ) ) @ ( relation_dom @ SV407 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2493,plain,
! [SV408: $i] :
( ( ( ~ ( relation @ SV408 ) )
= $true )
| ( ( ! [SY733: $i] :
( ~ ( relation @ SY733 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV408 @ SY733 ) ) @ ( relation_rng @ SY733 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2494,plain,
! [SV409: $i] :
( ( ( ~ ( relation @ SV409 ) )
= $true )
| ( ( ! [SY734: $i] :
( ~ ( relation @ SY734 )
| ~ ( subset @ ( relation_rng @ SV409 ) @ ( relation_dom @ SY734 ) )
| ( ( relation_dom @ ( relation_composition @ SV409 @ SY734 ) )
= ( relation_dom @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2495,plain,
! [SV410: $i] :
( ( ( ~ ( relation @ SV410 ) )
= $true )
| ( ( ! [SY735: $i] :
( ~ ( relation @ SY735 )
| ~ ( subset @ ( relation_dom @ SV410 ) @ ( relation_rng @ SY735 ) )
| ( ( relation_rng @ ( relation_composition @ SY735 @ SV410 ) )
= ( relation_rng @ SV410 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2496,plain,
! [SV411: $i] :
( ( ( ~ ( relation @ SV411 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK49_B @ SV411 ) @ ( sK50_SY332 @ SV411 ) ) @ SV411 )
| ( SV411 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2497,plain,
! [SV412: $i] :
( ( ( ~ ( empty @ SV412 ) )
= $true )
| ( ( relation @ SV412 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2498,plain,
! [SV413: $i] :
( ( ( ~ ( relation @ SV413 ) )
= $true )
| ( ( ( relation_field @ SV413 )
= ( set_union2 @ ( relation_dom @ SV413 ) @ ( relation_rng @ SV413 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2499,plain,
! [SV414: $i] :
( ( ( ~ ( relation @ SV414 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2500,plain,
! [SV499: $i,SV415: $i] :
( ( ~ ( relation @ SV415 )
| ~ ( relation @ SV499 )
| ( relation @ ( relation_composition @ SV415 @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2501,plain,
! [SV500: $i,SV416: $i] :
( ( ~ ( relation @ SV416 )
| ~ ( relation @ SV500 )
| ( relation @ ( set_union2 @ SV416 @ SV500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2502,plain,
! [SV417: $i] :
( ( ( ( empty @ SV417 )
| ~ ( relation @ SV417 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2375]) ).
thf(2503,plain,
! [SV418: $i] :
( ( ( ( empty @ SV418 )
| ~ ( relation @ SV418 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2504,plain,
! [SV419: $i] :
( ( ( ~ ( relation @ SV419 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV419 ) )
= SV419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2505,plain,
! [SV424: $i] :
( ( ( ~ ( empty @ SV424 ) )
= $true )
| ( ( SV424 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2506,plain,
! [SV501: $i,SV425: $i] :
( ( ~ ( in @ SV425 @ SV501 )
| ( ( set_union2 @ ( singleton @ SV425 ) @ SV501 )
= SV501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2507,plain,
! [SV502: $i,SV426: $i] :
( ( ~ ( disjoint @ ( singleton @ SV426 ) @ SV502 )
| ~ ( in @ SV426 @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2508,plain,
! [SV503: $i,SV427: $i] :
( ( ( in @ SV427 @ SV503 )
| ( disjoint @ ( singleton @ SV427 ) @ SV503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2509,plain,
! [SV428: $i,SV504: $i] :
( ( ~ ( element @ SV504 @ ( powerset @ SV428 ) )
| ! [SY911: $i] :
( ~ ( in @ SY911 @ SV504 )
| ( in @ SY911 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2510,plain,
! [SV505: $i,SV429: $i] :
( ( ~ ( subset @ SV429 @ SV505 )
| ! [SY912: $i] :
( ( in @ SY912 @ SV429 )
| ( subset @ SV429 @ ( set_difference @ SV505 @ ( singleton @ SY912 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2511,plain,
! [SV506: $i,SV430: $i] :
( ( ~ ( in @ SV430 @ SV506 )
| ( subset @ SV430 @ ( union @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2512,plain,
! [SV507: $i,SV431: $i] :
( ( ! [SY913: $i,SY914: $i] :
( ~ ( subset @ SV431 @ SV507 )
| ~ ( subset @ SY913 @ SY914 )
| ( subset @ ( cartesian_product2 @ SV431 @ SY913 ) @ ( cartesian_product2 @ SV507 @ SY914 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2513,plain,
! [SV508: $i,SV432: $i] :
( ( ~ ( subset @ SV432 @ SV508 )
| ( ( set_union2 @ SV432 @ SV508 )
= SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2514,plain,
! [SV509: $i,SV433: $i] :
( ( subset @ ( set_intersection2 @ SV433 @ SV509 ) @ SV433 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2515,plain,
! [SV510: $i,SV434: $i] :
( ( ! [SY915: $i] :
( ~ ( subset @ SV434 @ SV510 )
| ~ ( subset @ SV434 @ SY915 )
| ( subset @ SV434 @ ( set_intersection2 @ SV510 @ SY915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2516,plain,
! [SV511: $i,SV435: $i] :
( ( ! [SY916: $i] :
( ~ ( subset @ SV435 @ SV511 )
| ~ ( subset @ SV511 @ SY916 )
| ( subset @ SV435 @ SY916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2517,plain,
! [SV512: $i,SV436: $i] :
( ( ~ ( subset @ SV436 @ SV512 )
| ! [SY917: $i] : ( subset @ ( set_intersection2 @ SV436 @ SY917 ) @ ( set_intersection2 @ SV512 @ SY917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2518,plain,
! [SV513: $i,SV437: $i] :
( ( ~ ( subset @ SV437 @ SV513 )
| ( ( set_intersection2 @ SV437 @ SV513 )
= SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2519,plain,
! [SV514: $i,SV438: $i] :
( ( ~ ( subset @ SV438 @ SV514 )
| ! [SY918: $i] : ( subset @ ( set_difference @ SV438 @ SY918 ) @ ( set_difference @ SV514 @ SY918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2520,plain,
! [SV515: $i,SV439: $i] :
( ( subset @ ( set_difference @ SV439 @ SV515 ) @ SV439 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2521,plain,
! [SV516: $i,SV440: $i] :
( ( ( set_union2 @ SV440 @ ( set_difference @ SV516 @ SV440 ) )
= ( set_union2 @ SV440 @ SV516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2522,plain,
! [SV517: $i,SV441: $i] :
( ( ( set_difference @ ( set_union2 @ SV441 @ SV517 ) @ SV517 )
= ( set_difference @ SV441 @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2523,plain,
! [SV518: $i,SV442: $i] :
( ( ~ ( subset @ SV442 @ SV518 )
| ( SV518
= ( set_union2 @ SV442 @ ( set_difference @ SV518 @ SV442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2524,plain,
! [SV519: $i,SV443: $i] :
( ( ~ ( in @ SV443 @ SV519 )
| ( ( set_union2 @ ( singleton @ SV443 ) @ SV519 )
= SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2525,plain,
! [SV520: $i,SV444: $i] :
( ( ( set_difference @ SV444 @ ( set_difference @ SV444 @ SV520 ) )
= ( set_intersection2 @ SV444 @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2526,plain,
! [SV445: $i,SV521: $i] :
( ( ~ ( proper_subset @ SV521 @ SV445 )
| ~ ( subset @ SV445 @ SV521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2527,plain,
! [SV446: $i,SV522: $i] :
( ( ! [SY919: $i] :
( ~ ( disjoint @ SV522 @ SY919 )
| ~ ( subset @ SV446 @ SV522 )
| ( disjoint @ SV446 @ SY919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2528,plain,
! [SV523: $i,SV448: $i] :
( ( ~ ( subset @ ( singleton @ SV448 ) @ ( singleton @ SV523 ) )
| ( SV448 = SV523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2529,plain,
! [SV524: $i,SV449: $i] :
( ( subset @ SV449 @ ( set_union2 @ SV449 @ SV524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2530,plain,
! [SV525: $i,SV450: $i] :
( ( ! [SY920: $i] :
( ~ ( subset @ SV450 @ SV525 )
| ~ ( subset @ SY920 @ SV525 )
| ( subset @ ( set_union2 @ SV450 @ SY920 ) @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2531,plain,
! [SV526: $i,SV451: $i] :
( ( ! [SY921: $i] :
( ( singleton @ SV451 )
!= ( unordered_pair @ SV526 @ SY921 ) )
| ( SV451 = SV526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2532,plain,
! [SV527: $i,SV452: $i] :
( ( ~ ( in @ SV452 @ SV527 )
| ( subset @ SV452 @ ( union @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2533,plain,
! [SV528: $i,SV454: $i] :
( ( ! [SY922: $i] :
( ( ( singleton @ SV454 )
!= ( unordered_pair @ SV528 @ SY922 ) )
| ( SV528 = SY922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2534,plain,
! [SV529: $i,SV455: $i] :
( ( ~ ( in @ SV455 @ SV529 )
| ~ ( in @ SV529 @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2535,plain,
! [SV530: $i,SV456: $i] :
( ( ( set_union2 @ SV456 @ SV530 )
= ( set_union2 @ SV530 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(2536,plain,
! [SV531: $i,SV457: $i] :
( ( ( set_intersection2 @ SV457 @ SV531 )
= ( set_intersection2 @ SV531 @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2537,plain,
! [SV532: $i,SV458: $i] :
( ( ( ordered_pair @ SV458 @ SV532 )
= ( unordered_pair @ ( unordered_pair @ SV458 @ SV532 ) @ ( singleton @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2538,plain,
! [SV459: $i] :
( ( empty @ ( powerset @ SV459 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2539,plain,
! [SV533: $i,SV460: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV460 @ SV533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2540,plain,
! [SV461: $i] :
( ( empty @ ( singleton @ SV461 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2541,plain,
! [SV462: $i] :
( ( ( empty @ SV462 )
= $true )
| ( ( ! [SY783: $i] :
~ ( empty @ ( set_union2 @ SV462 @ SY783 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2542,plain,
! [SV534: $i,SV463: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV463 @ SV534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2543,plain,
! [SV464: $i] :
( ( ( empty @ SV464 )
= $true )
| ( ( ! [SY785: $i] :
~ ( empty @ ( set_union2 @ SY785 @ SV464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2544,plain,
! [SV535: $i,SV465: $i] :
( ( ( empty @ SV465 )
| ( empty @ SV535 )
| ~ ( empty @ ( cartesian_product2 @ SV465 @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(2545,plain,
! [SV536: $i,SV469: $i] :
( ( ~ ( disjoint @ SV469 @ SV536 )
| ( disjoint @ SV536 @ SV469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2546,plain,
! [SV537: $i,SV470: $i] :
( ( ~ ( in @ SV470 @ SV537 )
| ( element @ SV470 @ SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(2547,plain,
! [SV538: $i,SV471: $i] :
( ( ~ ( element @ SV471 @ SV538 )
| ( empty @ SV538 )
| ( in @ SV471 @ SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2548,plain,
! [SV472: $i,SV539: $i] :
( ( ! [SY923: $i] :
( ~ ( element @ SV539 @ ( powerset @ SY923 ) )
| ~ ( in @ SV472 @ SV539 )
| ( element @ SV472 @ SY923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(2549,plain,
! [SV473: $i,SV540: $i] :
( ( ! [SY924: $i] :
( ~ ( element @ SV540 @ ( powerset @ SY924 ) )
| ~ ( in @ SV473 @ SV540 )
| ~ ( empty @ SY924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2550,plain,
! [SV474: $i,SV541: $i] :
( ( ~ ( empty @ SV541 )
| ~ ( in @ SV474 @ SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2551,plain,
! [SV542: $i,SV475: $i] :
( ( ( SV475 = SV542 )
| ~ ( empty @ SV475 )
| ~ ( empty @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(2552,plain,
! [SV476: $i] :
( ( ~ ! [SY796: $i,SY797: $i] :
( ~ ( relation @ SY797 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY796 ) @ SY797 )
| ( in @ SV476 @ ( relation_field @ SY797 ) ) )
| ~ ! [SY798: $i,SY799: $i] :
( ~ ( relation @ SY799 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY798 ) @ SY799 )
| ( in @ SY798 @ ( relation_field @ SY799 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2553,plain,
! [SV477: $i] :
( ( ( ~ ( relation @ SV477 ) )
= $true )
| ( ( ! [SY800: $i] :
( ~ ( relation @ SY800 )
| ~ ( ~ ! [SY801: $i] :
( ~ ( relation @ SY801 )
| ~ ( ~ ( ! [SY802: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ SY802 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY802 @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY800 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY801 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK12_SY309 @ SY801 @ SY800 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY800 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY801 ) ) )
| ( SY801
= ( relation_composition @ SV477 @ SY800 ) ) )
| ~ ! [SY803: $i] :
( ~ ( relation @ SY803 )
| ( SY803
!= ( relation_composition @ SV477 @ SY800 ) )
| ~ ( ~ ! [SY804: $i,SY805: $i] :
( ! [SY806: $i] :
( ~ ( in @ ( ordered_pair @ SY804 @ SY806 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY806 @ SY805 ) @ SY800 ) )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SY803 ) )
| ~ ! [SY807: $i,SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY807 @ SY808 ) @ SY803 )
| ~ ( ~ ( in @ ( ordered_pair @ SY807 @ ( sK9_F @ SY808 @ SY807 @ SY803 @ SY800 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY808 @ SY807 @ SY803 @ SY800 @ SV477 ) @ SY808 ) @ SY800 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2554,plain,
! [SV478: $i] :
( ( ~ ! [SY809: $i] :
( ~ ( subset @ SY809 @ ( sK2_B @ SV478 ) )
| ( are_equipotent @ SY809 @ ( sK2_B @ SV478 ) )
| ( in @ SY809 @ ( sK2_B @ SV478 ) ) )
| ~ ~ ( ~ ! [SY810: $i] :
( ~ ( ~ ! [SY811: $i] :
( ~ ( subset @ SY811 @ SY810 )
| ( in @ SY811 @ ( sK3_SY300 @ SY810 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY810 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SY810 @ ( sK2_B @ SV478 ) ) )
| ~ ~ ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2555,plain,
! [SV479: $i] :
( ( ~ ! [SY814: $i] :
( ~ ( subset @ SV479 @ SY814 )
| ! [SY815: $i] : ( subset @ ( cartesian_product2 @ SV479 @ SY815 ) @ ( cartesian_product2 @ SY814 @ SY815 ) ) )
| ~ ! [SY816: $i] :
( ~ ( subset @ SV479 @ SY816 )
| ! [SY817: $i] : ( subset @ ( cartesian_product2 @ SY817 @ SV479 ) @ ( cartesian_product2 @ SY817 @ SY816 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2556,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2557,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)],[2439]) ).
thf(2558,plain,
! [SV543: $i,SV480: $i] :
( ( ~ ( ~ ! [SY925: $i] :
( ! [SY926: $i] :
( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SY925 @ SY926 ) )
| ( SV480 = SY925 ) )
| ~ ! [SY927: $i,SY928: $i] :
( ( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SY927 @ SY928 ) )
| ( SV543 = SY928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2559,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2560,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2561,plain,
! [SV481: $i] :
( ( ( ~ ( relation @ SV481 ) )
= $true )
| ( ( ~ ( ~ ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) ) )
| ( SY823
= ( relation_inverse @ SV481 ) ) )
| ~ ! [SY824: $i] :
( ~ ( relation @ SY824 )
| ( SY824
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY825: $i,SY826: $i] :
( ~ ( in @ ( ordered_pair @ SY825 @ SY826 ) @ SY824 )
| ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV481 ) )
| ~ ! [SY827: $i,SY828: $i] :
( ~ ( in @ ( ordered_pair @ SY828 @ SY827 ) @ SV481 )
| ( in @ ( ordered_pair @ SY827 @ SY828 ) @ SY824 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2562,plain,
! [SV544: $i,SV482: $i] :
( ( ~ ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( in @ SV482 @ SY929 )
| ~ ( in @ SV544 @ SY930 )
| ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY929 @ SY930 ) ) )
| ~ ~ ( ~ ! [SY931: $i] :
( ! [SY932: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY931 @ SY932 ) )
| ( in @ SV482 @ SY931 ) )
| ~ ! [SY933: $i,SY934: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY933 @ SY934 ) )
| ( in @ SV544 @ SY934 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2563,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2444]) ).
thf(2564,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2444]) ).
thf(2565,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2445]) ).
thf(2566,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)],[2445]) ).
thf(2567,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2446]) ).
thf(2568,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2446]) ).
thf(2569,plain,
! [SV483: $i,SV545: $i] :
( ( ~ ( ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV483 )
| ~ ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV545 ) )
| ( element @ SV483 @ ( powerset @ SV545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(2570,plain,
! [SV484: $i] :
( ( ( ~ ( relation @ SV484 ) )
= $true )
| ( ( ~ ( ~ ! [SY837: $i] :
( ~ ( relation @ SY837 )
| ~ ( subset @ SV484 @ SY837 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SY837 ) ) )
| ~ ! [SY838: $i] :
( ~ ( relation @ SY838 )
| ~ ( subset @ SV484 @ SY838 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SY838 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2571,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)],[2449]) ).
thf(2572,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2449]) ).
thf(2573,plain,
! [SV485: $i] :
( ( ~ ! [SY839: $i,SY840: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY839 ) ) )
| ~ ( ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY839 ) ) )
| ( SY840
= ( set_union2 @ SV485 @ SY839 ) ) )
| ~ ! [SY841: $i,SY842: $i] :
( ( SY842
!= ( set_union2 @ SV485 @ SY841 ) )
| ~ ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SY842 )
| ( in @ SY843 @ SV485 )
| ( in @ SY843 @ SY841 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV485 )
| ( in @ SY844 @ SY842 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY841 )
| ( in @ SX3 @ SY842 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2574,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2451]) ).
thf(2575,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2451]) ).
thf(2576,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[2452]) ).
thf(2577,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)],[2452]) ).
thf(2578,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_SY312 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY312 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2579,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)],[2453]) ).
thf(2580,plain,
! [SV486: $i] :
( ( ~ ! [SY846: $i,SY847: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY846 )
| ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) )
| ~ ( ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY846 )
| ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) ) ) )
| ( SY847
= ( set_intersection2 @ SV486 @ SY846 ) ) )
| ~ ! [SY848: $i,SY849: $i] :
( ( SY849
!= ( set_intersection2 @ SV486 @ SY848 ) )
| ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ SV486 )
| ~ ( in @ SY850 @ SY848 )
| ( in @ SY850 @ SY849 ) )
| ~ ~ ( ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY849 )
| ( in @ SY851 @ SV486 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY849 )
| ( in @ SX3 @ SY848 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2581,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2582,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2583,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2456]) ).
thf(2584,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2456]) ).
thf(2585,plain,
! [SV487: $i] :
( ( ~ ! [SY853: $i] :
( ~ ( subset @ SY853 @ ( sK32_B @ SV487 ) )
| ( are_equipotent @ SY853 @ ( sK32_B @ SV487 ) )
| ( in @ SY853 @ ( sK32_B @ SV487 ) ) )
| ~ ~ ( ~ ! [SY854: $i] :
( ~ ( in @ SY854 @ ( sK32_B @ SV487 ) )
| ( in @ ( powerset @ SY854 ) @ ( sK32_B @ SV487 ) ) )
| ~ ~ ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) )
| ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2586,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2458]) ).
thf(2587,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2458]) ).
thf(2588,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)],[2459]) ).
thf(2589,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)],[2459]) ).
thf(2590,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)],[2460]) ).
thf(2591,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2460]) ).
thf(2592,plain,
( ( ( ( relation_rng @ sK1_A )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2461]) ).
thf(2593,plain,
( ( ~ ( ( ( relation_dom @ sK1_A )
!= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2461]) ).
thf(2594,plain,
! [SV488: $i] :
( ( ( ~ ( relation @ SV488 ) )
= $true )
| ( ( ~ ( ~ ! [SY857: $i] :
( ~ ( ~ ( ! [SY858: $i] :
~ ( in @ ( ordered_pair @ SY858 @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY857 @ SV488 ) @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) ) )
| ( SY857
= ( relation_rng @ SV488 ) ) )
| ~ ! [SY859: $i] :
( ( SY859
!= ( relation_rng @ SV488 ) )
| ~ ( ~ ! [SY860: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY860 ) @ SV488 )
| ( in @ SY860 @ SY859 ) )
| ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY859 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY862 @ SY859 @ SV488 ) @ SY862 ) @ SV488 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2595,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)],[2463]) ).
thf(2596,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)],[2463]) ).
thf(2597,plain,
! [SV489: $i] :
( ( ~ ( element @ ( sK6_B @ SV489 ) @ ( powerset @ SV489 ) )
| ~ ( empty @ ( sK6_B @ SV489 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2598,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2599,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2600,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2601,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)],[2466]) ).
thf(2602,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2603,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2604,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2468]) ).
thf(2605,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2468]) ).
thf(2606,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2469]) ).
thf(2607,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2469]) ).
thf(2608,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2609,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2610,plain,
! [SV490: $i,SV546: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) )
| ~ ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) ) )
| ( SV490 = SV546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2611,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2472]) ).
thf(2612,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2472]) ).
thf(2613,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)],[2473]) ).
thf(2614,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK46_C @ SX1 @ SX0 ) @ ( sK47_SY329 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2473]) ).
thf(2615,plain,
! [SV491: $i] :
( ( ~ ! [SY864: $i,SY865: $i] :
( ~ ( in @ SV491 @ SY865 )
| ~ ( in @ SY864 @ SY865 )
| ( subset @ ( unordered_pair @ SV491 @ SY864 ) @ SY865 ) )
| ~ ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY866 ) @ SY867 )
| ( in @ SV491 @ SY867 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY868 ) @ SY869 )
| ( in @ SY868 @ SY869 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2616,plain,
! [SV492: $i] :
( ( ~ ! [SY870: $i,SY871: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
!= SY870 ) ) )
| ~ ( ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
= SV492 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
= SY870 ) ) )
| ( SY871
= ( unordered_pair @ SV492 @ SY870 ) ) )
| ~ ! [SY872: $i,SY873: $i] :
( ( SY873
!= ( unordered_pair @ SV492 @ SY872 ) )
| ~ ( ~ ! [SY874: $i] :
( ~ ( in @ SY874 @ SY873 )
| ( SY874 = SV492 )
| ( SY874 = SY872 ) )
| ~ ~ ( ~ ! [SY875: $i] :
( ( SY875 != SV492 )
| ( in @ SY875 @ SY873 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY872 )
| ( in @ SX3 @ SY873 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2617,plain,
! [SV547: $i,SV493: $i] :
( ( ~ ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( in @ SV493 @ SY935 )
| ~ ( in @ SV547 @ SY936 )
| ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY935 @ SY936 ) ) )
| ~ ~ ( ~ ! [SY937: $i] :
( ! [SY938: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY937 @ SY938 ) )
| ( in @ SV493 @ SY937 ) )
| ~ ! [SY939: $i,SY940: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY939 @ SY940 ) )
| ( in @ SV547 @ SY940 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2618,plain,
! [SV494: $i] :
( ( ~ ! [SY884: $i,SY885: $i] :
( ~ ( relation @ SY885 )
| ~ ( in @ ( ordered_pair @ SV494 @ SY884 ) @ SY885 )
| ( in @ SV494 @ ( relation_dom @ SY885 ) ) )
| ~ ! [SY886: $i,SY887: $i] :
( ~ ( relation @ SY887 )
| ~ ( in @ ( ordered_pair @ SV494 @ SY886 ) @ SY887 )
| ( in @ SY886 @ ( relation_rng @ SY887 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2619,plain,
( ( ~ ( empty @ sK35_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2478]) ).
thf(2620,plain,
( ( ~ ( relation @ sK35_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2478]) ).
thf(2621,plain,
( ( ~ ~ ( empty @ sK34_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2622,plain,
( ( ~ ( relation @ sK34_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2623,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2480]) ).
thf(2624,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2480]) ).
thf(2625,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)],[2481]) ).
thf(2626,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)],[2481]) ).
thf(2627,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2482]) ).
thf(2628,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)],[2482]) ).
thf(2629,plain,
! [SV495: $i] :
( ( ~ ! [SY888: $i,SY889: $i] :
( ~ ( ~ ( ! [SY890: $i,SY891: $i] :
( ~ ( in @ SY890 @ SV495 )
| ~ ( in @ SY891 @ SY888 )
| ( ( sK23_D @ SY889 @ SY888 @ SV495 )
!= ( ordered_pair @ SY890 @ SY891 ) ) )
| ~ ( in @ ( sK23_D @ SY889 @ SY888 @ SV495 ) @ SY889 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY889 @ SY888 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SY889 @ SY888 @ SV495 ) @ SY888 ) )
| ( ( sK23_D @ SY889 @ SY888 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SY889 @ SY888 @ SV495 ) @ ( sK25_SY318 @ SY889 @ SY888 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SY889 @ SY888 @ SV495 ) @ SY889 ) ) )
| ( SY889
= ( cartesian_product2 @ SV495 @ SY888 ) ) )
| ~ ! [SY892: $i,SY893: $i] :
( ( SY893
!= ( cartesian_product2 @ SV495 @ SY892 ) )
| ~ ( ~ ! [SY894: $i] :
( ! [SY895: $i,SY896: $i] :
( ~ ( in @ SY895 @ SV495 )
| ~ ( in @ SY896 @ SY892 )
| ( SY894
!= ( ordered_pair @ SY895 @ SY896 ) ) )
| ( in @ SY894 @ SY893 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SY893 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY897 @ SY893 @ SY892 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY897 @ SY893 @ SY892 @ SV495 ) @ SY892 ) )
| ( SY897
!= ( ordered_pair @ ( sK21_E @ SY897 @ SY893 @ SY892 @ SV495 ) @ ( sK22_SY313 @ SY897 @ SY893 @ SY892 @ SV495 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2630,plain,
! [SV496: $i] :
( ( ( empty @ SV496 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_B @ SV496 ) @ ( powerset @ SV496 ) )
| ~ ~ ( empty @ ( sK8_B @ SV496 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2631,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2632,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2633,plain,
! [SV497: $i] :
( ( ~ ! [SY898: $i,SY899: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY898 )
| ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY898 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) ) ) )
| ( SY899
= ( set_difference @ SV497 @ SY898 ) ) )
| ~ ! [SY900: $i,SY901: $i] :
( ( SY901
!= ( set_difference @ SV497 @ SY900 ) )
| ~ ( ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV497 )
| ( in @ SY902 @ SY900 )
| ( in @ SY902 @ SY901 ) )
| ~ ~ ( ~ ! [SY903: $i] :
( ~ ( in @ SY903 @ SY901 )
| ( in @ SY903 @ SV497 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY901 )
| ~ ( in @ SX3 @ SY900 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2634,plain,
! [SV498: $i] :
( ( ( ~ ( relation @ SV498 ) )
= $true )
| ( ( ~ ( ~ ! [SY905: $i] :
( ~ ( ~ ( ! [SY906: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ SY906 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ ( sK41_SY326 @ SY905 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) ) )
| ( SY905
= ( relation_dom @ SV498 ) ) )
| ~ ! [SY907: $i] :
( ( SY907
!= ( relation_dom @ SV498 ) )
| ~ ( ~ ! [SY908: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY908 @ SY909 ) @ SV498 )
| ( in @ SY908 @ SY907 ) )
| ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SY907 )
| ( in @ ( ordered_pair @ SY910 @ ( sK39_D @ SY910 @ SY907 @ SV498 ) ) @ SV498 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2635,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2636,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2637,plain,
! [SV404: $i] :
( ( ( relation @ SV404 )
= $false )
| ( ( subset @ SV404 @ ( cartesian_product2 @ ( relation_dom @ SV404 ) @ ( relation_rng @ SV404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2638,plain,
! [SV406: $i] :
( ( ( subset @ SV406 @ empty_set )
= $false )
| ( ( SV406 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2639,plain,
! [SV407: $i] :
( ( ( relation @ SV407 )
= $false )
| ( ( ! [SY732: $i] :
( ~ ( relation @ SY732 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV407 @ SY732 ) ) @ ( relation_dom @ SV407 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2640,plain,
! [SV408: $i] :
( ( ( relation @ SV408 )
= $false )
| ( ( ! [SY733: $i] :
( ~ ( relation @ SY733 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV408 @ SY733 ) ) @ ( relation_rng @ SY733 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2641,plain,
! [SV409: $i] :
( ( ( relation @ SV409 )
= $false )
| ( ( ! [SY734: $i] :
( ~ ( relation @ SY734 )
| ~ ( subset @ ( relation_rng @ SV409 ) @ ( relation_dom @ SY734 ) )
| ( ( relation_dom @ ( relation_composition @ SV409 @ SY734 ) )
= ( relation_dom @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2642,plain,
! [SV410: $i] :
( ( ( relation @ SV410 )
= $false )
| ( ( ! [SY735: $i] :
( ~ ( relation @ SY735 )
| ~ ( subset @ ( relation_dom @ SV410 ) @ ( relation_rng @ SY735 ) )
| ( ( relation_rng @ ( relation_composition @ SY735 @ SV410 ) )
= ( relation_rng @ SV410 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2643,plain,
! [SV411: $i] :
( ( ( relation @ SV411 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK49_B @ SV411 ) @ ( sK50_SY332 @ SV411 ) ) @ SV411 )
| ( SV411 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2644,plain,
! [SV412: $i] :
( ( ( empty @ SV412 )
= $false )
| ( ( relation @ SV412 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2645,plain,
! [SV413: $i] :
( ( ( relation @ SV413 )
= $false )
| ( ( ( relation_field @ SV413 )
= ( set_union2 @ ( relation_dom @ SV413 ) @ ( relation_rng @ SV413 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2646,plain,
! [SV414: $i] :
( ( ( relation @ SV414 )
= $false )
| ( ( relation @ ( relation_inverse @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2647,plain,
! [SV499: $i,SV415: $i] :
( ( ( ~ ( relation @ SV415 )
| ~ ( relation @ SV499 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV415 @ SV499 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2648,plain,
! [SV500: $i,SV416: $i] :
( ( ( ~ ( relation @ SV416 )
| ~ ( relation @ SV500 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV416 @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2649,plain,
! [SV417: $i] :
( ( ( empty @ SV417 )
= $true )
| ( ( ~ ( relation @ SV417 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2502]) ).
thf(2650,plain,
! [SV418: $i] :
( ( ( empty @ SV418 )
= $true )
| ( ( ~ ( relation @ SV418 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2651,plain,
! [SV419: $i] :
( ( ( relation @ SV419 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV419 ) )
= SV419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2652,plain,
! [SV424: $i] :
( ( ( empty @ SV424 )
= $false )
| ( ( SV424 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2653,plain,
! [SV501: $i,SV425: $i] :
( ( ( ~ ( in @ SV425 @ SV501 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV425 ) @ SV501 )
= SV501 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2654,plain,
! [SV502: $i,SV426: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV426 ) @ SV502 ) )
= $true )
| ( ( ~ ( in @ SV426 @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2655,plain,
! [SV503: $i,SV427: $i] :
( ( ( in @ SV427 @ SV503 )
= $true )
| ( ( disjoint @ ( singleton @ SV427 ) @ SV503 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2656,plain,
! [SV428: $i,SV504: $i] :
( ( ( ~ ( element @ SV504 @ ( powerset @ SV428 ) ) )
= $true )
| ( ( ! [SY911: $i] :
( ~ ( in @ SY911 @ SV504 )
| ( in @ SY911 @ SV428 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2657,plain,
! [SV505: $i,SV429: $i] :
( ( ( ~ ( subset @ SV429 @ SV505 ) )
= $true )
| ( ( ! [SY912: $i] :
( ( in @ SY912 @ SV429 )
| ( subset @ SV429 @ ( set_difference @ SV505 @ ( singleton @ SY912 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2658,plain,
! [SV506: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV506 ) )
= $true )
| ( ( subset @ SV430 @ ( union @ SV506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2659,plain,
! [SV548: $i,SV507: $i,SV431: $i] :
( ( ! [SY941: $i] :
( ~ ( subset @ SV431 @ SV507 )
| ~ ( subset @ SV548 @ SY941 )
| ( subset @ ( cartesian_product2 @ SV431 @ SV548 ) @ ( cartesian_product2 @ SV507 @ SY941 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2660,plain,
! [SV508: $i,SV432: $i] :
( ( ( ~ ( subset @ SV432 @ SV508 ) )
= $true )
| ( ( ( set_union2 @ SV432 @ SV508 )
= SV508 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2661,plain,
! [SV549: $i,SV510: $i,SV434: $i] :
( ( ~ ( subset @ SV434 @ SV510 )
| ~ ( subset @ SV434 @ SV549 )
| ( subset @ SV434 @ ( set_intersection2 @ SV510 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2662,plain,
! [SV550: $i,SV511: $i,SV435: $i] :
( ( ~ ( subset @ SV435 @ SV511 )
| ~ ( subset @ SV511 @ SV550 )
| ( subset @ SV435 @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(2663,plain,
! [SV512: $i,SV436: $i] :
( ( ( ~ ( subset @ SV436 @ SV512 ) )
= $true )
| ( ( ! [SY917: $i] : ( subset @ ( set_intersection2 @ SV436 @ SY917 ) @ ( set_intersection2 @ SV512 @ SY917 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2664,plain,
! [SV513: $i,SV437: $i] :
( ( ( ~ ( subset @ SV437 @ SV513 ) )
= $true )
| ( ( ( set_intersection2 @ SV437 @ SV513 )
= SV437 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2665,plain,
! [SV514: $i,SV438: $i] :
( ( ( ~ ( subset @ SV438 @ SV514 ) )
= $true )
| ( ( ! [SY918: $i] : ( subset @ ( set_difference @ SV438 @ SY918 ) @ ( set_difference @ SV514 @ SY918 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2666,plain,
! [SV518: $i,SV442: $i] :
( ( ( ~ ( subset @ SV442 @ SV518 ) )
= $true )
| ( ( SV518
= ( set_union2 @ SV442 @ ( set_difference @ SV518 @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2667,plain,
! [SV519: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV519 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV443 ) @ SV519 )
= SV519 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2668,plain,
! [SV445: $i,SV521: $i] :
( ( ( ~ ( proper_subset @ SV521 @ SV445 ) )
= $true )
| ( ( ~ ( subset @ SV445 @ SV521 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2669,plain,
! [SV446: $i,SV551: $i,SV522: $i] :
( ( ~ ( disjoint @ SV522 @ SV551 )
| ~ ( subset @ SV446 @ SV522 )
| ( disjoint @ SV446 @ SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2670,plain,
! [SV523: $i,SV448: $i] :
( ( ( ~ ( subset @ ( singleton @ SV448 ) @ ( singleton @ SV523 ) ) )
= $true )
| ( ( SV448 = SV523 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2671,plain,
! [SV552: $i,SV525: $i,SV450: $i] :
( ( ~ ( subset @ SV450 @ SV525 )
| ~ ( subset @ SV552 @ SV525 )
| ( subset @ ( set_union2 @ SV450 @ SV552 ) @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(2672,plain,
! [SV526: $i,SV451: $i] :
( ( ( ! [SY921: $i] :
( ( singleton @ SV451 )
!= ( unordered_pair @ SV526 @ SY921 ) ) )
= $true )
| ( ( SV451 = SV526 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2673,plain,
! [SV527: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ SV527 ) )
= $true )
| ( ( subset @ SV452 @ ( union @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2674,plain,
! [SV553: $i,SV528: $i,SV454: $i] :
( ( ( ( singleton @ SV454 )
!= ( unordered_pair @ SV528 @ SV553 ) )
| ( SV528 = SV553 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(2675,plain,
! [SV529: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV529 ) )
= $true )
| ( ( ~ ( in @ SV529 @ SV455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2534]) ).
thf(2676,plain,
! [SV533: $i,SV460: $i] :
( ( empty @ ( ordered_pair @ SV460 @ SV533 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2677,plain,
! [SV554: $i,SV462: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV462 @ SV554 ) ) )
= $true )
| ( ( empty @ SV462 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(2678,plain,
! [SV534: $i,SV463: $i] :
( ( empty @ ( unordered_pair @ SV463 @ SV534 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2679,plain,
! [SV464: $i,SV555: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV555 @ SV464 ) ) )
= $true )
| ( ( empty @ SV464 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2680,plain,
! [SV535: $i,SV465: $i] :
( ( ( ( empty @ SV465 )
| ( empty @ SV535 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV465 @ SV535 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2681,plain,
! [SV536: $i,SV469: $i] :
( ( ( ~ ( disjoint @ SV469 @ SV536 ) )
= $true )
| ( ( disjoint @ SV536 @ SV469 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2682,plain,
! [SV537: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV537 ) )
= $true )
| ( ( element @ SV470 @ SV537 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2683,plain,
! [SV538: $i,SV471: $i] :
( ( ( ~ ( element @ SV471 @ SV538 ) )
= $true )
| ( ( ( empty @ SV538 )
| ( in @ SV471 @ SV538 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2684,plain,
! [SV472: $i,SV556: $i,SV539: $i] :
( ( ~ ( element @ SV539 @ ( powerset @ SV556 ) )
| ~ ( in @ SV472 @ SV539 )
| ( element @ SV472 @ SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2685,plain,
! [SV473: $i,SV557: $i,SV540: $i] :
( ( ~ ( element @ SV540 @ ( powerset @ SV557 ) )
| ~ ( in @ SV473 @ SV540 )
| ~ ( empty @ SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2686,plain,
! [SV474: $i,SV541: $i] :
( ( ( ~ ( empty @ SV541 ) )
= $true )
| ( ( ~ ( in @ SV474 @ SV541 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2687,plain,
! [SV542: $i,SV475: $i] :
( ( ( ( SV475 = SV542 )
| ~ ( empty @ SV475 ) )
= $true )
| ( ( ~ ( empty @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2688,plain,
! [SV476: $i] :
( ( ~ ! [SY796: $i,SY797: $i] :
( ~ ( relation @ SY797 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY796 ) @ SY797 )
| ( in @ SV476 @ ( relation_field @ SY797 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2689,plain,
! [SV476: $i] :
( ( ~ ! [SY798: $i,SY799: $i] :
( ~ ( relation @ SY799 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY798 ) @ SY799 )
| ( in @ SY798 @ ( relation_field @ SY799 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2690,plain,
! [SV477: $i] :
( ( ( relation @ SV477 )
= $false )
| ( ( ! [SY800: $i] :
( ~ ( relation @ SY800 )
| ~ ( ~ ! [SY801: $i] :
( ~ ( relation @ SY801 )
| ~ ( ~ ( ! [SY802: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ SY802 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY802 @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY800 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY801 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK12_SY309 @ SY801 @ SY800 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY800 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY801 @ SY800 @ SV477 ) @ ( sK11_SY305 @ SY801 @ SY800 @ SV477 ) ) @ SY801 ) ) )
| ( SY801
= ( relation_composition @ SV477 @ SY800 ) ) )
| ~ ! [SY803: $i] :
( ~ ( relation @ SY803 )
| ( SY803
!= ( relation_composition @ SV477 @ SY800 ) )
| ~ ( ~ ! [SY804: $i,SY805: $i] :
( ! [SY806: $i] :
( ~ ( in @ ( ordered_pair @ SY804 @ SY806 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY806 @ SY805 ) @ SY800 ) )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SY803 ) )
| ~ ! [SY807: $i,SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY807 @ SY808 ) @ SY803 )
| ~ ( ~ ( in @ ( ordered_pair @ SY807 @ ( sK9_F @ SY808 @ SY807 @ SY803 @ SY800 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY808 @ SY807 @ SY803 @ SY800 @ SV477 ) @ SY808 ) @ SY800 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2691,plain,
! [SV478: $i] :
( ( ~ ! [SY809: $i] :
( ~ ( subset @ SY809 @ ( sK2_B @ SV478 ) )
| ( are_equipotent @ SY809 @ ( sK2_B @ SV478 ) )
| ( in @ SY809 @ ( sK2_B @ SV478 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2554]) ).
thf(2692,plain,
! [SV478: $i] :
( ( ~ ~ ( ~ ! [SY810: $i] :
( ~ ( ~ ! [SY811: $i] :
( ~ ( subset @ SY811 @ SY810 )
| ( in @ SY811 @ ( sK3_SY300 @ SY810 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY810 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SY810 @ ( sK2_B @ SV478 ) ) )
| ~ ~ ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2554]) ).
thf(2693,plain,
! [SV479: $i] :
( ( ~ ! [SY814: $i] :
( ~ ( subset @ SV479 @ SY814 )
| ! [SY815: $i] : ( subset @ ( cartesian_product2 @ SV479 @ SY815 ) @ ( cartesian_product2 @ SY814 @ SY815 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2555]) ).
thf(2694,plain,
! [SV479: $i] :
( ( ~ ! [SY816: $i] :
( ~ ( subset @ SV479 @ SY816 )
| ! [SY817: $i] : ( subset @ ( cartesian_product2 @ SY817 @ SV479 ) @ ( cartesian_product2 @ SY817 @ SY816 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2555]) ).
thf(2695,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2696,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)],[2557]) ).
thf(2697,plain,
! [SV543: $i,SV480: $i] :
( ( ~ ! [SY925: $i] :
( ! [SY926: $i] :
( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SY925 @ SY926 ) )
| ( SV480 = SY925 ) )
| ~ ! [SY927: $i,SY928: $i] :
( ( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SY927 @ SY928 ) )
| ( SV543 = SY928 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2698,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2559]) ).
thf(2699,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2700,plain,
! [SV481: $i] :
( ( ( relation @ SV481 )
= $false )
| ( ( ~ ( ~ ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) ) )
| ( SY823
= ( relation_inverse @ SV481 ) ) )
| ~ ! [SY824: $i] :
( ~ ( relation @ SY824 )
| ( SY824
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY825: $i,SY826: $i] :
( ~ ( in @ ( ordered_pair @ SY825 @ SY826 ) @ SY824 )
| ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV481 ) )
| ~ ! [SY827: $i,SY828: $i] :
( ~ ( in @ ( ordered_pair @ SY828 @ SY827 ) @ SV481 )
| ( in @ ( ordered_pair @ SY827 @ SY828 ) @ SY824 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2701,plain,
! [SV544: $i,SV482: $i] :
( ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( in @ SV482 @ SY929 )
| ~ ( in @ SV544 @ SY930 )
| ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY929 @ SY930 ) ) )
| ~ ~ ( ~ ! [SY931: $i] :
( ! [SY932: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY931 @ SY932 ) )
| ( in @ SV482 @ SY931 ) )
| ~ ! [SY933: $i,SY934: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY933 @ SY934 ) )
| ( in @ SV544 @ SY934 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2702,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2703,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2704,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2565]) ).
thf(2705,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)],[2566]) ).
thf(2706,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2707,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2568]) ).
thf(2708,plain,
! [SV483: $i,SV545: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV483 )
| ~ ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV545 ) ) )
= $true )
| ( ( element @ SV483 @ ( powerset @ SV545 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2569]) ).
thf(2709,plain,
! [SV484: $i] :
( ( ( relation @ SV484 )
= $false )
| ( ( ~ ( ~ ! [SY837: $i] :
( ~ ( relation @ SY837 )
| ~ ( subset @ SV484 @ SY837 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SY837 ) ) )
| ~ ! [SY838: $i] :
( ~ ( relation @ SY838 )
| ~ ( subset @ SV484 @ SY838 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SY838 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2710,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)],[2571]) ).
thf(2711,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2572]) ).
thf(2712,plain,
! [SV485: $i] :
( ( ~ ! [SY839: $i,SY840: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY839 ) ) )
| ~ ( ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY839 ) ) )
| ( SY840
= ( set_union2 @ SV485 @ SY839 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2573]) ).
thf(2713,plain,
! [SV485: $i] :
( ( ~ ! [SY841: $i,SY842: $i] :
( ( SY842
!= ( set_union2 @ SV485 @ SY841 ) )
| ~ ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SY842 )
| ( in @ SY843 @ SV485 )
| ( in @ SY843 @ SY841 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV485 )
| ( in @ SY844 @ SY842 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY841 )
| ( in @ SX3 @ SY842 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2573]) ).
thf(2714,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2574]) ).
thf(2715,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2575]) ).
thf(2716,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[2576]) ).
thf(2717,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)],[2577]) ).
thf(2718,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_SY312 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY312 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2719,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)],[2579]) ).
thf(2720,plain,
! [SV486: $i] :
( ( ~ ! [SY846: $i,SY847: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY846 )
| ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) )
| ~ ( ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY846 )
| ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) ) ) )
| ( SY847
= ( set_intersection2 @ SV486 @ SY846 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2721,plain,
! [SV486: $i] :
( ( ~ ! [SY848: $i,SY849: $i] :
( ( SY849
!= ( set_intersection2 @ SV486 @ SY848 ) )
| ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ SV486 )
| ~ ( in @ SY850 @ SY848 )
| ( in @ SY850 @ SY849 ) )
| ~ ~ ( ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY849 )
| ( in @ SY851 @ SV486 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY849 )
| ( in @ SX3 @ SY848 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2722,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2581]) ).
thf(2723,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2582]) ).
thf(2724,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2725,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2584]) ).
thf(2726,plain,
! [SV487: $i] :
( ( ~ ! [SY853: $i] :
( ~ ( subset @ SY853 @ ( sK32_B @ SV487 ) )
| ( are_equipotent @ SY853 @ ( sK32_B @ SV487 ) )
| ( in @ SY853 @ ( sK32_B @ SV487 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2727,plain,
! [SV487: $i] :
( ( ~ ~ ( ~ ! [SY854: $i] :
( ~ ( in @ SY854 @ ( sK32_B @ SV487 ) )
| ( in @ ( powerset @ SY854 ) @ ( sK32_B @ SV487 ) ) )
| ~ ~ ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) )
| ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2728,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2729,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2730,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)],[2588]) ).
thf(2731,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)],[2589]) ).
thf(2732,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)],[2590]) ).
thf(2733,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2734,plain,
( ( ( relation_rng @ sK1_A )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2592]) ).
thf(2735,plain,
( ( ( ( relation_dom @ sK1_A )
!= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2593]) ).
thf(2736,plain,
! [SV488: $i] :
( ( ( relation @ SV488 )
= $false )
| ( ( ~ ( ~ ! [SY857: $i] :
( ~ ( ~ ( ! [SY858: $i] :
~ ( in @ ( ordered_pair @ SY858 @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY857 @ SV488 ) @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) ) )
| ( SY857
= ( relation_rng @ SV488 ) ) )
| ~ ! [SY859: $i] :
( ( SY859
!= ( relation_rng @ SV488 ) )
| ~ ( ~ ! [SY860: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY860 ) @ SV488 )
| ( in @ SY860 @ SY859 ) )
| ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY859 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY862 @ SY859 @ SV488 ) @ SY862 ) @ SV488 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2737,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)],[2595]) ).
thf(2738,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)],[2596]) ).
thf(2739,plain,
! [SV489: $i] :
( ( ~ ( element @ ( sK6_B @ SV489 ) @ ( powerset @ SV489 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2597]) ).
thf(2740,plain,
! [SV489: $i] :
( ( ~ ( empty @ ( sK6_B @ SV489 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2597]) ).
thf(2741,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2742,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2743,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2600]) ).
thf(2744,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)],[2601]) ).
thf(2745,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2602]) ).
thf(2746,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2747,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2604]) ).
thf(2748,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2605]) ).
thf(2749,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2606]) ).
thf(2750,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2607]) ).
thf(2751,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2608]) ).
thf(2752,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2753,plain,
! [SV490: $i,SV546: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) )
| ~ ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) ) ) )
= $true )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2754,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2755,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2756,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)],[2613]) ).
thf(2757,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK46_C @ SX1 @ SX0 ) @ ( sK47_SY329 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2614]) ).
thf(2758,plain,
! [SV491: $i] :
( ( ~ ! [SY864: $i,SY865: $i] :
( ~ ( in @ SV491 @ SY865 )
| ~ ( in @ SY864 @ SY865 )
| ( subset @ ( unordered_pair @ SV491 @ SY864 ) @ SY865 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2759,plain,
! [SV491: $i] :
( ( ~ ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY866 ) @ SY867 )
| ( in @ SV491 @ SY867 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY868 ) @ SY869 )
| ( in @ SY868 @ SY869 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2760,plain,
! [SV492: $i] :
( ( ~ ! [SY870: $i,SY871: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
!= SY870 ) ) )
| ~ ( ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
= SV492 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
= SY870 ) ) )
| ( SY871
= ( unordered_pair @ SV492 @ SY870 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2616]) ).
thf(2761,plain,
! [SV492: $i] :
( ( ~ ! [SY872: $i,SY873: $i] :
( ( SY873
!= ( unordered_pair @ SV492 @ SY872 ) )
| ~ ( ~ ! [SY874: $i] :
( ~ ( in @ SY874 @ SY873 )
| ( SY874 = SV492 )
| ( SY874 = SY872 ) )
| ~ ~ ( ~ ! [SY875: $i] :
( ( SY875 != SV492 )
| ( in @ SY875 @ SY873 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY872 )
| ( in @ SX3 @ SY873 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2616]) ).
thf(2762,plain,
! [SV547: $i,SV493: $i] :
( ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( in @ SV493 @ SY935 )
| ~ ( in @ SV547 @ SY936 )
| ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY935 @ SY936 ) ) )
| ~ ~ ( ~ ! [SY937: $i] :
( ! [SY938: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY937 @ SY938 ) )
| ( in @ SV493 @ SY937 ) )
| ~ ! [SY939: $i,SY940: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY939 @ SY940 ) )
| ( in @ SV547 @ SY940 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2763,plain,
! [SV494: $i] :
( ( ~ ! [SY884: $i,SY885: $i] :
( ~ ( relation @ SY885 )
| ~ ( in @ ( ordered_pair @ SV494 @ SY884 ) @ SY885 )
| ( in @ SV494 @ ( relation_dom @ SY885 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2764,plain,
! [SV494: $i] :
( ( ~ ! [SY886: $i,SY887: $i] :
( ~ ( relation @ SY887 )
| ~ ( in @ ( ordered_pair @ SV494 @ SY886 ) @ SY887 )
| ( in @ SY886 @ ( relation_rng @ SY887 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2765,plain,
( ( empty @ sK35_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2619]) ).
thf(2766,plain,
( ( relation @ sK35_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2620]) ).
thf(2767,plain,
( ( ~ ( empty @ sK34_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2768,plain,
( ( relation @ sK34_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2622]) ).
thf(2769,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2623]) ).
thf(2770,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2624]) ).
thf(2771,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)],[2625]) ).
thf(2772,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)],[2626]) ).
thf(2773,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2627]) ).
thf(2774,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)],[2628]) ).
thf(2775,plain,
! [SV495: $i] :
( ( ~ ! [SY888: $i,SY889: $i] :
( ~ ( ~ ( ! [SY890: $i,SY891: $i] :
( ~ ( in @ SY890 @ SV495 )
| ~ ( in @ SY891 @ SY888 )
| ( ( sK23_D @ SY889 @ SY888 @ SV495 )
!= ( ordered_pair @ SY890 @ SY891 ) ) )
| ~ ( in @ ( sK23_D @ SY889 @ SY888 @ SV495 ) @ SY889 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY889 @ SY888 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SY889 @ SY888 @ SV495 ) @ SY888 ) )
| ( ( sK23_D @ SY889 @ SY888 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SY889 @ SY888 @ SV495 ) @ ( sK25_SY318 @ SY889 @ SY888 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SY889 @ SY888 @ SV495 ) @ SY889 ) ) )
| ( SY889
= ( cartesian_product2 @ SV495 @ SY888 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2629]) ).
thf(2776,plain,
! [SV495: $i] :
( ( ~ ! [SY892: $i,SY893: $i] :
( ( SY893
!= ( cartesian_product2 @ SV495 @ SY892 ) )
| ~ ( ~ ! [SY894: $i] :
( ! [SY895: $i,SY896: $i] :
( ~ ( in @ SY895 @ SV495 )
| ~ ( in @ SY896 @ SY892 )
| ( SY894
!= ( ordered_pair @ SY895 @ SY896 ) ) )
| ( in @ SY894 @ SY893 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SY893 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY897 @ SY893 @ SY892 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY897 @ SY893 @ SY892 @ SV495 ) @ SY892 ) )
| ( SY897
!= ( ordered_pair @ ( sK21_E @ SY897 @ SY893 @ SY892 @ SV495 ) @ ( sK22_SY313 @ SY897 @ SY893 @ SY892 @ SV495 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2629]) ).
thf(2777,plain,
! [SV496: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV496 ) @ ( powerset @ SV496 ) )
| ~ ~ ( empty @ ( sK8_B @ SV496 ) ) )
= $false )
| ( ( empty @ SV496 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2778,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2779,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2632]) ).
thf(2780,plain,
! [SV497: $i] :
( ( ~ ! [SY898: $i,SY899: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY898 )
| ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY898 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) ) ) )
| ( SY899
= ( set_difference @ SV497 @ SY898 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2633]) ).
thf(2781,plain,
! [SV497: $i] :
( ( ~ ! [SY900: $i,SY901: $i] :
( ( SY901
!= ( set_difference @ SV497 @ SY900 ) )
| ~ ( ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV497 )
| ( in @ SY902 @ SY900 )
| ( in @ SY902 @ SY901 ) )
| ~ ~ ( ~ ! [SY903: $i] :
( ~ ( in @ SY903 @ SY901 )
| ( in @ SY903 @ SV497 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY901 )
| ~ ( in @ SX3 @ SY900 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2633]) ).
thf(2782,plain,
! [SV498: $i] :
( ( ( relation @ SV498 )
= $false )
| ( ( ~ ( ~ ! [SY905: $i] :
( ~ ( ~ ( ! [SY906: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ SY906 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ ( sK41_SY326 @ SY905 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) ) )
| ( SY905
= ( relation_dom @ SV498 ) ) )
| ~ ! [SY907: $i] :
( ( SY907
!= ( relation_dom @ SV498 ) )
| ~ ( ~ ! [SY908: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY908 @ SY909 ) @ SV498 )
| ( in @ SY908 @ SY907 ) )
| ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SY907 )
| ( in @ ( ordered_pair @ SY910 @ ( sK39_D @ SY910 @ SY907 @ SV498 ) ) @ SV498 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2783,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2635]) ).
thf(2784,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2636]) ).
thf(2785,plain,
! [SV407: $i,SV558: $i] :
( ( ( ~ ( relation @ SV558 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV407 @ SV558 ) ) @ ( relation_dom @ SV407 ) ) )
= $true )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(2786,plain,
! [SV408: $i,SV559: $i] :
( ( ( ~ ( relation @ SV559 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV408 @ SV559 ) ) @ ( relation_rng @ SV559 ) ) )
= $true )
| ( ( relation @ SV408 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(2787,plain,
! [SV409: $i,SV560: $i] :
( ( ( ~ ( relation @ SV560 )
| ~ ( subset @ ( relation_rng @ SV409 ) @ ( relation_dom @ SV560 ) )
| ( ( relation_dom @ ( relation_composition @ SV409 @ SV560 ) )
= ( relation_dom @ SV409 ) ) )
= $true )
| ( ( relation @ SV409 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(2788,plain,
! [SV410: $i,SV561: $i] :
( ( ( ~ ( relation @ SV561 )
| ~ ( subset @ ( relation_dom @ SV410 ) @ ( relation_rng @ SV561 ) )
| ( ( relation_rng @ ( relation_composition @ SV561 @ SV410 ) )
= ( relation_rng @ SV410 ) ) )
= $true )
| ( ( relation @ SV410 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(2789,plain,
! [SV411: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_B @ SV411 ) @ ( sK50_SY332 @ SV411 ) ) @ SV411 )
= $true )
| ( ( SV411 = empty_set )
= $true )
| ( ( relation @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2790,plain,
! [SV499: $i,SV415: $i] :
( ( ( ~ ( relation @ SV415 ) )
= $true )
| ( ( ~ ( relation @ SV499 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV415 @ SV499 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(2791,plain,
! [SV500: $i,SV416: $i] :
( ( ( ~ ( relation @ SV416 ) )
= $true )
| ( ( ~ ( relation @ SV500 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV416 @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(2792,plain,
! [SV417: $i] :
( ( ( relation @ SV417 )
= $false )
| ( ( empty @ SV417 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2793,plain,
! [SV418: $i] :
( ( ( relation @ SV418 )
= $false )
| ( ( empty @ SV418 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2794,plain,
! [SV501: $i,SV425: $i] :
( ( ( in @ SV425 @ SV501 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV425 ) @ SV501 )
= SV501 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2795,plain,
! [SV502: $i,SV426: $i] :
( ( ( disjoint @ ( singleton @ SV426 ) @ SV502 )
= $false )
| ( ( ~ ( in @ SV426 @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2796,plain,
! [SV428: $i,SV504: $i] :
( ( ( element @ SV504 @ ( powerset @ SV428 ) )
= $false )
| ( ( ! [SY911: $i] :
( ~ ( in @ SY911 @ SV504 )
| ( in @ SY911 @ SV428 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(2797,plain,
! [SV505: $i,SV429: $i] :
( ( ( subset @ SV429 @ SV505 )
= $false )
| ( ( ! [SY912: $i] :
( ( in @ SY912 @ SV429 )
| ( subset @ SV429 @ ( set_difference @ SV505 @ ( singleton @ SY912 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2798,plain,
! [SV506: $i,SV430: $i] :
( ( ( in @ SV430 @ SV506 )
= $false )
| ( ( subset @ SV430 @ ( union @ SV506 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2799,plain,
! [SV562: $i,SV548: $i,SV507: $i,SV431: $i] :
( ( ~ ( subset @ SV431 @ SV507 )
| ~ ( subset @ SV548 @ SV562 )
| ( subset @ ( cartesian_product2 @ SV431 @ SV548 ) @ ( cartesian_product2 @ SV507 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(2800,plain,
! [SV508: $i,SV432: $i] :
( ( ( subset @ SV432 @ SV508 )
= $false )
| ( ( ( set_union2 @ SV432 @ SV508 )
= SV508 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2801,plain,
! [SV549: $i,SV510: $i,SV434: $i] :
( ( ( ~ ( subset @ SV434 @ SV510 )
| ~ ( subset @ SV434 @ SV549 ) )
= $true )
| ( ( subset @ SV434 @ ( set_intersection2 @ SV510 @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2802,plain,
! [SV550: $i,SV511: $i,SV435: $i] :
( ( ( ~ ( subset @ SV435 @ SV511 )
| ~ ( subset @ SV511 @ SV550 ) )
= $true )
| ( ( subset @ SV435 @ SV550 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2803,plain,
! [SV512: $i,SV436: $i] :
( ( ( subset @ SV436 @ SV512 )
= $false )
| ( ( ! [SY917: $i] : ( subset @ ( set_intersection2 @ SV436 @ SY917 ) @ ( set_intersection2 @ SV512 @ SY917 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2804,plain,
! [SV513: $i,SV437: $i] :
( ( ( subset @ SV437 @ SV513 )
= $false )
| ( ( ( set_intersection2 @ SV437 @ SV513 )
= SV437 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2805,plain,
! [SV514: $i,SV438: $i] :
( ( ( subset @ SV438 @ SV514 )
= $false )
| ( ( ! [SY918: $i] : ( subset @ ( set_difference @ SV438 @ SY918 ) @ ( set_difference @ SV514 @ SY918 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2806,plain,
! [SV518: $i,SV442: $i] :
( ( ( subset @ SV442 @ SV518 )
= $false )
| ( ( SV518
= ( set_union2 @ SV442 @ ( set_difference @ SV518 @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2807,plain,
! [SV519: $i,SV443: $i] :
( ( ( in @ SV443 @ SV519 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV443 ) @ SV519 )
= SV519 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2808,plain,
! [SV445: $i,SV521: $i] :
( ( ( proper_subset @ SV521 @ SV445 )
= $false )
| ( ( ~ ( subset @ SV445 @ SV521 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2809,plain,
! [SV446: $i,SV551: $i,SV522: $i] :
( ( ( ~ ( disjoint @ SV522 @ SV551 )
| ~ ( subset @ SV446 @ SV522 ) )
= $true )
| ( ( disjoint @ SV446 @ SV551 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2810,plain,
! [SV523: $i,SV448: $i] :
( ( ( subset @ ( singleton @ SV448 ) @ ( singleton @ SV523 ) )
= $false )
| ( ( SV448 = SV523 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2811,plain,
! [SV552: $i,SV525: $i,SV450: $i] :
( ( ( ~ ( subset @ SV450 @ SV525 )
| ~ ( subset @ SV552 @ SV525 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV450 @ SV552 ) @ SV525 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2812,plain,
! [SV563: $i,SV526: $i,SV451: $i] :
( ( ( ( ( singleton @ SV451 )
!= ( unordered_pair @ SV526 @ SV563 ) ) )
= $true )
| ( ( SV451 = SV526 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(2813,plain,
! [SV527: $i,SV452: $i] :
( ( ( in @ SV452 @ SV527 )
= $false )
| ( ( subset @ SV452 @ ( union @ SV527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2814,plain,
! [SV553: $i,SV528: $i,SV454: $i] :
( ( ( ( ( singleton @ SV454 )
!= ( unordered_pair @ SV528 @ SV553 ) ) )
= $true )
| ( ( SV528 = SV553 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2815,plain,
! [SV529: $i,SV455: $i] :
( ( ( in @ SV455 @ SV529 )
= $false )
| ( ( ~ ( in @ SV529 @ SV455 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2816,plain,
! [SV554: $i,SV462: $i] :
( ( ( empty @ ( set_union2 @ SV462 @ SV554 ) )
= $false )
| ( ( empty @ SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2817,plain,
! [SV464: $i,SV555: $i] :
( ( ( empty @ ( set_union2 @ SV555 @ SV464 ) )
= $false )
| ( ( empty @ SV464 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2818,plain,
! [SV535: $i,SV465: $i] :
( ( ( empty @ SV465 )
= $true )
| ( ( empty @ SV535 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV465 @ SV535 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2819,plain,
! [SV536: $i,SV469: $i] :
( ( ( disjoint @ SV469 @ SV536 )
= $false )
| ( ( disjoint @ SV536 @ SV469 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2820,plain,
! [SV537: $i,SV470: $i] :
( ( ( in @ SV470 @ SV537 )
= $false )
| ( ( element @ SV470 @ SV537 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2821,plain,
! [SV538: $i,SV471: $i] :
( ( ( element @ SV471 @ SV538 )
= $false )
| ( ( ( empty @ SV538 )
| ( in @ SV471 @ SV538 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2822,plain,
! [SV472: $i,SV556: $i,SV539: $i] :
( ( ( ~ ( element @ SV539 @ ( powerset @ SV556 ) )
| ~ ( in @ SV472 @ SV539 ) )
= $true )
| ( ( element @ SV472 @ SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2684]) ).
thf(2823,plain,
! [SV473: $i,SV557: $i,SV540: $i] :
( ( ( ~ ( element @ SV540 @ ( powerset @ SV557 ) )
| ~ ( in @ SV473 @ SV540 ) )
= $true )
| ( ( ~ ( empty @ SV557 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2685]) ).
thf(2824,plain,
! [SV474: $i,SV541: $i] :
( ( ( empty @ SV541 )
= $false )
| ( ( ~ ( in @ SV474 @ SV541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2825,plain,
! [SV542: $i,SV475: $i] :
( ( ( SV475 = SV542 )
= $true )
| ( ( ~ ( empty @ SV475 ) )
= $true )
| ( ( ~ ( empty @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2826,plain,
! [SV476: $i] :
( ( ! [SY796: $i,SY797: $i] :
( ~ ( relation @ SY797 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY796 ) @ SY797 )
| ( in @ SV476 @ ( relation_field @ SY797 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2688]) ).
thf(2827,plain,
! [SV476: $i] :
( ( ! [SY798: $i,SY799: $i] :
( ~ ( relation @ SY799 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY798 ) @ SY799 )
| ( in @ SY798 @ ( relation_field @ SY799 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2689]) ).
thf(2828,plain,
! [SV477: $i,SV564: $i] :
( ( ( ~ ( relation @ SV564 )
| ~ ( ~ ! [SY942: $i] :
( ~ ( relation @ SY942 )
| ~ ( ~ ( ! [SY943: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ SY943 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY943 @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) ) )
| ( SY942
= ( relation_composition @ SV477 @ SV564 ) ) )
| ~ ! [SY944: $i] :
( ~ ( relation @ SY944 )
| ( SY944
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY945: $i,SY946: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY945 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY946 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY945 @ SY946 ) @ SY944 ) )
| ~ ! [SY948: $i,SY949: $i] :
( ~ ( in @ ( ordered_pair @ SY948 @ SY949 ) @ SY944 )
| ~ ( ~ ( in @ ( ordered_pair @ SY948 @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) @ SY949 ) @ SV564 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(2829,plain,
! [SV478: $i] :
( ( ! [SY809: $i] :
( ~ ( subset @ SY809 @ ( sK2_B @ SV478 ) )
| ( are_equipotent @ SY809 @ ( sK2_B @ SV478 ) )
| ( in @ SY809 @ ( sK2_B @ SV478 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2830,plain,
! [SV478: $i] :
( ( ~ ( ~ ! [SY810: $i] :
( ~ ( ~ ! [SY811: $i] :
( ~ ( subset @ SY811 @ SY810 )
| ( in @ SY811 @ ( sK3_SY300 @ SY810 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY810 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SY810 @ ( sK2_B @ SV478 ) ) )
| ~ ~ ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2831,plain,
! [SV479: $i] :
( ( ! [SY814: $i] :
( ~ ( subset @ SV479 @ SY814 )
| ! [SY815: $i] : ( subset @ ( cartesian_product2 @ SV479 @ SY815 ) @ ( cartesian_product2 @ SY814 @ SY815 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2832,plain,
! [SV479: $i] :
( ( ! [SY816: $i] :
( ~ ( subset @ SV479 @ SY816 )
| ! [SY817: $i] : ( subset @ ( cartesian_product2 @ SY817 @ SV479 ) @ ( cartesian_product2 @ SY817 @ SY816 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2694]) ).
thf(2833,plain,
! [SV565: $i] :
( ( ! [SY950: $i] :
( ~ ( subset @ SV565 @ ( singleton @ SY950 ) )
| ( SV565 = empty_set )
| ( SV565
= ( singleton @ SY950 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(2834,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)],[2696]) ).
thf(2835,plain,
! [SV543: $i,SV480: $i] :
( ( ~ ! [SY925: $i] :
( ! [SY926: $i] :
( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SY925 @ SY926 ) )
| ( SV480 = SY925 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2697]) ).
thf(2836,plain,
! [SV543: $i,SV480: $i] :
( ( ~ ! [SY927: $i,SY928: $i] :
( ( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SY927 @ SY928 ) )
| ( SV543 = SY928 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2697]) ).
thf(2837,plain,
! [SV566: $i] :
( ( ! [SY951: $i] :
( ( ( set_difference @ SV566 @ SY951 )
!= empty_set )
| ( subset @ SV566 @ SY951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(2838,plain,
! [SV567: $i] :
( ( ! [SY952: $i] :
( ~ ( subset @ SV567 @ SY952 )
| ( ( set_difference @ SV567 @ SY952 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(2839,plain,
! [SV481: $i] :
( ( ( ~ ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) ) )
| ( SY823
= ( relation_inverse @ SV481 ) ) )
| ~ ! [SY824: $i] :
( ~ ( relation @ SY824 )
| ( SY824
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY825: $i,SY826: $i] :
( ~ ( in @ ( ordered_pair @ SY825 @ SY826 ) @ SY824 )
| ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV481 ) )
| ~ ! [SY827: $i,SY828: $i] :
( ~ ( in @ ( ordered_pair @ SY828 @ SY827 ) @ SV481 )
| ( in @ ( ordered_pair @ SY827 @ SY828 ) @ SY824 ) ) ) ) )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2840,plain,
! [SV544: $i,SV482: $i] :
( ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( in @ SV482 @ SY929 )
| ~ ( in @ SV544 @ SY930 )
| ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY929 @ SY930 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2701]) ).
thf(2841,plain,
! [SV544: $i,SV482: $i] :
( ( ~ ~ ( ~ ! [SY931: $i] :
( ! [SY932: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY931 @ SY932 ) )
| ( in @ SV482 @ SY931 ) )
| ~ ! [SY933: $i,SY934: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY933 @ SY934 ) )
| ( in @ SV544 @ SY934 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2701]) ).
thf(2842,plain,
! [SV568: $i] :
( ( ! [SY953: $i] :
( ( ( set_intersection2 @ SV568 @ SY953 )
!= empty_set )
| ( disjoint @ SV568 @ SY953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(2843,plain,
! [SV569: $i] :
( ( ! [SY954: $i] :
( ~ ( disjoint @ SV569 @ SY954 )
| ( ( set_intersection2 @ SV569 @ SY954 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(2844,plain,
! [SV570: $i] :
( ( ! [SY955: $i] :
( ~ ( subset @ SV570 @ SY955 )
| ~ ( subset @ SY955 @ SV570 )
| ( SV570 = SY955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(2845,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)],[2705]) ).
thf(2846,plain,
! [SV571: $i] :
( ( ! [SY956: $i] :
( ( ( set_difference @ SV571 @ ( singleton @ SY956 ) )
!= SV571 )
| ~ ( in @ SY956 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(2847,plain,
! [SV572: $i] :
( ( ! [SY957: $i] :
( ( in @ SY957 @ SV572 )
| ( ( set_difference @ SV572 @ ( singleton @ SY957 ) )
= SV572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(2848,plain,
! [SV483: $i,SV545: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV483 )
| ~ ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV545 ) )
= $false )
| ( ( element @ SV483 @ ( powerset @ SV545 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2849,plain,
! [SV484: $i] :
( ( ( ~ ! [SY837: $i] :
( ~ ( relation @ SY837 )
| ~ ( subset @ SV484 @ SY837 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SY837 ) ) )
| ~ ! [SY838: $i] :
( ~ ( relation @ SY838 )
| ~ ( subset @ SV484 @ SY838 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SY838 ) ) ) )
= $false )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2850,plain,
! [SV573: $i] :
( ( ! [SY958: $i] :
( ~ ( ~ ( in @ ( sK20_C @ SY958 @ SV573 ) @ SV573 )
| ~ ~ ( in @ ( sK20_C @ SY958 @ SV573 ) @ SY958 ) )
| ( subset @ SV573 @ SY958 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(2851,plain,
! [SV574: $i] :
( ( ! [SY959: $i] :
( ~ ( subset @ SV574 @ SY959 )
| ! [SY960: $i] :
( ~ ( in @ SY960 @ SV574 )
| ( in @ SY960 @ SY959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(2852,plain,
! [SV485: $i] :
( ( ! [SY839: $i,SY840: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ~ ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY839 ) ) )
| ~ ( ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY840 )
| ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SY840 @ SY839 @ SV485 ) @ SY839 ) ) )
| ( SY840
= ( set_union2 @ SV485 @ SY839 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2712]) ).
thf(2853,plain,
! [SV485: $i] :
( ( ! [SY841: $i,SY842: $i] :
( ( SY842
!= ( set_union2 @ SV485 @ SY841 ) )
| ~ ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SY842 )
| ( in @ SY843 @ SV485 )
| ( in @ SY843 @ SY841 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV485 )
| ( in @ SY844 @ SY842 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY841 )
| ( in @ SX3 @ SY842 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2713]) ).
thf(2854,plain,
! [SV575: $i] :
( ( ! [SY961: $i] :
( ~ ( in @ SV575 @ SY961 )
| ( subset @ ( singleton @ SV575 ) @ SY961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(2855,plain,
! [SV576: $i] :
( ( ! [SY962: $i] :
( ~ ( subset @ ( singleton @ SV576 ) @ SY962 )
| ( in @ SV576 @ SY962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(2856,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[2716]) ).
thf(2857,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)],[2717]) ).
thf(2858,plain,
! [SV577: $i] :
( ( ! [SY963: $i] :
( ~ ( ~ ( ! [SY964: $i] :
( ~ ( in @ ( sK17_C @ SY963 @ SV577 ) @ SY964 )
| ~ ( in @ SY964 @ SV577 ) )
| ~ ( in @ ( sK17_C @ SY963 @ SV577 ) @ SY963 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SY963 @ SV577 ) @ ( sK18_SY312 @ SY963 @ SV577 ) )
| ~ ( in @ ( sK18_SY312 @ SY963 @ SV577 ) @ SV577 ) )
| ( in @ ( sK17_C @ SY963 @ SV577 ) @ SY963 ) ) )
| ( SY963
= ( union @ SV577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(2859,plain,
! [SV578: $i] :
( ( ! [SY965: $i] :
( ( SY965
!= ( union @ SV578 ) )
| ~ ( ~ ! [SY966: $i] :
( ! [SY967: $i] :
( ~ ( in @ SY966 @ SY967 )
| ~ ( in @ SY967 @ SV578 ) )
| ( in @ SY966 @ SY965 ) )
| ~ ! [SY968: $i] :
( ~ ( in @ SY968 @ SY965 )
| ~ ( ~ ( in @ SY968 @ ( sK16_D @ SY968 @ SY965 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SY968 @ SY965 @ SV578 ) @ SV578 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(2860,plain,
! [SV486: $i] :
( ( ! [SY846: $i,SY847: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY846 )
| ~ ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) )
| ~ ( ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY846 )
| ( in @ ( sK19_D @ SY847 @ SY846 @ SV486 ) @ SY847 ) ) ) )
| ( SY847
= ( set_intersection2 @ SV486 @ SY846 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2720]) ).
thf(2861,plain,
! [SV486: $i] :
( ( ! [SY848: $i,SY849: $i] :
( ( SY849
!= ( set_intersection2 @ SV486 @ SY848 ) )
| ~ ( ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ SV486 )
| ~ ( in @ SY850 @ SY848 )
| ( in @ SY850 @ SY849 ) )
| ~ ~ ( ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY849 )
| ( in @ SY851 @ SV486 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY849 )
| ( in @ SX3 @ SY848 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2721]) ).
thf(2862,plain,
! [SV579: $i] :
( ( ~ ( empty @ SV579 )
| ( empty @ ( relation_dom @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(2863,plain,
! [SV580: $i] :
( ( ~ ( empty @ SV580 )
| ( relation @ ( relation_dom @ SV580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(2864,plain,
! [SV487: $i] :
( ( ! [SY853: $i] :
( ~ ( subset @ SY853 @ ( sK32_B @ SV487 ) )
| ( are_equipotent @ SY853 @ ( sK32_B @ SV487 ) )
| ( in @ SY853 @ ( sK32_B @ SV487 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2726]) ).
thf(2865,plain,
! [SV487: $i] :
( ( ~ ( ~ ! [SY854: $i] :
( ~ ( in @ SY854 @ ( sK32_B @ SV487 ) )
| ( in @ ( powerset @ SY854 ) @ ( sK32_B @ SV487 ) ) )
| ~ ~ ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) )
| ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2727]) ).
thf(2866,plain,
! [SV581: $i] :
( ( ~ ( empty @ SV581 )
| ( empty @ ( relation_rng @ SV581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(2867,plain,
! [SV582: $i] :
( ( ~ ( empty @ SV582 )
| ( relation @ ( relation_rng @ SV582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(2868,plain,
! [SV583: $i] :
( ( ! [SY969: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SY969 @ SV583 ) @ SY969 )
| ~ ( subset @ ( sK28_C @ SY969 @ SV583 ) @ SV583 ) )
| ~ ( ( in @ ( sK28_C @ SY969 @ SV583 ) @ SY969 )
| ( subset @ ( sK28_C @ SY969 @ SV583 ) @ SV583 ) ) )
| ( SY969
= ( powerset @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(2869,plain,
! [SV584: $i] :
( ( ! [SY970: $i] :
( ( SY970
!= ( powerset @ SV584 ) )
| ~ ( ~ ! [SY971: $i] :
( ~ ( in @ SY971 @ SY970 )
| ( subset @ SY971 @ SV584 ) )
| ~ ! [SY972: $i] :
( ~ ( subset @ SY972 @ SV584 )
| ( in @ SY972 @ SY970 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(2870,plain,
! [SV585: $i] :
( ( ! [SY973: $i] :
( ( disjoint @ SV585 @ SY973 )
| ~ ( ~ ( in @ ( sK31_C @ SY973 @ SV585 ) @ SV585 )
| ~ ( in @ ( sK31_C @ SY973 @ SV585 ) @ SY973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(2871,plain,
! [SV586: $i] :
( ( ! [SY974: $i] :
( ! [SY975: $i] :
( ~ ( in @ SY975 @ SV586 )
| ~ ( in @ SY975 @ SY974 ) )
| ~ ( disjoint @ SV586 @ SY974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(2872,plain,
( ( ( relation_dom @ sK1_A )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(2873,plain,
! [SV488: $i] :
( ( ( ~ ! [SY857: $i] :
( ~ ( ~ ( ! [SY858: $i] :
~ ( in @ ( ordered_pair @ SY858 @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY857 @ SV488 ) @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) ) )
| ( SY857
= ( relation_rng @ SV488 ) ) )
| ~ ! [SY859: $i] :
( ( SY859
!= ( relation_rng @ SV488 ) )
| ~ ( ~ ! [SY860: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY860 ) @ SV488 )
| ( in @ SY860 @ SY859 ) )
| ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY859 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY862 @ SY859 @ SV488 ) @ SY862 ) @ SV488 ) ) ) ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2874,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)],[2737]) ).
thf(2875,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)],[2738]) ).
thf(2876,plain,
! [SV489: $i] :
( ( element @ ( sK6_B @ SV489 ) @ ( powerset @ SV489 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2739]) ).
thf(2877,plain,
! [SV489: $i] :
( ( empty @ ( sK6_B @ SV489 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2740]) ).
thf(2878,plain,
! [SV587: $i] :
( ( ! [SY976: $i] :
( ~ ( in @ SV587 @ SY976 )
| ( subset @ ( singleton @ SV587 ) @ SY976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(2879,plain,
! [SV588: $i] :
( ( ! [SY977: $i] :
( ~ ( subset @ ( singleton @ SV588 ) @ SY977 )
| ( in @ SV588 @ SY977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(2880,plain,
! [SV589: $i] :
( ( ! [SY978: $i] :
( ~ ( subset @ SV589 @ ( singleton @ SY978 ) )
| ( SV589 = empty_set )
| ( SV589
= ( singleton @ SY978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(2881,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)],[2744]) ).
thf(2882,plain,
! [SV590: $i] :
( ( ( in @ ( sK42_B @ SV590 ) @ SV590 )
| ( SV590 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(2883,plain,
! [SV591: $i] :
( ( ( SV591 != empty_set )
| ! [SY979: $i] :
~ ( in @ SY979 @ SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(2884,plain,
! [SV592: $i] :
( ( ~ ( relation @ SV592 )
| ( ( relation_dom @ SV592 )
!= empty_set )
| ( SV592 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(2885,plain,
! [SV593: $i] :
( ( ~ ( relation @ SV593 )
| ( ( relation_rng @ SV593 )
!= empty_set )
| ( SV593 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(2886,plain,
! [SV594: $i] :
( ( ~ ( relation @ SV594 )
| ( ( relation_rng @ SV594 )
= ( relation_dom @ ( relation_inverse @ SV594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(2887,plain,
! [SV595: $i] :
( ( ~ ( relation @ SV595 )
| ( ( relation_dom @ SV595 )
= ( relation_rng @ ( relation_inverse @ SV595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(2888,plain,
! [SV596: $i] :
( ( ! [SY980: $i] :
( ( ( set_difference @ SV596 @ SY980 )
!= empty_set )
| ( subset @ SV596 @ SY980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(2889,plain,
! [SV597: $i] :
( ( ! [SY981: $i] :
( ~ ( subset @ SV597 @ SY981 )
| ( ( set_difference @ SV597 @ SY981 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(2890,plain,
! [SV490: $i,SV546: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) )
| ~ ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) ) )
= $false )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2891,plain,
! [SV598: $i] :
( ( ! [SY982: $i] :
( ~ ( element @ SV598 @ ( powerset @ SY982 ) )
| ( subset @ SV598 @ SY982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(2892,plain,
! [SV599: $i] :
( ( ! [SY983: $i] :
( ~ ( subset @ SV599 @ SY983 )
| ( element @ SV599 @ ( powerset @ SY983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(2893,plain,
! [SV600: $i] :
( ( ~ ( ~ ! [SY984: $i,SY985: $i] :
( ( sK48_B @ SV600 )
!= ( ordered_pair @ SY984 @ SY985 ) )
| ~ ( in @ ( sK48_B @ SV600 ) @ SV600 ) )
| ( relation @ SV600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(2894,plain,
! [SV601: $i] :
( ( ~ ( relation @ SV601 )
| ! [SY986: $i] :
( ( SY986
= ( ordered_pair @ ( sK46_C @ SY986 @ SV601 ) @ ( sK47_SY329 @ SY986 @ SV601 ) ) )
| ~ ( in @ SY986 @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(2895,plain,
! [SV491: $i] :
( ( ! [SY864: $i,SY865: $i] :
( ~ ( in @ SV491 @ SY865 )
| ~ ( in @ SY864 @ SY865 )
| ( subset @ ( unordered_pair @ SV491 @ SY864 ) @ SY865 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2758]) ).
thf(2896,plain,
! [SV491: $i] :
( ( ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY866 ) @ SY867 )
| ( in @ SV491 @ SY867 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY868 ) @ SY869 )
| ( in @ SY868 @ SY869 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2897,plain,
! [SV492: $i] :
( ( ! [SY870: $i,SY871: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
!= SY870 ) ) )
| ~ ( ( in @ ( sK27_D @ SY871 @ SY870 @ SV492 ) @ SY871 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
= SV492 )
| ( ( sK27_D @ SY871 @ SY870 @ SV492 )
= SY870 ) ) )
| ( SY871
= ( unordered_pair @ SV492 @ SY870 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2760]) ).
thf(2898,plain,
! [SV492: $i] :
( ( ! [SY872: $i,SY873: $i] :
( ( SY873
!= ( unordered_pair @ SV492 @ SY872 ) )
| ~ ( ~ ! [SY874: $i] :
( ~ ( in @ SY874 @ SY873 )
| ( SY874 = SV492 )
| ( SY874 = SY872 ) )
| ~ ~ ( ~ ! [SY875: $i] :
( ( SY875 != SV492 )
| ( in @ SY875 @ SY873 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY872 )
| ( in @ SX3 @ SY873 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2899,plain,
! [SV547: $i,SV493: $i] :
( ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( in @ SV493 @ SY935 )
| ~ ( in @ SV547 @ SY936 )
| ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY935 @ SY936 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2762]) ).
thf(2900,plain,
! [SV547: $i,SV493: $i] :
( ( ~ ~ ( ~ ! [SY937: $i] :
( ! [SY938: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY937 @ SY938 ) )
| ( in @ SV493 @ SY937 ) )
| ~ ! [SY939: $i,SY940: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY939 @ SY940 ) )
| ( in @ SV547 @ SY940 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2762]) ).
thf(2901,plain,
! [SV494: $i] :
( ( ! [SY884: $i,SY885: $i] :
( ~ ( relation @ SY885 )
| ~ ( in @ ( ordered_pair @ SV494 @ SY884 ) @ SY885 )
| ( in @ SV494 @ ( relation_dom @ SY885 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2763]) ).
thf(2902,plain,
! [SV494: $i] :
( ( ! [SY886: $i,SY887: $i] :
( ~ ( relation @ SY887 )
| ~ ( in @ ( ordered_pair @ SV494 @ SY886 ) @ SY887 )
| ( in @ SY886 @ ( relation_rng @ SY887 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2764]) ).
thf(2903,plain,
( ( empty @ sK34_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2904,plain,
! [SV602: $i] :
( ( ! [SY987: $i] :
( ( disjoint @ SV602 @ SY987 )
| ( in @ ( sK30_C @ SY987 @ SV602 ) @ ( set_intersection2 @ SV602 @ SY987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(2905,plain,
! [SV603: $i] :
( ( ! [SY988: $i] :
( ! [SY989: $i] :
~ ( in @ SY989 @ ( set_intersection2 @ SV603 @ SY988 ) )
| ~ ( disjoint @ SV603 @ SY988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(2906,plain,
! [SV604: $i] :
( ( ! [SY990: $i] :
( ~ ( ~ ( ( ( sK29_C @ SY990 @ SV604 )
!= SV604 )
| ~ ( in @ ( sK29_C @ SY990 @ SV604 ) @ SY990 ) )
| ~ ( ( ( sK29_C @ SY990 @ SV604 )
= SV604 )
| ( in @ ( sK29_C @ SY990 @ SV604 ) @ SY990 ) ) )
| ( SY990
= ( singleton @ SV604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(2907,plain,
! [SV605: $i] :
( ( ! [SY991: $i] :
( ( SY991
!= ( singleton @ SV605 ) )
| ~ ( ~ ! [SY992: $i] :
( ( SY992 != SV605 )
| ( in @ SY992 @ SY991 ) )
| ~ ! [SY993: $i] :
( ~ ( in @ SY993 @ SY991 )
| ( SY993 = SV605 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(2908,plain,
! [SV606: $i] :
( ( ! [SY994: $i] :
( ( SV606 = SY994 )
| ~ ( subset @ SV606 @ SY994 )
| ( proper_subset @ SV606 @ SY994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(2909,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)],[2774]) ).
thf(2910,plain,
! [SV495: $i] :
( ( ! [SY888: $i,SY889: $i] :
( ~ ( ~ ( ! [SY890: $i,SY891: $i] :
( ~ ( in @ SY890 @ SV495 )
| ~ ( in @ SY891 @ SY888 )
| ( ( sK23_D @ SY889 @ SY888 @ SV495 )
!= ( ordered_pair @ SY890 @ SY891 ) ) )
| ~ ( in @ ( sK23_D @ SY889 @ SY888 @ SV495 ) @ SY889 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY889 @ SY888 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SY889 @ SY888 @ SV495 ) @ SY888 ) )
| ( ( sK23_D @ SY889 @ SY888 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SY889 @ SY888 @ SV495 ) @ ( sK25_SY318 @ SY889 @ SY888 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SY889 @ SY888 @ SV495 ) @ SY889 ) ) )
| ( SY889
= ( cartesian_product2 @ SV495 @ SY888 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2775]) ).
thf(2911,plain,
! [SV495: $i] :
( ( ! [SY892: $i,SY893: $i] :
( ( SY893
!= ( cartesian_product2 @ SV495 @ SY892 ) )
| ~ ( ~ ! [SY894: $i] :
( ! [SY895: $i,SY896: $i] :
( ~ ( in @ SY895 @ SV495 )
| ~ ( in @ SY896 @ SY892 )
| ( SY894
!= ( ordered_pair @ SY895 @ SY896 ) ) )
| ( in @ SY894 @ SY893 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SY893 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY897 @ SY893 @ SY892 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY897 @ SY893 @ SY892 @ SV495 ) @ SY892 ) )
| ( SY897
!= ( ordered_pair @ ( sK21_E @ SY897 @ SY893 @ SY892 @ SV495 ) @ ( sK22_SY313 @ SY897 @ SY893 @ SY892 @ SV495 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2776]) ).
thf(2912,plain,
! [SV496: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV496 ) @ ( powerset @ SV496 ) ) )
= $false )
| ( ( empty @ SV496 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2777]) ).
thf(2913,plain,
! [SV496: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV496 ) ) )
= $false )
| ( ( empty @ SV496 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2777]) ).
thf(2914,plain,
! [SV607: $i] :
( ( ! [SY995: $i] :
( ( ( set_difference @ SV607 @ SY995 )
!= SV607 )
| ( disjoint @ SV607 @ SY995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(2915,plain,
! [SV608: $i] :
( ( ! [SY996: $i] :
( ~ ( disjoint @ SV608 @ SY996 )
| ( ( set_difference @ SV608 @ SY996 )
= SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(2916,plain,
! [SV497: $i] :
( ( ! [SY898: $i,SY899: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY898 )
| ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY898 )
| ( in @ ( sK15_D @ SY899 @ SY898 @ SV497 ) @ SY899 ) ) ) )
| ( SY899
= ( set_difference @ SV497 @ SY898 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2780]) ).
thf(2917,plain,
! [SV497: $i] :
( ( ! [SY900: $i,SY901: $i] :
( ( SY901
!= ( set_difference @ SV497 @ SY900 ) )
| ~ ( ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV497 )
| ( in @ SY902 @ SY900 )
| ( in @ SY902 @ SY901 ) )
| ~ ~ ( ~ ! [SY903: $i] :
( ~ ( in @ SY903 @ SY901 )
| ( in @ SY903 @ SV497 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY901 )
| ~ ( in @ SX3 @ SY900 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2781]) ).
thf(2918,plain,
! [SV498: $i] :
( ( ( ~ ! [SY905: $i] :
( ~ ( ~ ( ! [SY906: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ SY906 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ ( sK41_SY326 @ SY905 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) ) )
| ( SY905
= ( relation_dom @ SV498 ) ) )
| ~ ! [SY907: $i] :
( ( SY907
!= ( relation_dom @ SV498 ) )
| ~ ( ~ ! [SY908: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY908 @ SY909 ) @ SV498 )
| ( in @ SY908 @ SY907 ) )
| ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SY907 )
| ( in @ ( ordered_pair @ SY910 @ ( sK39_D @ SY910 @ SY907 @ SV498 ) ) @ SV498 ) ) ) ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(2919,plain,
! [SV407: $i,SV558: $i] :
( ( ( ~ ( relation @ SV558 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV407 @ SV558 ) ) @ ( relation_dom @ SV407 ) )
= $true )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(2920,plain,
! [SV408: $i,SV559: $i] :
( ( ( ~ ( relation @ SV559 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV408 @ SV559 ) ) @ ( relation_rng @ SV559 ) )
= $true )
| ( ( relation @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2786]) ).
thf(2921,plain,
! [SV409: $i,SV560: $i] :
( ( ( ~ ( relation @ SV560 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV409 ) @ ( relation_dom @ SV560 ) )
| ( ( relation_dom @ ( relation_composition @ SV409 @ SV560 ) )
= ( relation_dom @ SV409 ) ) )
= $true )
| ( ( relation @ SV409 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(2922,plain,
! [SV410: $i,SV561: $i] :
( ( ( ~ ( relation @ SV561 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV410 ) @ ( relation_rng @ SV561 ) )
| ( ( relation_rng @ ( relation_composition @ SV561 @ SV410 ) )
= ( relation_rng @ SV410 ) ) )
= $true )
| ( ( relation @ SV410 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(2923,plain,
! [SV499: $i,SV415: $i] :
( ( ( relation @ SV415 )
= $false )
| ( ( ~ ( relation @ SV499 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV415 @ SV499 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(2924,plain,
! [SV500: $i,SV416: $i] :
( ( ( relation @ SV416 )
= $false )
| ( ( ~ ( relation @ SV500 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV416 @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2925,plain,
! [SV417: $i] :
( ( ( empty @ ( relation_dom @ SV417 ) )
= $false )
| ( ( empty @ SV417 )
= $true )
| ( ( relation @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2926,plain,
! [SV418: $i] :
( ( ( empty @ ( relation_rng @ SV418 ) )
= $false )
| ( ( empty @ SV418 )
= $true )
| ( ( relation @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2927,plain,
! [SV502: $i,SV426: $i] :
( ( ( in @ SV426 @ SV502 )
= $false )
| ( ( disjoint @ ( singleton @ SV426 ) @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(2928,plain,
! [SV428: $i,SV504: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV504 )
| ( in @ SV609 @ SV428 ) )
= $true )
| ( ( element @ SV504 @ ( powerset @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(2929,plain,
! [SV505: $i,SV429: $i,SV610: $i] :
( ( ( ( in @ SV610 @ SV429 )
| ( subset @ SV429 @ ( set_difference @ SV505 @ ( singleton @ SV610 ) ) ) )
= $true )
| ( ( subset @ SV429 @ SV505 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(2930,plain,
! [SV562: $i,SV548: $i,SV507: $i,SV431: $i] :
( ( ( ~ ( subset @ SV431 @ SV507 )
| ~ ( subset @ SV548 @ SV562 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV431 @ SV548 ) @ ( cartesian_product2 @ SV507 @ SV562 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2799]) ).
thf(2931,plain,
! [SV549: $i,SV510: $i,SV434: $i] :
( ( ( ~ ( subset @ SV434 @ SV510 ) )
= $true )
| ( ( ~ ( subset @ SV434 @ SV549 ) )
= $true )
| ( ( subset @ SV434 @ ( set_intersection2 @ SV510 @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2801]) ).
thf(2932,plain,
! [SV550: $i,SV511: $i,SV435: $i] :
( ( ( ~ ( subset @ SV435 @ SV511 ) )
= $true )
| ( ( ~ ( subset @ SV511 @ SV550 ) )
= $true )
| ( ( subset @ SV435 @ SV550 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(2933,plain,
! [SV512: $i,SV611: $i,SV436: $i] :
( ( ( subset @ ( set_intersection2 @ SV436 @ SV611 ) @ ( set_intersection2 @ SV512 @ SV611 ) )
= $true )
| ( ( subset @ SV436 @ SV512 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(2934,plain,
! [SV514: $i,SV612: $i,SV438: $i] :
( ( ( subset @ ( set_difference @ SV438 @ SV612 ) @ ( set_difference @ SV514 @ SV612 ) )
= $true )
| ( ( subset @ SV438 @ SV514 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(2935,plain,
! [SV521: $i,SV445: $i] :
( ( ( subset @ SV445 @ SV521 )
= $false )
| ( ( proper_subset @ SV521 @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(2936,plain,
! [SV446: $i,SV551: $i,SV522: $i] :
( ( ( ~ ( disjoint @ SV522 @ SV551 ) )
= $true )
| ( ( ~ ( subset @ SV446 @ SV522 ) )
= $true )
| ( ( disjoint @ SV446 @ SV551 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(2937,plain,
! [SV552: $i,SV525: $i,SV450: $i] :
( ( ( ~ ( subset @ SV450 @ SV525 ) )
= $true )
| ( ( ~ ( subset @ SV552 @ SV525 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV450 @ SV552 ) @ SV525 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(2938,plain,
! [SV563: $i,SV526: $i,SV451: $i] :
( ( ( ( singleton @ SV451 )
= ( unordered_pair @ SV526 @ SV563 ) )
= $false )
| ( ( SV451 = SV526 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(2939,plain,
! [SV553: $i,SV528: $i,SV454: $i] :
( ( ( ( singleton @ SV454 )
= ( unordered_pair @ SV528 @ SV553 ) )
= $false )
| ( ( SV528 = SV553 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2940,plain,
! [SV455: $i,SV529: $i] :
( ( ( in @ SV529 @ SV455 )
= $false )
| ( ( in @ SV455 @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2941,plain,
! [SV535: $i,SV465: $i] :
( ( ( empty @ ( cartesian_product2 @ SV465 @ SV535 ) )
= $false )
| ( ( empty @ SV535 )
= $true )
| ( ( empty @ SV465 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(2942,plain,
! [SV471: $i,SV538: $i] :
( ( ( empty @ SV538 )
= $true )
| ( ( in @ SV471 @ SV538 )
= $true )
| ( ( element @ SV471 @ SV538 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2821]) ).
thf(2943,plain,
! [SV472: $i,SV556: $i,SV539: $i] :
( ( ( ~ ( element @ SV539 @ ( powerset @ SV556 ) ) )
= $true )
| ( ( ~ ( in @ SV472 @ SV539 ) )
= $true )
| ( ( element @ SV472 @ SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(2944,plain,
! [SV473: $i,SV557: $i,SV540: $i] :
( ( ( ~ ( element @ SV540 @ ( powerset @ SV557 ) ) )
= $true )
| ( ( ~ ( in @ SV473 @ SV540 ) )
= $true )
| ( ( ~ ( empty @ SV557 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(2945,plain,
! [SV541: $i,SV474: $i] :
( ( ( in @ SV474 @ SV541 )
= $false )
| ( ( empty @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(2946,plain,
! [SV542: $i,SV475: $i] :
( ( ( empty @ SV475 )
= $false )
| ( ( SV475 = SV542 )
= $true )
| ( ( ~ ( empty @ SV542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(2947,plain,
! [SV613: $i,SV476: $i] :
( ( ! [SY997: $i] :
( ~ ( relation @ SY997 )
| ~ ( in @ ( ordered_pair @ SV476 @ SV613 ) @ SY997 )
| ( in @ SV476 @ ( relation_field @ SY997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(2948,plain,
! [SV614: $i,SV476: $i] :
( ( ! [SY998: $i] :
( ~ ( relation @ SY998 )
| ~ ( in @ ( ordered_pair @ SV476 @ SV614 ) @ SY998 )
| ( in @ SV614 @ ( relation_field @ SY998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(2949,plain,
! [SV477: $i,SV564: $i] :
( ( ( ~ ( relation @ SV564 ) )
= $true )
| ( ( ~ ( ~ ! [SY942: $i] :
( ~ ( relation @ SY942 )
| ~ ( ~ ( ! [SY943: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ SY943 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY943 @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) ) )
| ( SY942
= ( relation_composition @ SV477 @ SV564 ) ) )
| ~ ! [SY944: $i] :
( ~ ( relation @ SY944 )
| ( SY944
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY945: $i,SY946: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY945 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY946 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY945 @ SY946 ) @ SY944 ) )
| ~ ! [SY948: $i,SY949: $i] :
( ~ ( in @ ( ordered_pair @ SY948 @ SY949 ) @ SY944 )
| ~ ( ~ ( in @ ( ordered_pair @ SY948 @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) @ SY949 ) @ SV564 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2828]) ).
thf(2950,plain,
! [SV478: $i,SV615: $i] :
( ( ~ ( subset @ SV615 @ ( sK2_B @ SV478 ) )
| ( are_equipotent @ SV615 @ ( sK2_B @ SV478 ) )
| ( in @ SV615 @ ( sK2_B @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(2951,plain,
! [SV478: $i] :
( ( ~ ! [SY810: $i] :
( ~ ( ~ ! [SY811: $i] :
( ~ ( subset @ SY811 @ SY810 )
| ( in @ SY811 @ ( sK3_SY300 @ SY810 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY810 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SY810 @ ( sK2_B @ SV478 ) ) )
| ~ ~ ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2952,plain,
! [SV616: $i,SV479: $i] :
( ( ~ ( subset @ SV479 @ SV616 )
| ! [SY999: $i] : ( subset @ ( cartesian_product2 @ SV479 @ SY999 ) @ ( cartesian_product2 @ SV616 @ SY999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(2953,plain,
! [SV617: $i,SV479: $i] :
( ( ~ ( subset @ SV479 @ SV617 )
| ! [SY1000: $i] : ( subset @ ( cartesian_product2 @ SY1000 @ SV479 ) @ ( cartesian_product2 @ SY1000 @ SV617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(2954,plain,
! [SV618: $i,SV565: $i] :
( ( ~ ( subset @ SV565 @ ( singleton @ SV618 ) )
| ( SV565 = empty_set )
| ( SV565
= ( singleton @ SV618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(2955,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2834]) ).
thf(2956,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2834]) ).
thf(2957,plain,
! [SV543: $i,SV480: $i] :
( ( ! [SY925: $i] :
( ! [SY926: $i] :
( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SY925 @ SY926 ) )
| ( SV480 = SY925 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2958,plain,
! [SV543: $i,SV480: $i] :
( ( ! [SY927: $i,SY928: $i] :
( ( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SY927 @ SY928 ) )
| ( SV543 = SY928 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(2959,plain,
! [SV619: $i,SV566: $i] :
( ( ( ( set_difference @ SV566 @ SV619 )
!= empty_set )
| ( subset @ SV566 @ SV619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(2960,plain,
! [SV620: $i,SV567: $i] :
( ( ~ ( subset @ SV567 @ SV620 )
| ( ( set_difference @ SV567 @ SV620 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(2961,plain,
! [SV481: $i] :
( ( ( ~ ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) ) )
| ( SY823
= ( relation_inverse @ SV481 ) ) ) )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(2962,plain,
! [SV481: $i] :
( ( ( ~ ! [SY824: $i] :
( ~ ( relation @ SY824 )
| ( SY824
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY825: $i,SY826: $i] :
( ~ ( in @ ( ordered_pair @ SY825 @ SY826 ) @ SY824 )
| ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV481 ) )
| ~ ! [SY827: $i,SY828: $i] :
( ~ ( in @ ( ordered_pair @ SY828 @ SY827 ) @ SV481 )
| ( in @ ( ordered_pair @ SY827 @ SY828 ) @ SY824 ) ) ) ) )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(2963,plain,
! [SV544: $i,SV482: $i] :
( ( ! [SY929: $i,SY930: $i] :
( ~ ( in @ SV482 @ SY929 )
| ~ ( in @ SV544 @ SY930 )
| ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY929 @ SY930 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2840]) ).
thf(2964,plain,
! [SV544: $i,SV482: $i] :
( ( ~ ( ~ ! [SY931: $i] :
( ! [SY932: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY931 @ SY932 ) )
| ( in @ SV482 @ SY931 ) )
| ~ ! [SY933: $i,SY934: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY933 @ SY934 ) )
| ( in @ SV544 @ SY934 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(2965,plain,
! [SV621: $i,SV568: $i] :
( ( ( ( set_intersection2 @ SV568 @ SV621 )
!= empty_set )
| ( disjoint @ SV568 @ SV621 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(2966,plain,
! [SV622: $i,SV569: $i] :
( ( ~ ( disjoint @ SV569 @ SV622 )
| ( ( set_intersection2 @ SV569 @ SV622 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(2967,plain,
! [SV623: $i,SV570: $i] :
( ( ~ ( subset @ SV570 @ SV623 )
| ~ ( subset @ SV623 @ SV570 )
| ( SV570 = SV623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(2968,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2845]) ).
thf(2969,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2845]) ).
thf(2970,plain,
! [SV624: $i,SV571: $i] :
( ( ( ( set_difference @ SV571 @ ( singleton @ SV624 ) )
!= SV571 )
| ~ ( in @ SV624 @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(2971,plain,
! [SV572: $i,SV625: $i] :
( ( ( in @ SV625 @ SV572 )
| ( ( set_difference @ SV572 @ ( singleton @ SV625 ) )
= SV572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(2972,plain,
! [SV483: $i,SV545: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV483 ) )
= $false )
| ( ( element @ SV483 @ ( powerset @ SV545 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2973,plain,
! [SV483: $i,SV545: $i] :
( ( ( ~ ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV545 ) )
= $false )
| ( ( element @ SV483 @ ( powerset @ SV545 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2974,plain,
! [SV484: $i] :
( ( ( ~ ! [SY837: $i] :
( ~ ( relation @ SY837 )
| ~ ( subset @ SV484 @ SY837 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SY837 ) ) ) )
= $false )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2975,plain,
! [SV484: $i] :
( ( ( ~ ! [SY838: $i] :
( ~ ( relation @ SY838 )
| ~ ( subset @ SV484 @ SY838 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SY838 ) ) ) )
= $false )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2976,plain,
! [SV573: $i,SV626: $i] :
( ( ~ ( ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV573 )
| ~ ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV626 ) )
| ( subset @ SV573 @ SV626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(2977,plain,
! [SV627: $i,SV574: $i] :
( ( ~ ( subset @ SV574 @ SV627 )
| ! [SY1001: $i] :
( ~ ( in @ SY1001 @ SV574 )
| ( in @ SY1001 @ SV627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(2978,plain,
! [SV485: $i,SV628: $i] :
( ( ! [SY1002: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY1002 @ SV628 @ SV485 ) @ SY1002 )
| ~ ( in @ ( sK26_D @ SY1002 @ SV628 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY1002 @ SV628 @ SV485 ) @ SY1002 )
| ~ ( in @ ( sK26_D @ SY1002 @ SV628 @ SV485 ) @ SV628 ) ) )
| ~ ( ( in @ ( sK26_D @ SY1002 @ SV628 @ SV485 ) @ SY1002 )
| ( in @ ( sK26_D @ SY1002 @ SV628 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SY1002 @ SV628 @ SV485 ) @ SV628 ) ) )
| ( SY1002
= ( set_union2 @ SV485 @ SV628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(2979,plain,
! [SV629: $i,SV485: $i] :
( ( ! [SY1003: $i] :
( ( SY1003
!= ( set_union2 @ SV485 @ SV629 ) )
| ~ ( ~ ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SY1003 )
| ( in @ SY1004 @ SV485 )
| ( in @ SY1004 @ SV629 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV485 )
| ( in @ SY844 @ SY1003 ) )
| ~ ! [SY1006: $i] :
( ~ ( in @ SY1006 @ SV629 )
| ( in @ SY1006 @ SY1003 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(2980,plain,
! [SV630: $i,SV575: $i] :
( ( ~ ( in @ SV575 @ SV630 )
| ( subset @ ( singleton @ SV575 ) @ SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(2981,plain,
! [SV631: $i,SV576: $i] :
( ( ~ ( subset @ ( singleton @ SV576 ) @ SV631 )
| ( in @ SV576 @ SV631 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(2982,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[2856]) ).
thf(2983,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)],[2856]) ).
thf(2984,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2857]) ).
thf(2985,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2857]) ).
thf(2986,plain,
! [SV577: $i,SV632: $i] :
( ( ~ ( ~ ( ! [SY1007: $i] :
( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SY1007 )
| ~ ( in @ SY1007 @ SV577 ) )
| ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) )
| ~ ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 ) )
| ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) ) )
| ( SV632
= ( union @ SV577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(2987,plain,
! [SV578: $i,SV633: $i] :
( ( ( SV633
!= ( union @ SV578 ) )
| ~ ( ~ ! [SY1008: $i] :
( ! [SY967: $i] :
( ~ ( in @ SY1008 @ SY967 )
| ~ ( in @ SY967 @ SV578 ) )
| ( in @ SY1008 @ SV633 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV633 )
| ~ ( ~ ( in @ SY1010 @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) @ SV578 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(2988,plain,
! [SV486: $i,SV634: $i] :
( ( ! [SY1011: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_D @ SY1011 @ SV634 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SY1011 @ SV634 @ SV486 ) @ SV634 )
| ~ ( in @ ( sK19_D @ SY1011 @ SV634 @ SV486 ) @ SY1011 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SY1011 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SY1011 @ SV634 @ SV486 ) @ SY1011 ) )
| ~ ( ( in @ ( sK19_D @ SY1011 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SY1011 @ SV634 @ SV486 ) @ SY1011 ) ) ) )
| ( SY1011
= ( set_intersection2 @ SV486 @ SV634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(2989,plain,
! [SV635: $i,SV486: $i] :
( ( ! [SY1012: $i] :
( ( SY1012
!= ( set_intersection2 @ SV486 @ SV635 ) )
| ~ ( ~ ! [SY1013: $i] :
( ~ ( in @ SY1013 @ SV486 )
| ~ ( in @ SY1013 @ SV635 )
| ( in @ SY1013 @ SY1012 ) )
| ~ ~ ( ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY1012 )
| ( in @ SY851 @ SV486 ) )
| ~ ! [SY1015: $i] :
( ~ ( in @ SY1015 @ SY1012 )
| ( in @ SY1015 @ SV635 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(2990,plain,
! [SV579: $i] :
( ( ( ~ ( empty @ SV579 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(2991,plain,
! [SV580: $i] :
( ( ( ~ ( empty @ SV580 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(2992,plain,
! [SV487: $i,SV636: $i] :
( ( ~ ( subset @ SV636 @ ( sK32_B @ SV487 ) )
| ( are_equipotent @ SV636 @ ( sK32_B @ SV487 ) )
| ( in @ SV636 @ ( sK32_B @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(2993,plain,
! [SV487: $i] :
( ( ~ ! [SY854: $i] :
( ~ ( in @ SY854 @ ( sK32_B @ SV487 ) )
| ( in @ ( powerset @ SY854 ) @ ( sK32_B @ SV487 ) ) )
| ~ ~ ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) )
| ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2994,plain,
! [SV581: $i] :
( ( ( ~ ( empty @ SV581 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV581 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(2995,plain,
! [SV582: $i] :
( ( ( ~ ( empty @ SV582 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(2996,plain,
! [SV583: $i,SV637: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ~ ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) )
| ~ ( ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) ) )
| ( SV637
= ( powerset @ SV583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(2997,plain,
! [SV584: $i,SV638: $i] :
( ( ( SV638
!= ( powerset @ SV584 ) )
| ~ ( ~ ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV638 )
| ( subset @ SY1016 @ SV584 ) )
| ~ ! [SY1017: $i] :
( ~ ( subset @ SY1017 @ SV584 )
| ( in @ SY1017 @ SV638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(2998,plain,
! [SV639: $i,SV585: $i] :
( ( ( disjoint @ SV585 @ SV639 )
| ~ ( ~ ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV585 )
| ~ ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(2999,plain,
! [SV640: $i,SV586: $i] :
( ( ! [SY1018: $i] :
( ~ ( in @ SY1018 @ SV586 )
| ~ ( in @ SY1018 @ SV640 ) )
| ~ ( disjoint @ SV586 @ SV640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3000,plain,
! [SV488: $i] :
( ( ( ~ ! [SY857: $i] :
( ~ ( ~ ( ! [SY858: $i] :
~ ( in @ ( ordered_pair @ SY858 @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY857 @ SV488 ) @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) ) )
| ( SY857
= ( relation_rng @ SV488 ) ) ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2873]) ).
thf(3001,plain,
! [SV488: $i] :
( ( ( ~ ! [SY859: $i] :
( ( SY859
!= ( relation_rng @ SV488 ) )
| ~ ( ~ ! [SY860: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY860 ) @ SV488 )
| ( in @ SY860 @ SY859 ) )
| ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY859 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY862 @ SY859 @ SV488 ) @ SY862 ) @ SV488 ) ) ) ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2873]) ).
thf(3002,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2874]) ).
thf(3003,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2874]) ).
thf(3004,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2875]) ).
thf(3005,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2875]) ).
thf(3006,plain,
! [SV641: $i,SV587: $i] :
( ( ~ ( in @ SV587 @ SV641 )
| ( subset @ ( singleton @ SV587 ) @ SV641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3007,plain,
! [SV642: $i,SV588: $i] :
( ( ~ ( subset @ ( singleton @ SV588 ) @ SV642 )
| ( in @ SV588 @ SV642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3008,plain,
! [SV643: $i,SV589: $i] :
( ( ~ ( subset @ SV589 @ ( singleton @ SV643 ) )
| ( SV589 = empty_set )
| ( SV589
= ( singleton @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3009,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2881]) ).
thf(3010,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2881]) ).
thf(3011,plain,
! [SV590: $i] :
( ( ( in @ ( sK42_B @ SV590 ) @ SV590 )
= $true )
| ( ( SV590 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(3012,plain,
! [SV591: $i] :
( ( ( ( SV591 != empty_set ) )
= $true )
| ( ( ! [SY979: $i] :
~ ( in @ SY979 @ SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(3013,plain,
! [SV592: $i] :
( ( ( ~ ( relation @ SV592 ) )
= $true )
| ( ( ( ( relation_dom @ SV592 )
!= empty_set )
| ( SV592 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2884]) ).
thf(3014,plain,
! [SV593: $i] :
( ( ( ~ ( relation @ SV593 ) )
= $true )
| ( ( ( ( relation_rng @ SV593 )
!= empty_set )
| ( SV593 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2885]) ).
thf(3015,plain,
! [SV594: $i] :
( ( ( ~ ( relation @ SV594 ) )
= $true )
| ( ( ( relation_rng @ SV594 )
= ( relation_dom @ ( relation_inverse @ SV594 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3016,plain,
! [SV595: $i] :
( ( ( ~ ( relation @ SV595 ) )
= $true )
| ( ( ( relation_dom @ SV595 )
= ( relation_rng @ ( relation_inverse @ SV595 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(3017,plain,
! [SV644: $i,SV596: $i] :
( ( ( ( set_difference @ SV596 @ SV644 )
!= empty_set )
| ( subset @ SV596 @ SV644 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3018,plain,
! [SV645: $i,SV597: $i] :
( ( ~ ( subset @ SV597 @ SV645 )
| ( ( set_difference @ SV597 @ SV645 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3019,plain,
! [SV490: $i,SV546: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) ) )
= $false )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(3020,plain,
! [SV490: $i,SV546: $i] :
( ( ( ~ ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) ) )
= $false )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(3021,plain,
! [SV646: $i,SV598: $i] :
( ( ~ ( element @ SV598 @ ( powerset @ SV646 ) )
| ( subset @ SV598 @ SV646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3022,plain,
! [SV647: $i,SV599: $i] :
( ( ~ ( subset @ SV599 @ SV647 )
| ( element @ SV599 @ ( powerset @ SV647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3023,plain,
! [SV600: $i] :
( ( ( ~ ( ~ ! [SY984: $i,SY985: $i] :
( ( sK48_B @ SV600 )
!= ( ordered_pair @ SY984 @ SY985 ) )
| ~ ( in @ ( sK48_B @ SV600 ) @ SV600 ) ) )
= $true )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2893]) ).
thf(3024,plain,
! [SV601: $i] :
( ( ( ~ ( relation @ SV601 ) )
= $true )
| ( ( ! [SY986: $i] :
( ( SY986
= ( ordered_pair @ ( sK46_C @ SY986 @ SV601 ) @ ( sK47_SY329 @ SY986 @ SV601 ) ) )
| ~ ( in @ SY986 @ SV601 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(3025,plain,
! [SV648: $i,SV491: $i] :
( ( ! [SY1019: $i] :
( ~ ( in @ SV491 @ SY1019 )
| ~ ( in @ SV648 @ SY1019 )
| ( subset @ ( unordered_pair @ SV491 @ SV648 ) @ SY1019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3026,plain,
! [SV491: $i] :
( ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY866 ) @ SY867 )
| ( in @ SV491 @ SY867 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY868 ) @ SY869 )
| ( in @ SY868 @ SY869 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(3027,plain,
! [SV492: $i,SV649: $i] :
( ( ! [SY1020: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY1020 @ SV649 @ SV492 ) @ SY1020 )
| ( ( sK27_D @ SY1020 @ SV649 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY1020 @ SV649 @ SV492 ) @ SY1020 )
| ( ( sK27_D @ SY1020 @ SV649 @ SV492 )
!= SV649 ) ) )
| ~ ( ( in @ ( sK27_D @ SY1020 @ SV649 @ SV492 ) @ SY1020 )
| ( ( sK27_D @ SY1020 @ SV649 @ SV492 )
= SV492 )
| ( ( sK27_D @ SY1020 @ SV649 @ SV492 )
= SV649 ) ) )
| ( SY1020
= ( unordered_pair @ SV492 @ SV649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3028,plain,
! [SV650: $i,SV492: $i] :
( ( ! [SY1021: $i] :
( ( SY1021
!= ( unordered_pair @ SV492 @ SV650 ) )
| ~ ( ~ ! [SY1022: $i] :
( ~ ( in @ SY1022 @ SY1021 )
| ( SY1022 = SV492 )
| ( SY1022 = SV650 ) )
| ~ ~ ( ~ ! [SY875: $i] :
( ( SY875 != SV492 )
| ( in @ SY875 @ SY1021 ) )
| ~ ! [SY1024: $i] :
( ( SY1024 != SV650 )
| ( in @ SY1024 @ SY1021 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3029,plain,
! [SV547: $i,SV493: $i] :
( ( ! [SY935: $i,SY936: $i] :
( ~ ( in @ SV493 @ SY935 )
| ~ ( in @ SV547 @ SY936 )
| ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY935 @ SY936 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2899]) ).
thf(3030,plain,
! [SV547: $i,SV493: $i] :
( ( ~ ( ~ ! [SY937: $i] :
( ! [SY938: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY937 @ SY938 ) )
| ( in @ SV493 @ SY937 ) )
| ~ ! [SY939: $i,SY940: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY939 @ SY940 ) )
| ( in @ SV547 @ SY940 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2900]) ).
thf(3031,plain,
! [SV651: $i,SV494: $i] :
( ( ! [SY1025: $i] :
( ~ ( relation @ SY1025 )
| ~ ( in @ ( ordered_pair @ SV494 @ SV651 ) @ SY1025 )
| ( in @ SV494 @ ( relation_dom @ SY1025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3032,plain,
! [SV652: $i,SV494: $i] :
( ( ! [SY1026: $i] :
( ~ ( relation @ SY1026 )
| ~ ( in @ ( ordered_pair @ SV494 @ SV652 ) @ SY1026 )
| ( in @ SV652 @ ( relation_rng @ SY1026 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3033,plain,
! [SV653: $i,SV602: $i] :
( ( ( disjoint @ SV602 @ SV653 )
| ( in @ ( sK30_C @ SV653 @ SV602 ) @ ( set_intersection2 @ SV602 @ SV653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3034,plain,
! [SV654: $i,SV603: $i] :
( ( ! [SY1027: $i] :
~ ( in @ SY1027 @ ( set_intersection2 @ SV603 @ SV654 ) )
| ~ ( disjoint @ SV603 @ SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3035,plain,
! [SV604: $i,SV655: $i] :
( ( ~ ( ~ ( ( ( sK29_C @ SV655 @ SV604 )
!= SV604 )
| ~ ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) )
| ~ ( ( ( sK29_C @ SV655 @ SV604 )
= SV604 )
| ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) ) )
| ( SV655
= ( singleton @ SV604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3036,plain,
! [SV605: $i,SV656: $i] :
( ( ( SV656
!= ( singleton @ SV605 ) )
| ~ ( ~ ! [SY1028: $i] :
( ( SY1028 != SV605 )
| ( in @ SY1028 @ SV656 ) )
| ~ ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV656 )
| ( SY1029 = SV605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3037,plain,
! [SV657: $i,SV606: $i] :
( ( ( SV606 = SV657 )
| ~ ( subset @ SV606 @ SV657 )
| ( proper_subset @ SV606 @ SV657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3038,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(3039,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(3040,plain,
! [SV658: $i,SV495: $i] :
( ( ! [SY1030: $i] :
( ~ ( ~ ( ! [SY1031: $i,SY1032: $i] :
( ~ ( in @ SY1031 @ SV495 )
| ~ ( in @ SY1032 @ SV658 )
| ( ( sK23_D @ SY1030 @ SV658 @ SV495 )
!= ( ordered_pair @ SY1031 @ SY1032 ) ) )
| ~ ( in @ ( sK23_D @ SY1030 @ SV658 @ SV495 ) @ SY1030 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SY1030 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SY1030 @ SV658 @ SV495 ) @ SV658 ) )
| ( ( sK23_D @ SY1030 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SY1030 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SY1030 @ SV658 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SY1030 @ SV658 @ SV495 ) @ SY1030 ) ) )
| ( SY1030
= ( cartesian_product2 @ SV495 @ SV658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3041,plain,
! [SV659: $i,SV495: $i] :
( ( ! [SY1033: $i] :
( ( SY1033
!= ( cartesian_product2 @ SV495 @ SV659 ) )
| ~ ( ~ ! [SY1034: $i] :
( ! [SY1035: $i,SY1036: $i] :
( ~ ( in @ SY1035 @ SV495 )
| ~ ( in @ SY1036 @ SV659 )
| ( SY1034
!= ( ordered_pair @ SY1035 @ SY1036 ) ) )
| ( in @ SY1034 @ SY1033 ) )
| ~ ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SY1033 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1037 @ SY1033 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY1037 @ SY1033 @ SV659 @ SV495 ) @ SV659 ) )
| ( SY1037
!= ( ordered_pair @ ( sK21_E @ SY1037 @ SY1033 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SY1037 @ SY1033 @ SV659 @ SV495 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3042,plain,
! [SV496: $i] :
( ( ( element @ ( sK8_B @ SV496 ) @ ( powerset @ SV496 ) )
= $true )
| ( ( empty @ SV496 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2912]) ).
thf(3043,plain,
! [SV496: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV496 ) ) )
= $true )
| ( ( empty @ SV496 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2913]) ).
thf(3044,plain,
! [SV660: $i,SV607: $i] :
( ( ( ( set_difference @ SV607 @ SV660 )
!= SV607 )
| ( disjoint @ SV607 @ SV660 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3045,plain,
! [SV661: $i,SV608: $i] :
( ( ~ ( disjoint @ SV608 @ SV661 )
| ( ( set_difference @ SV608 @ SV661 )
= SV608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3046,plain,
! [SV497: $i,SV662: $i] :
( ( ! [SY1038: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY1038 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY1038 @ SV662 @ SV497 ) @ SV662 )
| ~ ( in @ ( sK15_D @ SY1038 @ SV662 @ SV497 ) @ SY1038 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY1038 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SY1038 @ SV662 @ SV497 ) @ SY1038 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY1038 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SY1038 @ SV662 @ SV497 ) @ SY1038 ) ) ) )
| ( SY1038
= ( set_difference @ SV497 @ SV662 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3047,plain,
! [SV663: $i,SV497: $i] :
( ( ! [SY1039: $i] :
( ( SY1039
!= ( set_difference @ SV497 @ SV663 ) )
| ~ ( ~ ! [SY1040: $i] :
( ~ ( in @ SY1040 @ SV497 )
| ( in @ SY1040 @ SV663 )
| ( in @ SY1040 @ SY1039 ) )
| ~ ~ ( ~ ! [SY903: $i] :
( ~ ( in @ SY903 @ SY1039 )
| ( in @ SY903 @ SV497 ) )
| ~ ! [SY1042: $i] :
( ~ ( in @ SY1042 @ SY1039 )
| ~ ( in @ SY1042 @ SV663 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3048,plain,
! [SV498: $i] :
( ( ( ~ ! [SY905: $i] :
( ~ ( ~ ( ! [SY906: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ SY906 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ ( sK41_SY326 @ SY905 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) ) )
| ( SY905
= ( relation_dom @ SV498 ) ) ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2918]) ).
thf(3049,plain,
! [SV498: $i] :
( ( ( ~ ! [SY907: $i] :
( ( SY907
!= ( relation_dom @ SV498 ) )
| ~ ( ~ ! [SY908: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY908 @ SY909 ) @ SV498 )
| ( in @ SY908 @ SY907 ) )
| ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SY907 )
| ( in @ ( ordered_pair @ SY910 @ ( sK39_D @ SY910 @ SY907 @ SV498 ) ) @ SV498 ) ) ) ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2918]) ).
thf(3050,plain,
! [SV407: $i,SV558: $i] :
( ( ( relation @ SV558 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV407 @ SV558 ) ) @ ( relation_dom @ SV407 ) )
= $true )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3051,plain,
! [SV408: $i,SV559: $i] :
( ( ( relation @ SV559 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV408 @ SV559 ) ) @ ( relation_rng @ SV559 ) )
= $true )
| ( ( relation @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(3052,plain,
! [SV409: $i,SV560: $i] :
( ( ( relation @ SV560 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV409 ) @ ( relation_dom @ SV560 ) )
| ( ( relation_dom @ ( relation_composition @ SV409 @ SV560 ) )
= ( relation_dom @ SV409 ) ) )
= $true )
| ( ( relation @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(3053,plain,
! [SV410: $i,SV561: $i] :
( ( ( relation @ SV561 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV410 ) @ ( relation_rng @ SV561 ) )
| ( ( relation_rng @ ( relation_composition @ SV561 @ SV410 ) )
= ( relation_rng @ SV410 ) ) )
= $true )
| ( ( relation @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(3054,plain,
! [SV415: $i,SV499: $i] :
( ( ( relation @ SV499 )
= $false )
| ( ( relation @ SV415 )
= $false )
| ( ( relation @ ( relation_composition @ SV415 @ SV499 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(3055,plain,
! [SV416: $i,SV500: $i] :
( ( ( relation @ SV500 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( relation @ ( set_union2 @ SV416 @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(3056,plain,
! [SV428: $i,SV504: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV504 ) )
= $true )
| ( ( in @ SV609 @ SV428 )
= $true )
| ( ( element @ SV504 @ ( powerset @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2928]) ).
thf(3057,plain,
! [SV505: $i,SV429: $i,SV610: $i] :
( ( ( in @ SV610 @ SV429 )
= $true )
| ( ( subset @ SV429 @ ( set_difference @ SV505 @ ( singleton @ SV610 ) ) )
= $true )
| ( ( subset @ SV429 @ SV505 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2929]) ).
thf(3058,plain,
! [SV562: $i,SV548: $i,SV507: $i,SV431: $i] :
( ( ( ~ ( subset @ SV431 @ SV507 ) )
= $true )
| ( ( ~ ( subset @ SV548 @ SV562 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV431 @ SV548 ) @ ( cartesian_product2 @ SV507 @ SV562 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2930]) ).
thf(3059,plain,
! [SV549: $i,SV510: $i,SV434: $i] :
( ( ( subset @ SV434 @ SV510 )
= $false )
| ( ( ~ ( subset @ SV434 @ SV549 ) )
= $true )
| ( ( subset @ SV434 @ ( set_intersection2 @ SV510 @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2931]) ).
thf(3060,plain,
! [SV550: $i,SV511: $i,SV435: $i] :
( ( ( subset @ SV435 @ SV511 )
= $false )
| ( ( ~ ( subset @ SV511 @ SV550 ) )
= $true )
| ( ( subset @ SV435 @ SV550 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(3061,plain,
! [SV446: $i,SV551: $i,SV522: $i] :
( ( ( disjoint @ SV522 @ SV551 )
= $false )
| ( ( ~ ( subset @ SV446 @ SV522 ) )
= $true )
| ( ( disjoint @ SV446 @ SV551 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3062,plain,
! [SV552: $i,SV525: $i,SV450: $i] :
( ( ( subset @ SV450 @ SV525 )
= $false )
| ( ( ~ ( subset @ SV552 @ SV525 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV450 @ SV552 ) @ SV525 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3063,plain,
! [SV472: $i,SV556: $i,SV539: $i] :
( ( ( element @ SV539 @ ( powerset @ SV556 ) )
= $false )
| ( ( ~ ( in @ SV472 @ SV539 ) )
= $true )
| ( ( element @ SV472 @ SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3064,plain,
! [SV473: $i,SV557: $i,SV540: $i] :
( ( ( element @ SV540 @ ( powerset @ SV557 ) )
= $false )
| ( ( ~ ( in @ SV473 @ SV540 ) )
= $true )
| ( ( ~ ( empty @ SV557 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3065,plain,
! [SV475: $i,SV542: $i] :
( ( ( empty @ SV542 )
= $false )
| ( ( SV475 = SV542 )
= $true )
| ( ( empty @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3066,plain,
! [SV613: $i,SV476: $i,SV664: $i] :
( ( ~ ( relation @ SV664 )
| ~ ( in @ ( ordered_pair @ SV476 @ SV613 ) @ SV664 )
| ( in @ SV476 @ ( relation_field @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3067,plain,
! [SV614: $i,SV476: $i,SV665: $i] :
( ( ~ ( relation @ SV665 )
| ~ ( in @ ( ordered_pair @ SV476 @ SV614 ) @ SV665 )
| ( in @ SV614 @ ( relation_field @ SV665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3068,plain,
! [SV477: $i,SV564: $i] :
( ( ( relation @ SV564 )
= $false )
| ( ( ~ ( ~ ! [SY942: $i] :
( ~ ( relation @ SY942 )
| ~ ( ~ ( ! [SY943: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ SY943 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY943 @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) ) )
| ( SY942
= ( relation_composition @ SV477 @ SV564 ) ) )
| ~ ! [SY944: $i] :
( ~ ( relation @ SY944 )
| ( SY944
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY945: $i,SY946: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY945 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY946 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY945 @ SY946 ) @ SY944 ) )
| ~ ! [SY948: $i,SY949: $i] :
( ~ ( in @ ( ordered_pair @ SY948 @ SY949 ) @ SY944 )
| ~ ( ~ ( in @ ( ordered_pair @ SY948 @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) @ SY949 ) @ SV564 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3069,plain,
! [SV478: $i,SV615: $i] :
( ( ( ~ ( subset @ SV615 @ ( sK2_B @ SV478 ) )
| ( are_equipotent @ SV615 @ ( sK2_B @ SV478 ) ) )
= $true )
| ( ( in @ SV615 @ ( sK2_B @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3070,plain,
! [SV478: $i] :
( ( ~ ! [SY810: $i] :
( ~ ( ~ ! [SY811: $i] :
( ~ ( subset @ SY811 @ SY810 )
| ( in @ SY811 @ ( sK3_SY300 @ SY810 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY810 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SY810 @ ( sK2_B @ SV478 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2951]) ).
thf(3071,plain,
! [SV478: $i] :
( ( ~ ~ ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2951]) ).
thf(3072,plain,
! [SV616: $i,SV479: $i] :
( ( ( ~ ( subset @ SV479 @ SV616 ) )
= $true )
| ( ( ! [SY999: $i] : ( subset @ ( cartesian_product2 @ SV479 @ SY999 ) @ ( cartesian_product2 @ SV616 @ SY999 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2952]) ).
thf(3073,plain,
! [SV617: $i,SV479: $i] :
( ( ( ~ ( subset @ SV479 @ SV617 ) )
= $true )
| ( ( ! [SY1000: $i] : ( subset @ ( cartesian_product2 @ SY1000 @ SV479 ) @ ( cartesian_product2 @ SY1000 @ SV617 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3074,plain,
! [SV618: $i,SV565: $i] :
( ( ( ~ ( subset @ SV565 @ ( singleton @ SV618 ) ) )
= $true )
| ( ( ( SV565 = empty_set )
| ( SV565
= ( singleton @ SV618 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2954]) ).
thf(3075,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2955]) ).
thf(3076,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2956]) ).
thf(3077,plain,
! [SV666: $i,SV543: $i,SV480: $i] :
( ( ! [SY1043: $i] :
( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SV666 @ SY1043 ) )
| ( SV480 = SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3078,plain,
! [SV667: $i,SV543: $i,SV480: $i] :
( ( ! [SY1044: $i] :
( ( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SV667 @ SY1044 ) )
| ( SV543 = SY1044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3079,plain,
! [SV619: $i,SV566: $i] :
( ( ( ( ( set_difference @ SV566 @ SV619 )
!= empty_set ) )
= $true )
| ( ( subset @ SV566 @ SV619 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3080,plain,
! [SV620: $i,SV567: $i] :
( ( ( ~ ( subset @ SV567 @ SV620 ) )
= $true )
| ( ( ( set_difference @ SV567 @ SV620 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2960]) ).
thf(3081,plain,
! [SV481: $i] :
( ( ( ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY823 @ SV481 ) @ ( sK14_SY310 @ SY823 @ SV481 ) ) @ SY823 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SY823 @ SV481 ) @ ( sK13_C @ SY823 @ SV481 ) ) @ SV481 ) ) )
| ( SY823
= ( relation_inverse @ SV481 ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2961]) ).
thf(3082,plain,
! [SV481: $i] :
( ( ( ! [SY824: $i] :
( ~ ( relation @ SY824 )
| ( SY824
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY825: $i,SY826: $i] :
( ~ ( in @ ( ordered_pair @ SY825 @ SY826 ) @ SY824 )
| ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV481 ) )
| ~ ! [SY827: $i,SY828: $i] :
( ~ ( in @ ( ordered_pair @ SY828 @ SY827 ) @ SV481 )
| ( in @ ( ordered_pair @ SY827 @ SY828 ) @ SY824 ) ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2962]) ).
thf(3083,plain,
! [SV544: $i,SV668: $i,SV482: $i] :
( ( ! [SY1045: $i] :
( ~ ( in @ SV482 @ SV668 )
| ~ ( in @ SV544 @ SY1045 )
| ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV668 @ SY1045 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3084,plain,
! [SV544: $i,SV482: $i] :
( ( ~ ! [SY931: $i] :
( ! [SY932: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY931 @ SY932 ) )
| ( in @ SV482 @ SY931 ) )
| ~ ! [SY933: $i,SY934: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY933 @ SY934 ) )
| ( in @ SV544 @ SY934 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3085,plain,
! [SV621: $i,SV568: $i] :
( ( ( ( ( set_intersection2 @ SV568 @ SV621 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV568 @ SV621 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2965]) ).
thf(3086,plain,
! [SV622: $i,SV569: $i] :
( ( ( ~ ( disjoint @ SV569 @ SV622 ) )
= $true )
| ( ( ( set_intersection2 @ SV569 @ SV622 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3087,plain,
! [SV623: $i,SV570: $i] :
( ( ( ~ ( subset @ SV570 @ SV623 )
| ~ ( subset @ SV623 @ SV570 ) )
= $true )
| ( ( SV570 = SV623 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3088,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2968]) ).
thf(3089,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2969]) ).
thf(3090,plain,
! [SV624: $i,SV571: $i] :
( ( ( ( ( set_difference @ SV571 @ ( singleton @ SV624 ) )
!= SV571 ) )
= $true )
| ( ( ~ ( in @ SV624 @ SV571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2970]) ).
thf(3091,plain,
! [SV572: $i,SV625: $i] :
( ( ( in @ SV625 @ SV572 )
= $true )
| ( ( ( set_difference @ SV572 @ ( singleton @ SV625 ) )
= SV572 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2971]) ).
thf(3092,plain,
! [SV483: $i,SV545: $i] :
( ( ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV483 )
= $true )
| ( ( element @ SV483 @ ( powerset @ SV545 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2972]) ).
thf(3093,plain,
! [SV483: $i,SV545: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV545 ) )
= $true )
| ( ( element @ SV483 @ ( powerset @ SV545 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2973]) ).
thf(3094,plain,
! [SV484: $i] :
( ( ( ! [SY837: $i] :
( ~ ( relation @ SY837 )
| ~ ( subset @ SV484 @ SY837 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SY837 ) ) ) )
= $true )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2974]) ).
thf(3095,plain,
! [SV484: $i] :
( ( ( ! [SY838: $i] :
( ~ ( relation @ SY838 )
| ~ ( subset @ SV484 @ SY838 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SY838 ) ) ) )
= $true )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2975]) ).
thf(3096,plain,
! [SV573: $i,SV626: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV573 )
| ~ ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV626 ) ) )
= $true )
| ( ( subset @ SV573 @ SV626 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3097,plain,
! [SV627: $i,SV574: $i] :
( ( ( ~ ( subset @ SV574 @ SV627 ) )
= $true )
| ( ( ! [SY1001: $i] :
( ~ ( in @ SY1001 @ SV574 )
| ( in @ SY1001 @ SV627 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(3098,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) )
| ~ ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) )
| ( SV669
= ( set_union2 @ SV485 @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3099,plain,
! [SV629: $i,SV485: $i,SV670: $i] :
( ( ( SV670
!= ( set_union2 @ SV485 @ SV629 ) )
| ~ ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV670 )
| ( in @ SY1046 @ SV485 )
| ( in @ SY1046 @ SV629 ) )
| ~ ~ ( ~ ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) )
| ~ ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3100,plain,
! [SV630: $i,SV575: $i] :
( ( ( ~ ( in @ SV575 @ SV630 ) )
= $true )
| ( ( subset @ ( singleton @ SV575 ) @ SV630 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3101,plain,
! [SV631: $i,SV576: $i] :
( ( ( ~ ( subset @ ( singleton @ SV576 ) @ SV631 ) )
= $true )
| ( ( in @ SV576 @ SV631 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2981]) ).
thf(3102,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY327 @ 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)],[2982]) ).
thf(3103,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)],[2983]) ).
thf(3104,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2984]) ).
thf(3105,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2985]) ).
thf(3106,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( ~ ( ! [SY1007: $i] :
( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SY1007 )
| ~ ( in @ SY1007 @ SV577 ) )
| ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) )
| ~ ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 ) )
| ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) ) ) )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2986]) ).
thf(3107,plain,
! [SV578: $i,SV633: $i] :
( ( ( ( SV633
!= ( union @ SV578 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1008: $i] :
( ! [SY967: $i] :
( ~ ( in @ SY1008 @ SY967 )
| ~ ( in @ SY967 @ SV578 ) )
| ( in @ SY1008 @ SV633 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV633 )
| ~ ( ~ ( in @ SY1010 @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) @ SV578 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2987]) ).
thf(3108,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) ) )
| ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3109,plain,
! [SV635: $i,SV486: $i,SV672: $i] :
( ( ( SV672
!= ( set_intersection2 @ SV486 @ SV635 ) )
| ~ ( ~ ! [SY1049: $i] :
( ~ ( in @ SY1049 @ SV486 )
| ~ ( in @ SY1049 @ SV635 )
| ( in @ SY1049 @ SV672 ) )
| ~ ~ ( ~ ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) )
| ~ ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3110,plain,
! [SV579: $i] :
( ( ( empty @ SV579 )
= $false )
| ( ( empty @ ( relation_dom @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3111,plain,
! [SV580: $i] :
( ( ( empty @ SV580 )
= $false )
| ( ( relation @ ( relation_dom @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3112,plain,
! [SV487: $i,SV636: $i] :
( ( ( ~ ( subset @ SV636 @ ( sK32_B @ SV487 ) )
| ( are_equipotent @ SV636 @ ( sK32_B @ SV487 ) ) )
= $true )
| ( ( in @ SV636 @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3113,plain,
! [SV487: $i] :
( ( ~ ! [SY854: $i] :
( ~ ( in @ SY854 @ ( sK32_B @ SV487 ) )
| ( in @ ( powerset @ SY854 ) @ ( sK32_B @ SV487 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2993]) ).
thf(3114,plain,
! [SV487: $i] :
( ( ~ ~ ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) )
| ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2993]) ).
thf(3115,plain,
! [SV581: $i] :
( ( ( empty @ SV581 )
= $false )
| ( ( empty @ ( relation_rng @ SV581 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3116,plain,
! [SV582: $i] :
( ( ( empty @ SV582 )
= $false )
| ( ( relation @ ( relation_rng @ SV582 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3117,plain,
! [SV583: $i,SV637: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ~ ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) )
| ~ ( ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) ) ) )
= $true )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3118,plain,
! [SV584: $i,SV638: $i] :
( ( ( ( SV638
!= ( powerset @ SV584 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV638 )
| ( subset @ SY1016 @ SV584 ) )
| ~ ! [SY1017: $i] :
( ~ ( subset @ SY1017 @ SV584 )
| ( in @ SY1017 @ SV638 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3119,plain,
! [SV639: $i,SV585: $i] :
( ( ( disjoint @ SV585 @ SV639 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV585 )
| ~ ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV639 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2998]) ).
thf(3120,plain,
! [SV640: $i,SV586: $i] :
( ( ( ! [SY1018: $i] :
( ~ ( in @ SY1018 @ SV586 )
| ~ ( in @ SY1018 @ SV640 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV586 @ SV640 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2999]) ).
thf(3121,plain,
! [SV488: $i] :
( ( ( ! [SY857: $i] :
( ~ ( ~ ( ! [SY858: $i] :
~ ( in @ ( ordered_pair @ SY858 @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SY857 @ SV488 ) @ ( sK37_C @ SY857 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SY857 @ SV488 ) @ SY857 ) ) )
| ( SY857
= ( relation_rng @ SV488 ) ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3000]) ).
thf(3122,plain,
! [SV488: $i] :
( ( ( ! [SY859: $i] :
( ( SY859
!= ( relation_rng @ SV488 ) )
| ~ ( ~ ! [SY860: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY860 ) @ SV488 )
| ( in @ SY860 @ SY859 ) )
| ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY859 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY862 @ SY859 @ SV488 ) @ SY862 ) @ SV488 ) ) ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3001]) ).
thf(3123,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3124,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3003]) ).
thf(3125,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3004]) ).
thf(3126,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3127,plain,
! [SV641: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV641 ) )
= $true )
| ( ( subset @ ( singleton @ SV587 ) @ SV641 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3128,plain,
! [SV642: $i,SV588: $i] :
( ( ( ~ ( subset @ ( singleton @ SV588 ) @ SV642 ) )
= $true )
| ( ( in @ SV588 @ SV642 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3129,plain,
! [SV643: $i,SV589: $i] :
( ( ( ~ ( subset @ SV589 @ ( singleton @ SV643 ) ) )
= $true )
| ( ( ( SV589 = empty_set )
| ( SV589
= ( singleton @ SV643 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3130,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3009]) ).
thf(3131,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3010]) ).
thf(3132,plain,
! [SV591: $i] :
( ( ( SV591 = empty_set )
= $false )
| ( ( ! [SY979: $i] :
~ ( in @ SY979 @ SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3133,plain,
! [SV592: $i] :
( ( ( relation @ SV592 )
= $false )
| ( ( ( ( relation_dom @ SV592 )
!= empty_set )
| ( SV592 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3134,plain,
! [SV593: $i] :
( ( ( relation @ SV593 )
= $false )
| ( ( ( ( relation_rng @ SV593 )
!= empty_set )
| ( SV593 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3135,plain,
! [SV594: $i] :
( ( ( relation @ SV594 )
= $false )
| ( ( ( relation_rng @ SV594 )
= ( relation_dom @ ( relation_inverse @ SV594 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3136,plain,
! [SV595: $i] :
( ( ( relation @ SV595 )
= $false )
| ( ( ( relation_dom @ SV595 )
= ( relation_rng @ ( relation_inverse @ SV595 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3137,plain,
! [SV644: $i,SV596: $i] :
( ( ( ( ( set_difference @ SV596 @ SV644 )
!= empty_set ) )
= $true )
| ( ( subset @ SV596 @ SV644 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3138,plain,
! [SV645: $i,SV597: $i] :
( ( ( ~ ( subset @ SV597 @ SV645 ) )
= $true )
| ( ( ( set_difference @ SV597 @ SV645 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3139,plain,
! [SV490: $i,SV546: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) )
= $true )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3140,plain,
! [SV490: $i,SV546: $i] :
( ( ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
| ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) )
= $true )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3020]) ).
thf(3141,plain,
! [SV646: $i,SV598: $i] :
( ( ( ~ ( element @ SV598 @ ( powerset @ SV646 ) ) )
= $true )
| ( ( subset @ SV598 @ SV646 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3021]) ).
thf(3142,plain,
! [SV647: $i,SV599: $i] :
( ( ( ~ ( subset @ SV599 @ SV647 ) )
= $true )
| ( ( element @ SV599 @ ( powerset @ SV647 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3022]) ).
thf(3143,plain,
! [SV600: $i] :
( ( ( ~ ! [SY984: $i,SY985: $i] :
( ( sK48_B @ SV600 )
!= ( ordered_pair @ SY984 @ SY985 ) )
| ~ ( in @ ( sK48_B @ SV600 ) @ SV600 ) )
= $false )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3144,plain,
! [SV601: $i] :
( ( ( relation @ SV601 )
= $false )
| ( ( ! [SY986: $i] :
( ( SY986
= ( ordered_pair @ ( sK46_C @ SY986 @ SV601 ) @ ( sK47_SY329 @ SY986 @ SV601 ) ) )
| ~ ( in @ SY986 @ SV601 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3145,plain,
! [SV648: $i,SV673: $i,SV491: $i] :
( ( ~ ( in @ SV491 @ SV673 )
| ~ ( in @ SV648 @ SV673 )
| ( subset @ ( unordered_pair @ SV491 @ SV648 ) @ SV673 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3146,plain,
! [SV491: $i] :
( ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY866 ) @ SY867 )
| ( in @ SV491 @ SY867 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3147,plain,
! [SV491: $i] :
( ( ~ ! [SY868: $i,SY869: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY868 ) @ SY869 )
| ( in @ SY868 @ SY869 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3148,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) ) )
| ~ ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV492 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV649 ) ) )
| ( SV674
= ( unordered_pair @ SV492 @ SV649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3149,plain,
! [SV650: $i,SV492: $i,SV675: $i] :
( ( ( SV675
!= ( unordered_pair @ SV492 @ SV650 ) )
| ~ ( ~ ! [SY1052: $i] :
( ~ ( in @ SY1052 @ SV675 )
| ( SY1052 = SV492 )
| ( SY1052 = SV650 ) )
| ~ ~ ( ~ ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) )
| ~ ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3150,plain,
! [SV547: $i,SV676: $i,SV493: $i] :
( ( ! [SY1055: $i] :
( ~ ( in @ SV493 @ SV676 )
| ~ ( in @ SV547 @ SY1055 )
| ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV676 @ SY1055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3151,plain,
! [SV547: $i,SV493: $i] :
( ( ~ ! [SY937: $i] :
( ! [SY938: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY937 @ SY938 ) )
| ( in @ SV493 @ SY937 ) )
| ~ ! [SY939: $i,SY940: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY939 @ SY940 ) )
| ( in @ SV547 @ SY940 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3030]) ).
thf(3152,plain,
! [SV651: $i,SV494: $i,SV677: $i] :
( ( ~ ( relation @ SV677 )
| ~ ( in @ ( ordered_pair @ SV494 @ SV651 ) @ SV677 )
| ( in @ SV494 @ ( relation_dom @ SV677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3153,plain,
! [SV652: $i,SV494: $i,SV678: $i] :
( ( ~ ( relation @ SV678 )
| ~ ( in @ ( ordered_pair @ SV494 @ SV652 ) @ SV678 )
| ( in @ SV652 @ ( relation_rng @ SV678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3154,plain,
! [SV653: $i,SV602: $i] :
( ( ( disjoint @ SV602 @ SV653 )
= $true )
| ( ( in @ ( sK30_C @ SV653 @ SV602 ) @ ( set_intersection2 @ SV602 @ SV653 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3033]) ).
thf(3155,plain,
! [SV654: $i,SV603: $i] :
( ( ( ! [SY1027: $i] :
~ ( in @ SY1027 @ ( set_intersection2 @ SV603 @ SV654 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV603 @ SV654 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3034]) ).
thf(3156,plain,
! [SV604: $i,SV655: $i] :
( ( ( ~ ( ~ ( ( ( sK29_C @ SV655 @ SV604 )
!= SV604 )
| ~ ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) )
| ~ ( ( ( sK29_C @ SV655 @ SV604 )
= SV604 )
| ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) ) ) )
= $true )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3157,plain,
! [SV605: $i,SV656: $i] :
( ( ( ( SV656
!= ( singleton @ SV605 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1028: $i] :
( ( SY1028 != SV605 )
| ( in @ SY1028 @ SV656 ) )
| ~ ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV656 )
| ( SY1029 = SV605 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3158,plain,
! [SV657: $i,SV606: $i] :
( ( ( ( SV606 = SV657 )
| ~ ( subset @ SV606 @ SV657 ) )
= $true )
| ( ( proper_subset @ SV606 @ SV657 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3159,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3038]) ).
thf(3160,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3161,plain,
! [SV679: $i,SV658: $i,SV495: $i] :
( ( ~ ( ~ ( ! [SY1056: $i,SY1057: $i] :
( ~ ( in @ SY1056 @ SV495 )
| ~ ( in @ SY1057 @ SV658 )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SY1056 @ SY1057 ) ) )
| ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) ) )
| ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3162,plain,
! [SV659: $i,SV495: $i,SV680: $i] :
( ( ( SV680
!= ( cartesian_product2 @ SV495 @ SV659 ) )
| ~ ( ~ ! [SY1058: $i] :
( ! [SY1035: $i,SY1036: $i] :
( ~ ( in @ SY1035 @ SV495 )
| ~ ( in @ SY1036 @ SV659 )
| ( SY1058
!= ( ordered_pair @ SY1035 @ SY1036 ) ) )
| ( in @ SY1058 @ SV680 ) )
| ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV680 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SY1061
!= ( ordered_pair @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3163,plain,
! [SV496: $i] :
( ( ( empty @ ( sK8_B @ SV496 ) )
= $false )
| ( ( empty @ SV496 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3164,plain,
! [SV660: $i,SV607: $i] :
( ( ( ( ( set_difference @ SV607 @ SV660 )
!= SV607 ) )
= $true )
| ( ( disjoint @ SV607 @ SV660 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3165,plain,
! [SV661: $i,SV608: $i] :
( ( ( ~ ( disjoint @ SV608 @ SV661 ) )
= $true )
| ( ( ( set_difference @ SV608 @ SV661 )
= SV608 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3045]) ).
thf(3166,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) ) )
| ( SV681
= ( set_difference @ SV497 @ SV662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3167,plain,
! [SV663: $i,SV497: $i,SV682: $i] :
( ( ( SV682
!= ( set_difference @ SV497 @ SV663 ) )
| ~ ( ~ ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV497 )
| ( in @ SY1062 @ SV663 )
| ( in @ SY1062 @ SV682 ) )
| ~ ~ ( ~ ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) )
| ~ ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3168,plain,
! [SV498: $i] :
( ( ( ! [SY905: $i] :
( ~ ( ~ ( ! [SY906: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ SY906 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY905 @ SV498 ) @ ( sK41_SY326 @ SY905 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SY905 @ SV498 ) @ SY905 ) ) )
| ( SY905
= ( relation_dom @ SV498 ) ) ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3048]) ).
thf(3169,plain,
! [SV498: $i] :
( ( ( ! [SY907: $i] :
( ( SY907
!= ( relation_dom @ SV498 ) )
| ~ ( ~ ! [SY908: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY908 @ SY909 ) @ SV498 )
| ( in @ SY908 @ SY907 ) )
| ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SY907 )
| ( in @ ( ordered_pair @ SY910 @ ( sK39_D @ SY910 @ SY907 @ SV498 ) ) @ SV498 ) ) ) ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3049]) ).
thf(3170,plain,
! [SV560: $i,SV409: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV409 ) @ ( relation_dom @ SV560 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV409 @ SV560 ) )
= ( relation_dom @ SV409 ) )
= $true )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV409 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3052]) ).
thf(3171,plain,
! [SV561: $i,SV410: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV410 ) @ ( relation_rng @ SV561 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV561 @ SV410 ) )
= ( relation_rng @ SV410 ) )
= $true )
| ( ( relation @ SV561 )
= $false )
| ( ( relation @ SV410 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3053]) ).
thf(3172,plain,
! [SV428: $i,SV504: $i,SV609: $i] :
( ( ( in @ SV609 @ SV504 )
= $false )
| ( ( in @ SV609 @ SV428 )
= $true )
| ( ( element @ SV504 @ ( powerset @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3173,plain,
! [SV562: $i,SV548: $i,SV507: $i,SV431: $i] :
( ( ( subset @ SV431 @ SV507 )
= $false )
| ( ( ~ ( subset @ SV548 @ SV562 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV431 @ SV548 ) @ ( cartesian_product2 @ SV507 @ SV562 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3174,plain,
! [SV510: $i,SV549: $i,SV434: $i] :
( ( ( subset @ SV434 @ SV549 )
= $false )
| ( ( subset @ SV434 @ SV510 )
= $false )
| ( ( subset @ SV434 @ ( set_intersection2 @ SV510 @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3175,plain,
! [SV435: $i,SV550: $i,SV511: $i] :
( ( ( subset @ SV511 @ SV550 )
= $false )
| ( ( subset @ SV435 @ SV511 )
= $false )
| ( ( subset @ SV435 @ SV550 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3176,plain,
! [SV551: $i,SV522: $i,SV446: $i] :
( ( ( subset @ SV446 @ SV522 )
= $false )
| ( ( disjoint @ SV522 @ SV551 )
= $false )
| ( ( disjoint @ SV446 @ SV551 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3177,plain,
! [SV450: $i,SV525: $i,SV552: $i] :
( ( ( subset @ SV552 @ SV525 )
= $false )
| ( ( subset @ SV450 @ SV525 )
= $false )
| ( ( subset @ ( set_union2 @ SV450 @ SV552 ) @ SV525 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3178,plain,
! [SV556: $i,SV539: $i,SV472: $i] :
( ( ( in @ SV472 @ SV539 )
= $false )
| ( ( element @ SV539 @ ( powerset @ SV556 ) )
= $false )
| ( ( element @ SV472 @ SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3179,plain,
! [SV557: $i,SV540: $i,SV473: $i] :
( ( ( in @ SV473 @ SV540 )
= $false )
| ( ( element @ SV540 @ ( powerset @ SV557 ) )
= $false )
| ( ( ~ ( empty @ SV557 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3180,plain,
! [SV613: $i,SV476: $i,SV664: $i] :
( ( ( ~ ( relation @ SV664 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV613 ) @ SV664 )
| ( in @ SV476 @ ( relation_field @ SV664 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3066]) ).
thf(3181,plain,
! [SV614: $i,SV476: $i,SV665: $i] :
( ( ( ~ ( relation @ SV665 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV614 ) @ SV665 )
| ( in @ SV614 @ ( relation_field @ SV665 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3067]) ).
thf(3182,plain,
! [SV477: $i,SV564: $i] :
( ( ( ~ ! [SY942: $i] :
( ~ ( relation @ SY942 )
| ~ ( ~ ( ! [SY943: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ SY943 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY943 @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) ) )
| ( SY942
= ( relation_composition @ SV477 @ SV564 ) ) )
| ~ ! [SY944: $i] :
( ~ ( relation @ SY944 )
| ( SY944
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY945: $i,SY946: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY945 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY946 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY945 @ SY946 ) @ SY944 ) )
| ~ ! [SY948: $i,SY949: $i] :
( ~ ( in @ ( ordered_pair @ SY948 @ SY949 ) @ SY944 )
| ~ ( ~ ( in @ ( ordered_pair @ SY948 @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) @ SY949 ) @ SV564 ) ) ) ) ) )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3183,plain,
! [SV478: $i,SV615: $i] :
( ( ( ~ ( subset @ SV615 @ ( sK2_B @ SV478 ) ) )
= $true )
| ( ( are_equipotent @ SV615 @ ( sK2_B @ SV478 ) )
= $true )
| ( ( in @ SV615 @ ( sK2_B @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3069]) ).
thf(3184,plain,
! [SV478: $i] :
( ( ! [SY810: $i] :
( ~ ( ~ ! [SY811: $i] :
( ~ ( subset @ SY811 @ SY810 )
| ( in @ SY811 @ ( sK3_SY300 @ SY810 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SY810 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SY810 @ ( sK2_B @ SV478 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3070]) ).
thf(3185,plain,
! [SV478: $i] :
( ( ~ ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3071]) ).
thf(3186,plain,
! [SV616: $i,SV479: $i] :
( ( ( subset @ SV479 @ SV616 )
= $false )
| ( ( ! [SY999: $i] : ( subset @ ( cartesian_product2 @ SV479 @ SY999 ) @ ( cartesian_product2 @ SV616 @ SY999 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3187,plain,
! [SV617: $i,SV479: $i] :
( ( ( subset @ SV479 @ SV617 )
= $false )
| ( ( ! [SY1000: $i] : ( subset @ ( cartesian_product2 @ SY1000 @ SV479 ) @ ( cartesian_product2 @ SY1000 @ SV617 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3188,plain,
! [SV618: $i,SV565: $i] :
( ( ( subset @ SV565 @ ( singleton @ SV618 ) )
= $false )
| ( ( ( SV565 = empty_set )
| ( SV565
= ( singleton @ SV618 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3074]) ).
thf(3189,plain,
! [SV683: $i] :
( ( ( SV683 != empty_set )
| ! [SY1065: $i] : ( subset @ SV683 @ ( singleton @ SY1065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3190,plain,
! [SV684: $i] :
( ( ! [SY1066: $i] :
( ( SV684
!= ( singleton @ SY1066 ) )
| ( subset @ SV684 @ ( singleton @ SY1066 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3191,plain,
! [SV666: $i,SV543: $i,SV480: $i] :
( ( ( ! [SY1043: $i] :
( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SV666 @ SY1043 ) ) )
= $true )
| ( ( SV480 = SV666 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3192,plain,
! [SV685: $i,SV667: $i,SV543: $i,SV480: $i] :
( ( ( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SV667 @ SV685 ) )
| ( SV543 = SV685 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3193,plain,
! [SV619: $i,SV566: $i] :
( ( ( ( set_difference @ SV566 @ SV619 )
= empty_set )
= $false )
| ( ( subset @ SV566 @ SV619 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3194,plain,
! [SV620: $i,SV567: $i] :
( ( ( subset @ SV567 @ SV620 )
= $false )
| ( ( ( set_difference @ SV567 @ SV620 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3080]) ).
thf(3195,plain,
! [SV481: $i,SV686: $i] :
( ( ( ~ ( relation @ SV686 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) ) )
| ( SV686
= ( relation_inverse @ SV481 ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3196,plain,
! [SV481: $i,SV687: $i] :
( ( ( ~ ( relation @ SV687 )
| ( SV687
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1068 @ SY1067 ) @ SV481 ) )
| ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1070 @ SY1069 ) @ SV481 )
| ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV687 ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3197,plain,
! [SV688: $i,SV544: $i,SV668: $i,SV482: $i] :
( ( ~ ( in @ SV482 @ SV668 )
| ~ ( in @ SV544 @ SV688 )
| ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV668 @ SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3198,plain,
! [SV544: $i,SV482: $i] :
( ( ~ ! [SY931: $i] :
( ! [SY932: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY931 @ SY932 ) )
| ( in @ SV482 @ SY931 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3084]) ).
thf(3199,plain,
! [SV544: $i,SV482: $i] :
( ( ~ ! [SY933: $i,SY934: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY933 @ SY934 ) )
| ( in @ SV544 @ SY934 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3084]) ).
thf(3200,plain,
! [SV621: $i,SV568: $i] :
( ( ( ( set_intersection2 @ SV568 @ SV621 )
= empty_set )
= $false )
| ( ( disjoint @ SV568 @ SV621 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3201,plain,
! [SV622: $i,SV569: $i] :
( ( ( disjoint @ SV569 @ SV622 )
= $false )
| ( ( ( set_intersection2 @ SV569 @ SV622 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3202,plain,
! [SV623: $i,SV570: $i] :
( ( ( ~ ( subset @ SV570 @ SV623 ) )
= $true )
| ( ( ~ ( subset @ SV623 @ SV570 ) )
= $true )
| ( ( SV570 = SV623 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3087]) ).
thf(3203,plain,
! [SV689: $i] :
( ( ! [SY1071: $i] :
( ( SV689 != SY1071 )
| ( subset @ SV689 @ SY1071 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3204,plain,
! [SV690: $i] :
( ( ! [SY1072: $i] :
( ( SV690 != SY1072 )
| ( subset @ SY1072 @ SV690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3205,plain,
! [SV624: $i,SV571: $i] :
( ( ( ( set_difference @ SV571 @ ( singleton @ SV624 ) )
= SV571 )
= $false )
| ( ( ~ ( in @ SV624 @ SV571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3206,plain,
! [SV483: $i,SV545: $i] :
( ( ( in @ ( sK33_C @ SV545 @ SV483 ) @ SV545 )
= $false )
| ( ( element @ SV483 @ ( powerset @ SV545 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3207,plain,
! [SV484: $i,SV691: $i] :
( ( ( ~ ( relation @ SV691 )
| ~ ( subset @ SV484 @ SV691 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SV691 ) ) )
= $true )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3208,plain,
! [SV484: $i,SV692: $i] :
( ( ( ~ ( relation @ SV692 )
| ~ ( subset @ SV484 @ SV692 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SV692 ) ) )
= $true )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3209,plain,
! [SV573: $i,SV626: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV573 )
| ~ ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV626 ) )
= $false )
| ( ( subset @ SV573 @ SV626 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3210,plain,
! [SV627: $i,SV574: $i] :
( ( ( subset @ SV574 @ SV627 )
= $false )
| ( ( ! [SY1001: $i] :
( ~ ( in @ SY1001 @ SV574 )
| ( in @ SY1001 @ SV627 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3211,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) )
| ~ ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3098]) ).
thf(3212,plain,
! [SV629: $i,SV485: $i,SV670: $i] :
( ( ( ( SV670
!= ( set_union2 @ SV485 @ SV629 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV670 )
| ( in @ SY1046 @ SV485 )
| ( in @ SY1046 @ SV629 ) )
| ~ ~ ( ~ ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) )
| ~ ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3099]) ).
thf(3213,plain,
! [SV630: $i,SV575: $i] :
( ( ( in @ SV575 @ SV630 )
= $false )
| ( ( subset @ ( singleton @ SV575 ) @ SV630 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3214,plain,
! [SV631: $i,SV576: $i] :
( ( ( subset @ ( singleton @ SV576 ) @ SV631 )
= $false )
| ( ( in @ SV576 @ SV631 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3101]) ).
thf(3215,plain,
! [SV693: $i] :
( ( ( SV693 = empty_set )
| ! [SY1073: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SY1073 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SY1073 @ SV693 ) @ ( sK45_SY327 @ SY1073 @ SV693 ) ) )
| ~ ( in @ ( sK44_C @ SY1073 @ SV693 ) @ SY1073 ) )
| ~ ( ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SV693 )
| ( in @ ( sK44_C @ SY1073 @ SV693 ) @ SY1074 ) )
| ( in @ ( sK44_C @ SY1073 @ SV693 ) @ SY1073 ) ) )
| ( SY1073
= ( set_meet @ SV693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3216,plain,
! [SV694: $i] :
( ( ( SV694 = empty_set )
| ! [SY1075: $i] :
( ( SY1075
!= ( set_meet @ SV694 ) )
| ~ ( ~ ! [SY1076: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY1076 @ SY1075 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SY1076 @ ( sK43_D @ SY1076 @ SY1075 @ SV694 ) ) )
| ( in @ SY1076 @ SY1075 ) )
| ~ ! [SY1077: $i] :
( ~ ( in @ SY1077 @ SY1075 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV694 )
| ( in @ SY1077 @ SY1078 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3217,plain,
! [SV695: $i] :
( ( ( SV695 != empty_set )
| ! [SY1079: $i] :
( ( SY1079
!= ( set_meet @ SV695 ) )
| ( SY1079 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3218,plain,
! [SV696: $i] :
( ( ( SV696 != empty_set )
| ! [SY1080: $i] :
( ( SY1080 != empty_set )
| ( SY1080
= ( set_meet @ SV696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3219,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( ! [SY1007: $i] :
( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SY1007 )
| ~ ( in @ SY1007 @ SV577 ) )
| ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) )
| ~ ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 ) )
| ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) ) )
= $false )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3106]) ).
thf(3220,plain,
! [SV578: $i,SV633: $i] :
( ( ( SV633
= ( union @ SV578 ) )
= $false )
| ( ( ~ ( ~ ! [SY1008: $i] :
( ! [SY967: $i] :
( ~ ( in @ SY1008 @ SY967 )
| ~ ( in @ SY967 @ SV578 ) )
| ( in @ SY1008 @ SV633 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV633 )
| ~ ( ~ ( in @ SY1010 @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) @ SV578 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3221,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) ) ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3222,plain,
! [SV635: $i,SV486: $i,SV672: $i] :
( ( ( ( SV672
!= ( set_intersection2 @ SV486 @ SV635 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1049: $i] :
( ~ ( in @ SY1049 @ SV486 )
| ~ ( in @ SY1049 @ SV635 )
| ( in @ SY1049 @ SV672 ) )
| ~ ~ ( ~ ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) )
| ~ ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3223,plain,
! [SV487: $i,SV636: $i] :
( ( ( ~ ( subset @ SV636 @ ( sK32_B @ SV487 ) ) )
= $true )
| ( ( are_equipotent @ SV636 @ ( sK32_B @ SV487 ) )
= $true )
| ( ( in @ SV636 @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3224,plain,
! [SV487: $i] :
( ( ! [SY854: $i] :
( ~ ( in @ SY854 @ ( sK32_B @ SV487 ) )
| ( in @ ( powerset @ SY854 ) @ ( sK32_B @ SV487 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3225,plain,
! [SV487: $i] :
( ( ~ ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) )
| ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3114]) ).
thf(3226,plain,
! [SV583: $i,SV637: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ~ ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) )
| ~ ( ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) ) )
= $false )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3227,plain,
! [SV584: $i,SV638: $i] :
( ( ( SV638
= ( powerset @ SV584 ) )
= $false )
| ( ( ~ ( ~ ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV638 )
| ( subset @ SY1016 @ SV584 ) )
| ~ ! [SY1017: $i] :
( ~ ( subset @ SY1017 @ SV584 )
| ( in @ SY1017 @ SV638 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3228,plain,
! [SV585: $i,SV639: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV585 )
| ~ ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV639 ) )
= $false )
| ( ( disjoint @ SV585 @ SV639 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3119]) ).
thf(3229,plain,
! [SV640: $i,SV586: $i,SV697: $i] :
( ( ( ~ ( in @ SV697 @ SV586 )
| ~ ( in @ SV697 @ SV640 ) )
= $true )
| ( ( ~ ( disjoint @ SV586 @ SV640 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3230,plain,
! [SV488: $i,SV698: $i] :
( ( ( ~ ( ~ ( ! [SY1081: $i] :
~ ( in @ ( ordered_pair @ SY1081 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV698 @ SV488 ) @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) ) )
| ( SV698
= ( relation_rng @ SV488 ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3231,plain,
! [SV488: $i,SV699: $i] :
( ( ( ( SV699
!= ( relation_rng @ SV488 ) )
| ~ ( ~ ! [SY1082: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY1082 ) @ SV488 )
| ( in @ SY1082 @ SV699 ) )
| ~ ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV699 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY1084 @ SV699 @ SV488 ) @ SY1084 ) @ SV488 ) ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3232,plain,
! [SV700: $i] :
( ( ( empty @ SV700 )
| ! [SY1085: $i] :
( ~ ( element @ SY1085 @ SV700 )
| ( in @ SY1085 @ SV700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3233,plain,
! [SV701: $i] :
( ( ( empty @ SV701 )
| ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV701 )
| ( element @ SY1086 @ SV701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3234,plain,
! [SV702: $i] :
( ( ~ ( empty @ SV702 )
| ! [SY1087: $i] :
( ~ ( element @ SY1087 @ SV702 )
| ( empty @ SY1087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3235,plain,
! [SV703: $i] :
( ( ~ ( empty @ SV703 )
| ! [SY1088: $i] :
( ~ ( empty @ SY1088 )
| ( element @ SY1088 @ SV703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3236,plain,
! [SV641: $i,SV587: $i] :
( ( ( in @ SV587 @ SV641 )
= $false )
| ( ( subset @ ( singleton @ SV587 ) @ SV641 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3237,plain,
! [SV642: $i,SV588: $i] :
( ( ( subset @ ( singleton @ SV588 ) @ SV642 )
= $false )
| ( ( in @ SV588 @ SV642 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3238,plain,
! [SV643: $i,SV589: $i] :
( ( ( subset @ SV589 @ ( singleton @ SV643 ) )
= $false )
| ( ( ( SV589 = empty_set )
| ( SV589
= ( singleton @ SV643 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3239,plain,
! [SV704: $i] :
( ( ( SV704 != empty_set )
| ! [SY1089: $i] : ( subset @ SV704 @ ( singleton @ SY1089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3240,plain,
! [SV705: $i] :
( ( ! [SY1090: $i] :
( ( SV705
!= ( singleton @ SY1090 ) )
| ( subset @ SV705 @ ( singleton @ SY1090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3241,plain,
! [SV591: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ SV591 ) )
= $true )
| ( ( SV591 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3242,plain,
! [SV592: $i] :
( ( ( ( ( relation_dom @ SV592 )
!= empty_set ) )
= $true )
| ( ( SV592 = empty_set )
= $true )
| ( ( relation @ SV592 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3243,plain,
! [SV593: $i] :
( ( ( ( ( relation_rng @ SV593 )
!= empty_set ) )
= $true )
| ( ( SV593 = empty_set )
= $true )
| ( ( relation @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3134]) ).
thf(3244,plain,
! [SV644: $i,SV596: $i] :
( ( ( ( set_difference @ SV596 @ SV644 )
= empty_set )
= $false )
| ( ( subset @ SV596 @ SV644 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3245,plain,
! [SV645: $i,SV597: $i] :
( ( ( subset @ SV597 @ SV645 )
= $false )
| ( ( ( set_difference @ SV597 @ SV645 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3138]) ).
thf(3246,plain,
! [SV490: $i,SV546: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) )
= $true )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3247,plain,
! [SV490: $i,SV546: $i] :
( ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
= $true )
| ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 )
= $true )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3140]) ).
thf(3248,plain,
! [SV646: $i,SV598: $i] :
( ( ( element @ SV598 @ ( powerset @ SV646 ) )
= $false )
| ( ( subset @ SV598 @ SV646 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3249,plain,
! [SV647: $i,SV599: $i] :
( ( ( subset @ SV599 @ SV647 )
= $false )
| ( ( element @ SV599 @ ( powerset @ SV647 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3250,plain,
! [SV600: $i] :
( ( ( ~ ! [SY984: $i,SY985: $i] :
( ( sK48_B @ SV600 )
!= ( ordered_pair @ SY984 @ SY985 ) ) )
= $false )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3143]) ).
thf(3251,plain,
! [SV600: $i] :
( ( ( ~ ( in @ ( sK48_B @ SV600 ) @ SV600 ) )
= $false )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3143]) ).
thf(3252,plain,
! [SV601: $i,SV707: $i] :
( ( ( ( SV707
= ( ordered_pair @ ( sK46_C @ SV707 @ SV601 ) @ ( sK47_SY329 @ SV707 @ SV601 ) ) )
| ~ ( in @ SV707 @ SV601 ) )
= $true )
| ( ( relation @ SV601 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3253,plain,
! [SV648: $i,SV673: $i,SV491: $i] :
( ( ( ~ ( in @ SV491 @ SV673 )
| ~ ( in @ SV648 @ SV673 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV491 @ SV648 ) @ SV673 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3254,plain,
! [SV491: $i] :
( ( ! [SY866: $i,SY867: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY866 ) @ SY867 )
| ( in @ SV491 @ SY867 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3146]) ).
thf(3255,plain,
! [SV491: $i] :
( ( ! [SY868: $i,SY869: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SY868 ) @ SY869 )
| ( in @ SY868 @ SY869 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3147]) ).
thf(3256,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) ) )
| ~ ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV492 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV649 ) ) ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3257,plain,
! [SV650: $i,SV492: $i,SV675: $i] :
( ( ( ( SV675
!= ( unordered_pair @ SV492 @ SV650 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1052: $i] :
( ~ ( in @ SY1052 @ SV675 )
| ( SY1052 = SV492 )
| ( SY1052 = SV650 ) )
| ~ ~ ( ~ ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) )
| ~ ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3258,plain,
! [SV708: $i,SV547: $i,SV676: $i,SV493: $i] :
( ( ~ ( in @ SV493 @ SV676 )
| ~ ( in @ SV547 @ SV708 )
| ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV676 @ SV708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3259,plain,
! [SV547: $i,SV493: $i] :
( ( ~ ! [SY937: $i] :
( ! [SY938: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY937 @ SY938 ) )
| ( in @ SV493 @ SY937 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3151]) ).
thf(3260,plain,
! [SV547: $i,SV493: $i] :
( ( ~ ! [SY939: $i,SY940: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY939 @ SY940 ) )
| ( in @ SV547 @ SY940 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3151]) ).
thf(3261,plain,
! [SV651: $i,SV494: $i,SV677: $i] :
( ( ( ~ ( relation @ SV677 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV494 @ SV651 ) @ SV677 )
| ( in @ SV494 @ ( relation_dom @ SV677 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3152]) ).
thf(3262,plain,
! [SV652: $i,SV494: $i,SV678: $i] :
( ( ( ~ ( relation @ SV678 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV494 @ SV652 ) @ SV678 )
| ( in @ SV652 @ ( relation_rng @ SV678 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3153]) ).
thf(3263,plain,
! [SV654: $i,SV603: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ ( set_intersection2 @ SV603 @ SV654 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV603 @ SV654 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3264,plain,
! [SV604: $i,SV655: $i] :
( ( ( ~ ( ( ( sK29_C @ SV655 @ SV604 )
!= SV604 )
| ~ ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) )
| ~ ( ( ( sK29_C @ SV655 @ SV604 )
= SV604 )
| ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) ) )
= $false )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3156]) ).
thf(3265,plain,
! [SV605: $i,SV656: $i] :
( ( ( SV656
= ( singleton @ SV605 ) )
= $false )
| ( ( ~ ( ~ ! [SY1028: $i] :
( ( SY1028 != SV605 )
| ( in @ SY1028 @ SV656 ) )
| ~ ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV656 )
| ( SY1029 = SV605 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3157]) ).
thf(3266,plain,
! [SV657: $i,SV606: $i] :
( ( ( SV606 = SV657 )
= $true )
| ( ( ~ ( subset @ SV606 @ SV657 ) )
= $true )
| ( ( proper_subset @ SV606 @ SV657 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3158]) ).
thf(3267,plain,
! [SV710: $i] :
( ( ! [SY1091: $i] :
( ~ ( proper_subset @ SV710 @ SY1091 )
| ( SV710 != SY1091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3268,plain,
! [SV711: $i] :
( ( ! [SY1092: $i] :
( ~ ( proper_subset @ SV711 @ SY1092 )
| ( subset @ SV711 @ SY1092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3269,plain,
! [SV679: $i,SV658: $i,SV495: $i] :
( ( ( ~ ( ~ ( ! [SY1056: $i,SY1057: $i] :
( ~ ( in @ SY1056 @ SV495 )
| ~ ( in @ SY1057 @ SV658 )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SY1056 @ SY1057 ) ) )
| ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) ) ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3161]) ).
thf(3270,plain,
! [SV659: $i,SV495: $i,SV680: $i] :
( ( ( ( SV680
!= ( cartesian_product2 @ SV495 @ SV659 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1058: $i] :
( ! [SY1035: $i,SY1036: $i] :
( ~ ( in @ SY1035 @ SV495 )
| ~ ( in @ SY1036 @ SV659 )
| ( SY1058
!= ( ordered_pair @ SY1035 @ SY1036 ) ) )
| ( in @ SY1058 @ SV680 ) )
| ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV680 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SY1061
!= ( ordered_pair @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3271,plain,
! [SV660: $i,SV607: $i] :
( ( ( ( set_difference @ SV607 @ SV660 )
= SV607 )
= $false )
| ( ( disjoint @ SV607 @ SV660 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3272,plain,
! [SV661: $i,SV608: $i] :
( ( ( disjoint @ SV608 @ SV661 )
= $false )
| ( ( ( set_difference @ SV608 @ SV661 )
= SV608 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3273,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) ) ) )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3274,plain,
! [SV663: $i,SV497: $i,SV682: $i] :
( ( ( ( SV682
!= ( set_difference @ SV497 @ SV663 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV497 )
| ( in @ SY1062 @ SV663 )
| ( in @ SY1062 @ SV682 ) )
| ~ ~ ( ~ ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) )
| ~ ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3275,plain,
! [SV498: $i,SV712: $i] :
( ( ( ~ ( ~ ( ! [SY1093: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SY1093 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ ( sK41_SY326 @ SV712 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) ) )
| ( SV712
= ( relation_dom @ SV498 ) ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3276,plain,
! [SV498: $i,SV713: $i] :
( ( ( ( SV713
!= ( relation_dom @ SV498 ) )
| ~ ( ~ ! [SY1094: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY1094 @ SY909 ) @ SV498 )
| ( in @ SY1094 @ SV713 ) )
| ~ ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV713 )
| ( in @ ( ordered_pair @ SY1096 @ ( sK39_D @ SY1096 @ SV713 @ SV498 ) ) @ SV498 ) ) ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3277,plain,
! [SV560: $i,SV409: $i] :
( ( ( subset @ ( relation_rng @ SV409 ) @ ( relation_dom @ SV560 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV409 @ SV560 ) )
= ( relation_dom @ SV409 ) )
= $true )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3170]) ).
thf(3278,plain,
! [SV561: $i,SV410: $i] :
( ( ( subset @ ( relation_dom @ SV410 ) @ ( relation_rng @ SV561 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV561 @ SV410 ) )
= ( relation_rng @ SV410 ) )
= $true )
| ( ( relation @ SV561 )
= $false )
| ( ( relation @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3171]) ).
thf(3279,plain,
! [SV507: $i,SV431: $i,SV562: $i,SV548: $i] :
( ( ( subset @ SV548 @ SV562 )
= $false )
| ( ( subset @ SV431 @ SV507 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV431 @ SV548 ) @ ( cartesian_product2 @ SV507 @ SV562 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3173]) ).
thf(3280,plain,
! [SV473: $i,SV540: $i,SV557: $i] :
( ( ( empty @ SV557 )
= $false )
| ( ( element @ SV540 @ ( powerset @ SV557 ) )
= $false )
| ( ( in @ SV473 @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3179]) ).
thf(3281,plain,
! [SV613: $i,SV476: $i,SV664: $i] :
( ( ( relation @ SV664 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV613 ) @ SV664 )
| ( in @ SV476 @ ( relation_field @ SV664 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3282,plain,
! [SV614: $i,SV476: $i,SV665: $i] :
( ( ( relation @ SV665 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV614 ) @ SV665 )
| ( in @ SV614 @ ( relation_field @ SV665 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3283,plain,
! [SV477: $i,SV564: $i] :
( ( ( ~ ! [SY942: $i] :
( ~ ( relation @ SY942 )
| ~ ( ~ ( ! [SY943: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ SY943 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY943 @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) ) )
| ( SY942
= ( relation_composition @ SV477 @ SV564 ) ) ) )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3182]) ).
thf(3284,plain,
! [SV564: $i,SV477: $i] :
( ( ( ~ ! [SY944: $i] :
( ~ ( relation @ SY944 )
| ( SY944
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY945: $i,SY946: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY945 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY946 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY945 @ SY946 ) @ SY944 ) )
| ~ ! [SY948: $i,SY949: $i] :
( ~ ( in @ ( ordered_pair @ SY948 @ SY949 ) @ SY944 )
| ~ ( ~ ( in @ ( ordered_pair @ SY948 @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) @ SY949 ) @ SV564 ) ) ) ) ) )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3182]) ).
thf(3285,plain,
! [SV478: $i,SV615: $i] :
( ( ( subset @ SV615 @ ( sK2_B @ SV478 ) )
= $false )
| ( ( are_equipotent @ SV615 @ ( sK2_B @ SV478 ) )
= $true )
| ( ( in @ SV615 @ ( sK2_B @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3286,plain,
! [SV478: $i,SV714: $i] :
( ( ~ ( ~ ! [SY1097: $i] :
( ~ ( subset @ SY1097 @ SV714 )
| ( in @ SY1097 @ ( sK3_SY300 @ SV714 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SV714 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3287,plain,
! [SV478: $i] :
( ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) )
| ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3288,plain,
! [SV616: $i,SV715: $i,SV479: $i] :
( ( ( subset @ ( cartesian_product2 @ SV479 @ SV715 ) @ ( cartesian_product2 @ SV616 @ SV715 ) )
= $true )
| ( ( subset @ SV479 @ SV616 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3289,plain,
! [SV617: $i,SV479: $i,SV716: $i] :
( ( ( subset @ ( cartesian_product2 @ SV716 @ SV479 ) @ ( cartesian_product2 @ SV716 @ SV617 ) )
= $true )
| ( ( subset @ SV479 @ SV617 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3290,plain,
! [SV618: $i,SV565: $i] :
( ( ( SV565 = empty_set )
= $true )
| ( ( SV565
= ( singleton @ SV618 ) )
= $true )
| ( ( subset @ SV565 @ ( singleton @ SV618 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3188]) ).
thf(3291,plain,
! [SV683: $i] :
( ( ( ( SV683 != empty_set ) )
= $true )
| ( ( ! [SY1065: $i] : ( subset @ SV683 @ ( singleton @ SY1065 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3292,plain,
! [SV717: $i,SV684: $i] :
( ( ( SV684
!= ( singleton @ SV717 ) )
| ( subset @ SV684 @ ( singleton @ SV717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3293,plain,
! [SV718: $i,SV666: $i,SV543: $i,SV480: $i] :
( ( ( ( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SV666 @ SV718 ) ) )
= $true )
| ( ( SV480 = SV666 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3294,plain,
! [SV685: $i,SV667: $i,SV543: $i,SV480: $i] :
( ( ( ( ( ordered_pair @ SV480 @ SV543 )
!= ( ordered_pair @ SV667 @ SV685 ) ) )
= $true )
| ( ( SV543 = SV685 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3192]) ).
thf(3295,plain,
! [SV481: $i,SV686: $i] :
( ( ( ~ ( relation @ SV686 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) ) )
| ( SV686
= ( relation_inverse @ SV481 ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3296,plain,
! [SV481: $i,SV687: $i] :
( ( ( ~ ( relation @ SV687 ) )
= $true )
| ( ( ( SV687
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1068 @ SY1067 ) @ SV481 ) )
| ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1070 @ SY1069 ) @ SV481 )
| ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV687 ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3297,plain,
! [SV688: $i,SV544: $i,SV668: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV668 )
| ~ ( in @ SV544 @ SV688 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV668 @ SV688 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3197]) ).
thf(3298,plain,
! [SV544: $i,SV482: $i] :
( ( ! [SY931: $i] :
( ! [SY932: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY931 @ SY932 ) )
| ( in @ SV482 @ SY931 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3198]) ).
thf(3299,plain,
! [SV544: $i,SV482: $i] :
( ( ! [SY933: $i,SY934: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SY933 @ SY934 ) )
| ( in @ SV544 @ SY934 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3199]) ).
thf(3300,plain,
! [SV623: $i,SV570: $i] :
( ( ( subset @ SV570 @ SV623 )
= $false )
| ( ( ~ ( subset @ SV623 @ SV570 ) )
= $true )
| ( ( SV570 = SV623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3202]) ).
thf(3301,plain,
! [SV719: $i,SV689: $i] :
( ( ( SV689 != SV719 )
| ( subset @ SV689 @ SV719 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3302,plain,
! [SV720: $i,SV690: $i] :
( ( ( SV690 != SV720 )
| ( subset @ SV720 @ SV690 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(3303,plain,
! [SV571: $i,SV624: $i] :
( ( ( in @ SV624 @ SV571 )
= $false )
| ( ( ( set_difference @ SV571 @ ( singleton @ SV624 ) )
= SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3304,plain,
! [SV484: $i,SV691: $i] :
( ( ( ~ ( relation @ SV691 ) )
= $true )
| ( ( ~ ( subset @ SV484 @ SV691 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SV691 ) ) )
= $true )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3305,plain,
! [SV484: $i,SV692: $i] :
( ( ( ~ ( relation @ SV692 ) )
= $true )
| ( ( ~ ( subset @ SV484 @ SV692 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SV692 ) ) )
= $true )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3306,plain,
! [SV573: $i,SV626: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV573 ) )
= $false )
| ( ( subset @ SV573 @ SV626 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3209]) ).
thf(3307,plain,
! [SV573: $i,SV626: $i] :
( ( ( ~ ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV626 ) )
= $false )
| ( ( subset @ SV573 @ SV626 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3209]) ).
thf(3308,plain,
! [SV627: $i,SV574: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV574 )
| ( in @ SV721 @ SV627 ) )
= $true )
| ( ( subset @ SV574 @ SV627 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3309,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) )
| ~ ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) )
= $false )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3211]) ).
thf(3310,plain,
! [SV629: $i,SV485: $i,SV670: $i] :
( ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false )
| ( ( ~ ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV670 )
| ( in @ SY1046 @ SV485 )
| ( in @ SY1046 @ SV629 ) )
| ~ ~ ( ~ ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) )
| ~ ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3311,plain,
! [SV693: $i] :
( ( ( SV693 = empty_set )
= $true )
| ( ( ! [SY1073: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SY1073 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SY1073 @ SV693 ) @ ( sK45_SY327 @ SY1073 @ SV693 ) ) )
| ~ ( in @ ( sK44_C @ SY1073 @ SV693 ) @ SY1073 ) )
| ~ ( ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SV693 )
| ( in @ ( sK44_C @ SY1073 @ SV693 ) @ SY1074 ) )
| ( in @ ( sK44_C @ SY1073 @ SV693 ) @ SY1073 ) ) )
| ( SY1073
= ( set_meet @ SV693 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3215]) ).
thf(3312,plain,
! [SV694: $i] :
( ( ( SV694 = empty_set )
= $true )
| ( ( ! [SY1075: $i] :
( ( SY1075
!= ( set_meet @ SV694 ) )
| ~ ( ~ ! [SY1076: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY1076 @ SY1075 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SY1076 @ ( sK43_D @ SY1076 @ SY1075 @ SV694 ) ) )
| ( in @ SY1076 @ SY1075 ) )
| ~ ! [SY1077: $i] :
( ~ ( in @ SY1077 @ SY1075 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV694 )
| ( in @ SY1077 @ SY1078 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3313,plain,
! [SV695: $i] :
( ( ( ( SV695 != empty_set ) )
= $true )
| ( ( ! [SY1079: $i] :
( ( SY1079
!= ( set_meet @ SV695 ) )
| ( SY1079 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3217]) ).
thf(3314,plain,
! [SV696: $i] :
( ( ( ( SV696 != empty_set ) )
= $true )
| ( ( ! [SY1080: $i] :
( ( SY1080 != empty_set )
| ( SY1080
= ( set_meet @ SV696 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3218]) ).
thf(3315,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( ! [SY1007: $i] :
( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SY1007 )
| ~ ( in @ SY1007 @ SV577 ) )
| ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) ) )
= $false )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3219]) ).
thf(3316,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) )
| ~ ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 ) )
| ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) ) )
= $false )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3219]) ).
thf(3317,plain,
! [SV633: $i,SV578: $i] :
( ( ( ~ ! [SY1008: $i] :
( ! [SY967: $i] :
( ~ ( in @ SY1008 @ SY967 )
| ~ ( in @ SY967 @ SV578 ) )
| ( in @ SY1008 @ SV633 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV633 )
| ~ ( ~ ( in @ SY1010 @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) @ SV578 ) ) ) )
= $false )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3220]) ).
thf(3318,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ~ ( ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) ) )
= $false )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3319,plain,
! [SV635: $i,SV486: $i,SV672: $i] :
( ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false )
| ( ( ~ ( ~ ! [SY1049: $i] :
( ~ ( in @ SY1049 @ SV486 )
| ~ ( in @ SY1049 @ SV635 )
| ( in @ SY1049 @ SV672 ) )
| ~ ~ ( ~ ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) )
| ~ ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3320,plain,
! [SV487: $i,SV636: $i] :
( ( ( subset @ SV636 @ ( sK32_B @ SV487 ) )
= $false )
| ( ( are_equipotent @ SV636 @ ( sK32_B @ SV487 ) )
= $true )
| ( ( in @ SV636 @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3223]) ).
thf(3321,plain,
! [SV487: $i,SV722: $i] :
( ( ~ ( in @ SV722 @ ( sK32_B @ SV487 ) )
| ( in @ ( powerset @ SV722 ) @ ( sK32_B @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3322,plain,
! [SV487: $i] :
( ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) )
| ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3225]) ).
thf(3323,plain,
! [SV583: $i,SV637: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ~ ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) ) )
= $false )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3226]) ).
thf(3324,plain,
! [SV583: $i,SV637: $i] :
( ( ( ~ ( ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) ) )
= $false )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3226]) ).
thf(3325,plain,
! [SV584: $i,SV638: $i] :
( ( ( ~ ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV638 )
| ( subset @ SY1016 @ SV584 ) )
| ~ ! [SY1017: $i] :
( ~ ( subset @ SY1017 @ SV584 )
| ( in @ SY1017 @ SV638 ) ) )
= $false )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3326,plain,
! [SV585: $i,SV639: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV585 ) )
= $false )
| ( ( disjoint @ SV585 @ SV639 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3228]) ).
thf(3327,plain,
! [SV585: $i,SV639: $i] :
( ( ( ~ ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV639 ) )
= $false )
| ( ( disjoint @ SV585 @ SV639 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3228]) ).
thf(3328,plain,
! [SV640: $i,SV586: $i,SV697: $i] :
( ( ( ~ ( in @ SV697 @ SV586 ) )
= $true )
| ( ( ~ ( in @ SV697 @ SV640 ) )
= $true )
| ( ( ~ ( disjoint @ SV586 @ SV640 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3329,plain,
! [SV488: $i,SV698: $i] :
( ( ( ~ ( ~ ( ! [SY1081: $i] :
~ ( in @ ( ordered_pair @ SY1081 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV698 @ SV488 ) @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) ) ) )
= $true )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3330,plain,
! [SV488: $i,SV699: $i] :
( ( ( ( SV699
!= ( relation_rng @ SV488 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1082: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY1082 ) @ SV488 )
| ( in @ SY1082 @ SV699 ) )
| ~ ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV699 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY1084 @ SV699 @ SV488 ) @ SY1084 ) @ SV488 ) ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3231]) ).
thf(3331,plain,
! [SV700: $i] :
( ( ( empty @ SV700 )
= $true )
| ( ( ! [SY1085: $i] :
( ~ ( element @ SY1085 @ SV700 )
| ( in @ SY1085 @ SV700 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3232]) ).
thf(3332,plain,
! [SV701: $i] :
( ( ( empty @ SV701 )
= $true )
| ( ( ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV701 )
| ( element @ SY1086 @ SV701 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3333,plain,
! [SV702: $i] :
( ( ( ~ ( empty @ SV702 ) )
= $true )
| ( ( ! [SY1087: $i] :
( ~ ( element @ SY1087 @ SV702 )
| ( empty @ SY1087 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3234]) ).
thf(3334,plain,
! [SV703: $i] :
( ( ( ~ ( empty @ SV703 ) )
= $true )
| ( ( ! [SY1088: $i] :
( ~ ( empty @ SY1088 )
| ( element @ SY1088 @ SV703 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3235]) ).
thf(3335,plain,
! [SV643: $i,SV589: $i] :
( ( ( SV589 = empty_set )
= $true )
| ( ( SV589
= ( singleton @ SV643 ) )
= $true )
| ( ( subset @ SV589 @ ( singleton @ SV643 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3336,plain,
! [SV704: $i] :
( ( ( ( SV704 != empty_set ) )
= $true )
| ( ( ! [SY1089: $i] : ( subset @ SV704 @ ( singleton @ SY1089 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3337,plain,
! [SV723: $i,SV705: $i] :
( ( ( SV705
!= ( singleton @ SV723 ) )
| ( subset @ SV705 @ ( singleton @ SV723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3338,plain,
! [SV591: $i,SV706: $i] :
( ( ( in @ SV706 @ SV591 )
= $false )
| ( ( SV591 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3339,plain,
! [SV592: $i] :
( ( ( ( relation_dom @ SV592 )
= empty_set )
= $false )
| ( ( SV592 = empty_set )
= $true )
| ( ( relation @ SV592 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3340,plain,
! [SV593: $i] :
( ( ( ( relation_rng @ SV593 )
= empty_set )
= $false )
| ( ( SV593 = empty_set )
= $true )
| ( ( relation @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3341,plain,
! [SV490: $i,SV546: $i] :
( ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 ) )
= $true )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3342,plain,
! [SV600: $i] :
( ( ( ! [SY984: $i,SY985: $i] :
( ( sK48_B @ SV600 )
!= ( ordered_pair @ SY984 @ SY985 ) ) )
= $true )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3250]) ).
thf(3343,plain,
! [SV600: $i] :
( ( ( in @ ( sK48_B @ SV600 ) @ SV600 )
= $true )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3251]) ).
thf(3344,plain,
! [SV601: $i,SV707: $i] :
( ( ( SV707
= ( ordered_pair @ ( sK46_C @ SV707 @ SV601 ) @ ( sK47_SY329 @ SV707 @ SV601 ) ) )
= $true )
| ( ( ~ ( in @ SV707 @ SV601 ) )
= $true )
| ( ( relation @ SV601 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3345,plain,
! [SV648: $i,SV673: $i,SV491: $i] :
( ( ( ~ ( in @ SV491 @ SV673 ) )
= $true )
| ( ( ~ ( in @ SV648 @ SV673 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV491 @ SV648 ) @ SV673 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3253]) ).
thf(3346,plain,
! [SV724: $i,SV491: $i] :
( ( ! [SY1098: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SV724 ) @ SY1098 )
| ( in @ SV491 @ SY1098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(3347,plain,
! [SV725: $i,SV491: $i] :
( ( ! [SY1099: $i] :
( ~ ( subset @ ( unordered_pair @ SV491 @ SV725 ) @ SY1099 )
| ( in @ SV725 @ SY1099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3348,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) ) )
| ~ ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV492 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV649 ) ) )
= $false )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3256]) ).
thf(3349,plain,
! [SV650: $i,SV492: $i,SV675: $i] :
( ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false )
| ( ( ~ ( ~ ! [SY1052: $i] :
( ~ ( in @ SY1052 @ SV675 )
| ( SY1052 = SV492 )
| ( SY1052 = SV650 ) )
| ~ ~ ( ~ ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) )
| ~ ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3350,plain,
! [SV708: $i,SV547: $i,SV676: $i,SV493: $i] :
( ( ( ~ ( in @ SV493 @ SV676 )
| ~ ( in @ SV547 @ SV708 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV676 @ SV708 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3351,plain,
! [SV547: $i,SV493: $i] :
( ( ! [SY937: $i] :
( ! [SY938: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY937 @ SY938 ) )
| ( in @ SV493 @ SY937 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3259]) ).
thf(3352,plain,
! [SV547: $i,SV493: $i] :
( ( ! [SY939: $i,SY940: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SY939 @ SY940 ) )
| ( in @ SV547 @ SY940 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3353,plain,
! [SV651: $i,SV494: $i,SV677: $i] :
( ( ( relation @ SV677 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV494 @ SV651 ) @ SV677 )
| ( in @ SV494 @ ( relation_dom @ SV677 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3354,plain,
! [SV652: $i,SV494: $i,SV678: $i] :
( ( ( relation @ SV678 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV494 @ SV652 ) @ SV678 )
| ( in @ SV652 @ ( relation_rng @ SV678 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3355,plain,
! [SV654: $i,SV603: $i,SV709: $i] :
( ( ( in @ SV709 @ ( set_intersection2 @ SV603 @ SV654 ) )
= $false )
| ( ( ~ ( disjoint @ SV603 @ SV654 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3263]) ).
thf(3356,plain,
! [SV604: $i,SV655: $i] :
( ( ( ~ ( ( ( sK29_C @ SV655 @ SV604 )
!= SV604 )
| ~ ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) ) )
= $false )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3264]) ).
thf(3357,plain,
! [SV604: $i,SV655: $i] :
( ( ( ~ ( ( ( sK29_C @ SV655 @ SV604 )
= SV604 )
| ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) ) )
= $false )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3264]) ).
thf(3358,plain,
! [SV656: $i,SV605: $i] :
( ( ( ~ ! [SY1028: $i] :
( ( SY1028 != SV605 )
| ( in @ SY1028 @ SV656 ) )
| ~ ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV656 )
| ( SY1029 = SV605 ) ) )
= $false )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3359,plain,
! [SV657: $i,SV606: $i] :
( ( ( subset @ SV606 @ SV657 )
= $false )
| ( ( SV606 = SV657 )
= $true )
| ( ( proper_subset @ SV606 @ SV657 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3360,plain,
! [SV726: $i,SV710: $i] :
( ( ~ ( proper_subset @ SV710 @ SV726 )
| ( SV710 != SV726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3361,plain,
! [SV727: $i,SV711: $i] :
( ( ~ ( proper_subset @ SV711 @ SV727 )
| ( subset @ SV711 @ SV727 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(3362,plain,
! [SV679: $i,SV658: $i,SV495: $i] :
( ( ( ~ ( ! [SY1056: $i,SY1057: $i] :
( ~ ( in @ SY1056 @ SV495 )
| ~ ( in @ SY1057 @ SV658 )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SY1056 @ SY1057 ) ) )
| ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) ) )
= $false )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3269]) ).
thf(3363,plain,
! [SV659: $i,SV495: $i,SV680: $i] :
( ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false )
| ( ( ~ ( ~ ! [SY1058: $i] :
( ! [SY1035: $i,SY1036: $i] :
( ~ ( in @ SY1035 @ SV495 )
| ~ ( in @ SY1036 @ SV659 )
| ( SY1058
!= ( ordered_pair @ SY1035 @ SY1036 ) ) )
| ( in @ SY1058 @ SV680 ) )
| ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV680 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SY1061
!= ( ordered_pair @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3270]) ).
thf(3364,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) ) )
= $false )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3365,plain,
! [SV663: $i,SV497: $i,SV682: $i] :
( ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false )
| ( ( ~ ( ~ ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV497 )
| ( in @ SY1062 @ SV663 )
| ( in @ SY1062 @ SV682 ) )
| ~ ~ ( ~ ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) )
| ~ ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3274]) ).
thf(3366,plain,
! [SV498: $i,SV712: $i] :
( ( ( ~ ( ~ ( ! [SY1093: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SY1093 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ ( sK41_SY326 @ SV712 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) ) ) )
= $true )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3275]) ).
thf(3367,plain,
! [SV498: $i,SV713: $i] :
( ( ( ( SV713
!= ( relation_dom @ SV498 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1094: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY1094 @ SY909 ) @ SV498 )
| ( in @ SY1094 @ SV713 ) )
| ~ ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV713 )
| ( in @ ( ordered_pair @ SY1096 @ ( sK39_D @ SY1096 @ SV713 @ SV498 ) ) @ SV498 ) ) ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3368,plain,
! [SV664: $i,SV613: $i,SV476: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV613 ) @ SV664 ) )
= $true )
| ( ( in @ SV476 @ ( relation_field @ SV664 ) )
= $true )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3281]) ).
thf(3369,plain,
! [SV665: $i,SV614: $i,SV476: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV614 ) @ SV665 ) )
= $true )
| ( ( in @ SV614 @ ( relation_field @ SV665 ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3370,plain,
! [SV477: $i,SV564: $i] :
( ( ( ! [SY942: $i] :
( ~ ( relation @ SY942 )
| ~ ( ~ ( ! [SY943: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ SY943 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY943 @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY942 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SY942 @ SV564 @ SV477 ) ) @ SY942 ) ) )
| ( SY942
= ( relation_composition @ SV477 @ SV564 ) ) ) )
= $true )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3283]) ).
thf(3371,plain,
! [SV564: $i,SV477: $i] :
( ( ( ! [SY944: $i] :
( ~ ( relation @ SY944 )
| ( SY944
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY945: $i,SY946: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY945 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY946 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY945 @ SY946 ) @ SY944 ) )
| ~ ! [SY948: $i,SY949: $i] :
( ~ ( in @ ( ordered_pair @ SY948 @ SY949 ) @ SY944 )
| ~ ( ~ ( in @ ( ordered_pair @ SY948 @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY949 @ SY948 @ SY944 @ SV564 @ SV477 ) @ SY949 ) @ SV564 ) ) ) ) ) )
= $true )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3284]) ).
thf(3372,plain,
! [SV478: $i,SV714: $i] :
( ( ( ~ ( ~ ! [SY1097: $i] :
( ~ ( subset @ SY1097 @ SV714 )
| ( in @ SY1097 @ ( sK3_SY300 @ SV714 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SV714 @ SV478 ) @ ( sK2_B @ SV478 ) ) ) )
= $true )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3373,plain,
! [SV478: $i] :
( ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3287]) ).
thf(3374,plain,
! [SV478: $i] :
( ( ~ ( in @ SV478 @ ( sK2_B @ SV478 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3287]) ).
thf(3375,plain,
! [SV683: $i] :
( ( ( SV683 = empty_set )
= $false )
| ( ( ! [SY1065: $i] : ( subset @ SV683 @ ( singleton @ SY1065 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3376,plain,
! [SV717: $i,SV684: $i] :
( ( ( ( SV684
!= ( singleton @ SV717 ) ) )
= $true )
| ( ( subset @ SV684 @ ( singleton @ SV717 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3377,plain,
! [SV718: $i,SV666: $i,SV543: $i,SV480: $i] :
( ( ( ( ordered_pair @ SV480 @ SV543 )
= ( ordered_pair @ SV666 @ SV718 ) )
= $false )
| ( ( SV480 = SV666 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3293]) ).
thf(3378,plain,
! [SV685: $i,SV667: $i,SV543: $i,SV480: $i] :
( ( ( ( ordered_pair @ SV480 @ SV543 )
= ( ordered_pair @ SV667 @ SV685 ) )
= $false )
| ( ( SV543 = SV685 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3294]) ).
thf(3379,plain,
! [SV481: $i,SV686: $i] :
( ( ( relation @ SV686 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) ) )
| ( SV686
= ( relation_inverse @ SV481 ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3380,plain,
! [SV481: $i,SV687: $i] :
( ( ( relation @ SV687 )
= $false )
| ( ( ( SV687
!= ( relation_inverse @ SV481 ) )
| ~ ( ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1068 @ SY1067 ) @ SV481 ) )
| ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1070 @ SY1069 ) @ SV481 )
| ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV687 ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3296]) ).
thf(3381,plain,
! [SV688: $i,SV544: $i,SV668: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV668 ) )
= $true )
| ( ( ~ ( in @ SV544 @ SV688 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV668 @ SV688 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3382,plain,
! [SV728: $i,SV544: $i,SV482: $i] :
( ( ! [SY1100: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV728 @ SY1100 ) )
| ( in @ SV482 @ SV728 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(3383,plain,
! [SV729: $i,SV544: $i,SV482: $i] :
( ( ! [SY1101: $i] :
( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV729 @ SY1101 ) )
| ( in @ SV544 @ SY1101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(3384,plain,
! [SV570: $i,SV623: $i] :
( ( ( subset @ SV623 @ SV570 )
= $false )
| ( ( subset @ SV570 @ SV623 )
= $false )
| ( ( SV570 = SV623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3300]) ).
thf(3385,plain,
! [SV719: $i,SV689: $i] :
( ( ( ( SV689 != SV719 ) )
= $true )
| ( ( subset @ SV689 @ SV719 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3386,plain,
! [SV720: $i,SV690: $i] :
( ( ( ( SV690 != SV720 ) )
= $true )
| ( ( subset @ SV720 @ SV690 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3387,plain,
! [SV484: $i,SV691: $i] :
( ( ( relation @ SV691 )
= $false )
| ( ( ~ ( subset @ SV484 @ SV691 )
| ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SV691 ) ) )
= $true )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3388,plain,
! [SV484: $i,SV692: $i] :
( ( ( relation @ SV692 )
= $false )
| ( ( ~ ( subset @ SV484 @ SV692 )
| ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SV692 ) ) )
= $true )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3389,plain,
! [SV573: $i,SV626: $i] :
( ( ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV573 )
= $true )
| ( ( subset @ SV573 @ SV626 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3306]) ).
thf(3390,plain,
! [SV573: $i,SV626: $i] :
( ( ( ~ ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV626 ) )
= $true )
| ( ( subset @ SV573 @ SV626 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3307]) ).
thf(3391,plain,
! [SV627: $i,SV574: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV574 ) )
= $true )
| ( ( in @ SV721 @ SV627 )
= $true )
| ( ( subset @ SV574 @ SV627 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3308]) ).
thf(3392,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) ) )
= $false )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3309]) ).
thf(3393,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) )
= $false )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3309]) ).
thf(3394,plain,
! [SV629: $i,SV485: $i,SV670: $i] :
( ( ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV670 )
| ( in @ SY1046 @ SV485 )
| ( in @ SY1046 @ SV629 ) )
| ~ ~ ( ~ ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) )
| ~ ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) ) )
= $false )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3395,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) )
| ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
| ~ ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV693 )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SY1102 ) )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) ) )
| ( SV730
= ( set_meet @ SV693 ) ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3396,plain,
! [SV694: $i,SV731: $i] :
( ( ( ( SV731
!= ( set_meet @ SV694 ) )
| ~ ( ~ ! [SY1103: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SY1103 @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) ) )
| ( in @ SY1103 @ SV731 ) )
| ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV731 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV694 )
| ( in @ SY1104 @ SY1078 ) ) ) ) )
= $true )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3397,plain,
! [SV695: $i] :
( ( ( SV695 = empty_set )
= $false )
| ( ( ! [SY1079: $i] :
( ( SY1079
!= ( set_meet @ SV695 ) )
| ( SY1079 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3398,plain,
! [SV696: $i] :
( ( ( SV696 = empty_set )
= $false )
| ( ( ! [SY1080: $i] :
( ( SY1080 != empty_set )
| ( SY1080
= ( set_meet @ SV696 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3399,plain,
! [SV577: $i,SV632: $i] :
( ( ( ! [SY1007: $i] :
( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SY1007 )
| ~ ( in @ SY1007 @ SV577 ) )
| ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3315]) ).
thf(3400,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) )
| ~ ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 ) )
| ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3316]) ).
thf(3401,plain,
! [SV633: $i,SV578: $i] :
( ( ( ~ ! [SY1008: $i] :
( ! [SY967: $i] :
( ~ ( in @ SY1008 @ SY967 )
| ~ ( in @ SY967 @ SV578 ) )
| ( in @ SY1008 @ SV633 ) ) )
= $false )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3317]) ).
thf(3402,plain,
! [SV578: $i,SV633: $i] :
( ( ( ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV633 )
| ~ ( ~ ( in @ SY1010 @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) @ SV578 ) ) ) )
= $false )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3317]) ).
thf(3403,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) )
= $false )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3318]) ).
thf(3404,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) ) )
= $false )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3318]) ).
thf(3405,plain,
! [SV672: $i,SV635: $i,SV486: $i] :
( ( ( ~ ! [SY1049: $i] :
( ~ ( in @ SY1049 @ SV486 )
| ~ ( in @ SY1049 @ SV635 )
| ( in @ SY1049 @ SV672 ) )
| ~ ~ ( ~ ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) )
| ~ ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) ) )
= $false )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3319]) ).
thf(3406,plain,
! [SV487: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ ( sK32_B @ SV487 ) ) )
= $true )
| ( ( in @ ( powerset @ SV722 ) @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3321]) ).
thf(3407,plain,
! [SV487: $i] :
( ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3322]) ).
thf(3408,plain,
! [SV487: $i] :
( ( ~ ( in @ SV487 @ ( sK32_B @ SV487 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3322]) ).
thf(3409,plain,
! [SV583: $i,SV637: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ~ ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) )
= $true )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3323]) ).
thf(3410,plain,
! [SV583: $i,SV637: $i] :
( ( ( ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
| ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) )
= $true )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3324]) ).
thf(3411,plain,
! [SV584: $i,SV638: $i] :
( ( ( ~ ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV638 )
| ( subset @ SY1016 @ SV584 ) ) )
= $false )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3325]) ).
thf(3412,plain,
! [SV638: $i,SV584: $i] :
( ( ( ~ ! [SY1017: $i] :
( ~ ( subset @ SY1017 @ SV584 )
| ( in @ SY1017 @ SV638 ) ) )
= $false )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3325]) ).
thf(3413,plain,
! [SV585: $i,SV639: $i] :
( ( ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV585 )
= $true )
| ( ( disjoint @ SV585 @ SV639 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3326]) ).
thf(3414,plain,
! [SV585: $i,SV639: $i] :
( ( ( in @ ( sK31_C @ SV639 @ SV585 ) @ SV639 )
= $true )
| ( ( disjoint @ SV585 @ SV639 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3327]) ).
thf(3415,plain,
! [SV640: $i,SV586: $i,SV697: $i] :
( ( ( in @ SV697 @ SV586 )
= $false )
| ( ( ~ ( in @ SV697 @ SV640 ) )
= $true )
| ( ( ~ ( disjoint @ SV586 @ SV640 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3416,plain,
! [SV488: $i,SV698: $i] :
( ( ( ~ ( ! [SY1081: $i] :
~ ( in @ ( ordered_pair @ SY1081 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV698 @ SV488 ) @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) ) )
= $false )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3329]) ).
thf(3417,plain,
! [SV488: $i,SV699: $i] :
( ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( ~ ( ~ ! [SY1082: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY1082 ) @ SV488 )
| ( in @ SY1082 @ SV699 ) )
| ~ ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV699 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY1084 @ SV699 @ SV488 ) @ SY1084 ) @ SV488 ) ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3418,plain,
! [SV700: $i,SV732: $i] :
( ( ( ~ ( element @ SV732 @ SV700 )
| ( in @ SV732 @ SV700 ) )
= $true )
| ( ( empty @ SV700 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3419,plain,
! [SV701: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV701 )
| ( element @ SV733 @ SV701 ) )
= $true )
| ( ( empty @ SV701 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(3420,plain,
! [SV702: $i] :
( ( ( empty @ SV702 )
= $false )
| ( ( ! [SY1087: $i] :
( ~ ( element @ SY1087 @ SV702 )
| ( empty @ SY1087 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3421,plain,
! [SV703: $i] :
( ( ( empty @ SV703 )
= $false )
| ( ( ! [SY1088: $i] :
( ~ ( empty @ SY1088 )
| ( element @ SY1088 @ SV703 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3422,plain,
! [SV704: $i] :
( ( ( SV704 = empty_set )
= $false )
| ( ( ! [SY1089: $i] : ( subset @ SV704 @ ( singleton @ SY1089 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3336]) ).
thf(3423,plain,
! [SV723: $i,SV705: $i] :
( ( ( ( SV705
!= ( singleton @ SV723 ) ) )
= $true )
| ( ( subset @ SV705 @ ( singleton @ SV723 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3337]) ).
thf(3424,plain,
! [SV490: $i,SV546: $i] :
( ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV546 )
= $false )
| ( ( in @ ( sK4_C @ SV546 @ SV490 ) @ SV490 )
= $false )
| ( ( SV490 = SV546 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3425,plain,
! [SV734: $i,SV600: $i] :
( ( ( ! [SY1106: $i] :
( ( sK48_B @ SV600 )
!= ( ordered_pair @ SV734 @ SY1106 ) ) )
= $true )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(3426,plain,
! [SV601: $i,SV707: $i] :
( ( ( in @ SV707 @ SV601 )
= $false )
| ( ( SV707
= ( ordered_pair @ ( sK46_C @ SV707 @ SV601 ) @ ( sK47_SY329 @ SV707 @ SV601 ) ) )
= $true )
| ( ( relation @ SV601 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3427,plain,
! [SV648: $i,SV673: $i,SV491: $i] :
( ( ( in @ SV491 @ SV673 )
= $false )
| ( ( ~ ( in @ SV648 @ SV673 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV491 @ SV648 ) @ SV673 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3428,plain,
! [SV735: $i,SV724: $i,SV491: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV491 @ SV724 ) @ SV735 )
| ( in @ SV491 @ SV735 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3429,plain,
! [SV736: $i,SV725: $i,SV491: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV491 @ SV725 ) @ SV736 )
| ( in @ SV725 @ SV736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(3430,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) ) ) )
= $false )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3348]) ).
thf(3431,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV492 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV649 ) ) )
= $false )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3348]) ).
thf(3432,plain,
! [SV650: $i,SV492: $i,SV675: $i] :
( ( ( ~ ! [SY1052: $i] :
( ~ ( in @ SY1052 @ SV675 )
| ( SY1052 = SV492 )
| ( SY1052 = SV650 ) )
| ~ ~ ( ~ ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) )
| ~ ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) ) )
= $false )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3433,plain,
! [SV708: $i,SV547: $i,SV676: $i,SV493: $i] :
( ( ( ~ ( in @ SV493 @ SV676 ) )
= $true )
| ( ( ~ ( in @ SV547 @ SV708 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV676 @ SV708 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3350]) ).
thf(3434,plain,
! [SV737: $i,SV547: $i,SV493: $i] :
( ( ! [SY1107: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV737 @ SY1107 ) )
| ( in @ SV493 @ SV737 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3435,plain,
! [SV738: $i,SV547: $i,SV493: $i] :
( ( ! [SY1108: $i] :
( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV738 @ SY1108 ) )
| ( in @ SV547 @ SY1108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3436,plain,
! [SV677: $i,SV651: $i,SV494: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV494 @ SV651 ) @ SV677 ) )
= $true )
| ( ( in @ SV494 @ ( relation_dom @ SV677 ) )
= $true )
| ( ( relation @ SV677 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3437,plain,
! [SV678: $i,SV652: $i,SV494: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV494 @ SV652 ) @ SV678 ) )
= $true )
| ( ( in @ SV652 @ ( relation_rng @ SV678 ) )
= $true )
| ( ( relation @ SV678 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3438,plain,
! [SV709: $i,SV654: $i,SV603: $i] :
( ( ( disjoint @ SV603 @ SV654 )
= $false )
| ( ( in @ SV709 @ ( set_intersection2 @ SV603 @ SV654 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3355]) ).
thf(3439,plain,
! [SV604: $i,SV655: $i] :
( ( ( ( ( sK29_C @ SV655 @ SV604 )
!= SV604 )
| ~ ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) )
= $true )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3356]) ).
thf(3440,plain,
! [SV604: $i,SV655: $i] :
( ( ( ( ( sK29_C @ SV655 @ SV604 )
= SV604 )
| ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) )
= $true )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3357]) ).
thf(3441,plain,
! [SV656: $i,SV605: $i] :
( ( ( ~ ! [SY1028: $i] :
( ( SY1028 != SV605 )
| ( in @ SY1028 @ SV656 ) ) )
= $false )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3358]) ).
thf(3442,plain,
! [SV605: $i,SV656: $i] :
( ( ( ~ ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV656 )
| ( SY1029 = SV605 ) ) )
= $false )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3358]) ).
thf(3443,plain,
! [SV726: $i,SV710: $i] :
( ( ( ~ ( proper_subset @ SV710 @ SV726 ) )
= $true )
| ( ( ( SV710 != SV726 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3360]) ).
thf(3444,plain,
! [SV727: $i,SV711: $i] :
( ( ( ~ ( proper_subset @ SV711 @ SV727 ) )
= $true )
| ( ( subset @ SV711 @ SV727 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3361]) ).
thf(3445,plain,
! [SV679: $i,SV658: $i,SV495: $i] :
( ( ( ~ ( ! [SY1056: $i,SY1057: $i] :
( ~ ( in @ SY1056 @ SV495 )
| ~ ( in @ SY1057 @ SV658 )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SY1056 @ SY1057 ) ) )
| ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) ) )
= $false )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3362]) ).
thf(3446,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) ) )
= $false )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3362]) ).
thf(3447,plain,
! [SV680: $i,SV659: $i,SV495: $i] :
( ( ( ~ ! [SY1058: $i] :
( ! [SY1035: $i,SY1036: $i] :
( ~ ( in @ SY1035 @ SV495 )
| ~ ( in @ SY1036 @ SV659 )
| ( SY1058
!= ( ordered_pair @ SY1035 @ SY1036 ) ) )
| ( in @ SY1058 @ SV680 ) )
| ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV680 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SY1061
!= ( ordered_pair @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) ) ) ) ) )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3363]) ).
thf(3448,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) )
= $false )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3364]) ).
thf(3449,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) ) )
= $false )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3364]) ).
thf(3450,plain,
! [SV682: $i,SV663: $i,SV497: $i] :
( ( ( ~ ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV497 )
| ( in @ SY1062 @ SV663 )
| ( in @ SY1062 @ SV682 ) )
| ~ ~ ( ~ ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) )
| ~ ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) ) )
= $false )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3365]) ).
thf(3451,plain,
! [SV498: $i,SV712: $i] :
( ( ( ~ ( ! [SY1093: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SY1093 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ ( sK41_SY326 @ SV712 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) ) )
= $false )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3452,plain,
! [SV498: $i,SV713: $i] :
( ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( ~ ( ~ ! [SY1094: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY1094 @ SY909 ) @ SV498 )
| ( in @ SY1094 @ SV713 ) )
| ~ ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV713 )
| ( in @ ( ordered_pair @ SY1096 @ ( sK39_D @ SY1096 @ SV713 @ SV498 ) ) @ SV498 ) ) ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(3453,plain,
! [SV664: $i,SV613: $i,SV476: $i] :
( ( ( in @ ( ordered_pair @ SV476 @ SV613 ) @ SV664 )
= $false )
| ( ( in @ SV476 @ ( relation_field @ SV664 ) )
= $true )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3454,plain,
! [SV665: $i,SV614: $i,SV476: $i] :
( ( ( in @ ( ordered_pair @ SV476 @ SV614 ) @ SV665 )
= $false )
| ( ( in @ SV614 @ ( relation_field @ SV665 ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3455,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( relation @ SV739 )
| ~ ( ~ ( ! [SY1109: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SY1109 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1109 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) ) )
| ( SV739
= ( relation_composition @ SV477 @ SV564 ) ) )
= $true )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(3456,plain,
! [SV564: $i,SV477: $i,SV740: $i] :
( ( ( ~ ( relation @ SV740 )
| ( SV740
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY1110: $i,SY1111: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY1110 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY1111 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY1110 @ SY1111 ) @ SV740 ) )
| ~ ! [SY1113: $i,SY1114: $i] :
( ~ ( in @ ( ordered_pair @ SY1113 @ SY1114 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1113 @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) @ SY1114 ) @ SV564 ) ) ) ) )
= $true )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3457,plain,
! [SV478: $i,SV714: $i] :
( ( ( ~ ! [SY1097: $i] :
( ~ ( subset @ SY1097 @ SV714 )
| ( in @ SY1097 @ ( sK3_SY300 @ SV714 @ SV478 ) ) )
| ~ ( in @ ( sK3_SY300 @ SV714 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
= $false )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3372]) ).
thf(3458,plain,
! [SV478: $i] :
( ( ! [SY812: $i,SY813: $i] :
( ~ ( in @ SY812 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY813 @ SY812 )
| ( in @ SY813 @ ( sK2_B @ SV478 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3373]) ).
thf(3459,plain,
! [SV478: $i] :
( ( in @ SV478 @ ( sK2_B @ SV478 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3374]) ).
thf(3460,plain,
! [SV741: $i,SV683: $i] :
( ( ( subset @ SV683 @ ( singleton @ SV741 ) )
= $true )
| ( ( SV683 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3461,plain,
! [SV717: $i,SV684: $i] :
( ( ( SV684
= ( singleton @ SV717 ) )
= $false )
| ( ( subset @ SV684 @ ( singleton @ SV717 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(3462,plain,
! [SV481: $i,SV686: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) ) ) )
= $true )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(3463,plain,
! [SV481: $i,SV687: $i] :
( ( ( ( SV687
!= ( relation_inverse @ SV481 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1068 @ SY1067 ) @ SV481 ) )
| ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1070 @ SY1069 ) @ SV481 )
| ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV687 ) ) ) )
= $true )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3380]) ).
thf(3464,plain,
! [SV688: $i,SV544: $i,SV668: $i,SV482: $i] :
( ( ( in @ SV482 @ SV668 )
= $false )
| ( ( ~ ( in @ SV544 @ SV688 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV668 @ SV688 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3465,plain,
! [SV728: $i,SV544: $i,SV482: $i] :
( ( ( ! [SY1100: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV728 @ SY1100 ) ) )
= $true )
| ( ( in @ SV482 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3466,plain,
! [SV742: $i,SV729: $i,SV544: $i,SV482: $i] :
( ( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV729 @ SV742 ) )
| ( in @ SV544 @ SV742 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3467,plain,
! [SV719: $i,SV689: $i] :
( ( ( SV689 = SV719 )
= $false )
| ( ( subset @ SV689 @ SV719 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3468,plain,
! [SV720: $i,SV690: $i] :
( ( ( SV690 = SV720 )
= $false )
| ( ( subset @ SV720 @ SV690 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3469,plain,
! [SV691: $i,SV484: $i] :
( ( ( ~ ( subset @ SV484 @ SV691 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SV691 ) )
= $true )
| ( ( relation @ SV691 )
= $false )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3470,plain,
! [SV692: $i,SV484: $i] :
( ( ( ~ ( subset @ SV484 @ SV692 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SV692 ) )
= $true )
| ( ( relation @ SV692 )
= $false )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3388]) ).
thf(3471,plain,
! [SV573: $i,SV626: $i] :
( ( ( in @ ( sK20_C @ SV626 @ SV573 ) @ SV626 )
= $false )
| ( ( subset @ SV573 @ SV626 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3472,plain,
! [SV627: $i,SV574: $i,SV721: $i] :
( ( ( in @ SV721 @ SV574 )
= $false )
| ( ( in @ SV721 @ SV627 )
= $true )
| ( ( subset @ SV574 @ SV627 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3473,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3392]) ).
thf(3474,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3393]) ).
thf(3475,plain,
! [SV629: $i,SV485: $i,SV670: $i] :
( ( ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV670 )
| ( in @ SY1046 @ SV485 )
| ( in @ SY1046 @ SV629 ) ) )
= $false )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3394]) ).
thf(3476,plain,
! [SV629: $i,SV670: $i,SV485: $i] :
( ( ( ~ ~ ( ~ ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) )
| ~ ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) ) )
= $false )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3394]) ).
thf(3477,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) )
| ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
| ~ ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV693 )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SY1102 ) )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) ) ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3395]) ).
thf(3478,plain,
! [SV694: $i,SV731: $i] :
( ( ( ( SV731
!= ( set_meet @ SV694 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1103: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SY1103 @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) ) )
| ( in @ SY1103 @ SV731 ) )
| ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV731 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV694 )
| ( in @ SY1104 @ SY1078 ) ) ) ) )
= $true )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3479,plain,
! [SV695: $i,SV743: $i] :
( ( ( ( SV743
!= ( set_meet @ SV695 ) )
| ( SV743 = empty_set ) )
= $true )
| ( ( SV695 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(3480,plain,
! [SV696: $i,SV744: $i] :
( ( ( ( SV744 != empty_set )
| ( SV744
= ( set_meet @ SV696 ) ) )
= $true )
| ( ( SV696 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(3481,plain,
! [SV577: $i,SV632: $i] :
( ( ( ! [SY1007: $i] :
( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SY1007 )
| ~ ( in @ SY1007 @ SV577 ) ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3399]) ).
thf(3482,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) )
| ~ ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 ) ) )
= $true )
| ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3483,plain,
! [SV633: $i,SV578: $i] :
( ( ( ! [SY1008: $i] :
( ! [SY967: $i] :
( ~ ( in @ SY1008 @ SY967 )
| ~ ( in @ SY967 @ SV578 ) )
| ( in @ SY1008 @ SV633 ) ) )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3401]) ).
thf(3484,plain,
! [SV578: $i,SV633: $i] :
( ( ( ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV633 )
| ~ ( ~ ( in @ SY1010 @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SY1010 @ SV633 @ SV578 ) @ SV578 ) ) ) )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3402]) ).
thf(3485,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3403]) ).
thf(3486,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3404]) ).
thf(3487,plain,
! [SV672: $i,SV635: $i,SV486: $i] :
( ( ( ~ ! [SY1049: $i] :
( ~ ( in @ SY1049 @ SV486 )
| ~ ( in @ SY1049 @ SV635 )
| ( in @ SY1049 @ SV672 ) ) )
= $false )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3405]) ).
thf(3488,plain,
! [SV635: $i,SV486: $i,SV672: $i] :
( ( ( ~ ~ ( ~ ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) )
| ~ ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) ) )
= $false )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3405]) ).
thf(3489,plain,
! [SV487: $i,SV722: $i] :
( ( ( in @ SV722 @ ( sK32_B @ SV487 ) )
= $false )
| ( ( in @ ( powerset @ SV722 ) @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3406]) ).
thf(3490,plain,
! [SV487: $i] :
( ( ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY855 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY856 @ SY855 )
| ( in @ SY856 @ ( sK32_B @ SV487 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3407]) ).
thf(3491,plain,
! [SV487: $i] :
( ( in @ SV487 @ ( sK32_B @ SV487 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3408]) ).
thf(3492,plain,
! [SV583: $i,SV637: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 ) )
= $true )
| ( ( ~ ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) )
= $true )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3409]) ).
thf(3493,plain,
! [SV583: $i,SV637: $i] :
( ( ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
= $true )
| ( ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 )
= $true )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3410]) ).
thf(3494,plain,
! [SV584: $i,SV638: $i] :
( ( ( ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV638 )
| ( subset @ SY1016 @ SV584 ) ) )
= $true )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3411]) ).
thf(3495,plain,
! [SV638: $i,SV584: $i] :
( ( ( ! [SY1017: $i] :
( ~ ( subset @ SY1017 @ SV584 )
| ( in @ SY1017 @ SV638 ) ) )
= $true )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3412]) ).
thf(3496,plain,
! [SV586: $i,SV640: $i,SV697: $i] :
( ( ( in @ SV697 @ SV640 )
= $false )
| ( ( in @ SV697 @ SV586 )
= $false )
| ( ( ~ ( disjoint @ SV586 @ SV640 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3497,plain,
! [SV488: $i,SV698: $i] :
( ( ( ~ ( ! [SY1081: $i] :
~ ( in @ ( ordered_pair @ SY1081 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) ) )
= $false )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3416]) ).
thf(3498,plain,
! [SV488: $i,SV698: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV698 @ SV488 ) @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) ) )
= $false )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3416]) ).
thf(3499,plain,
! [SV699: $i,SV488: $i] :
( ( ( ~ ! [SY1082: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY1082 ) @ SV488 )
| ( in @ SY1082 @ SV699 ) )
| ~ ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV699 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY1084 @ SV699 @ SV488 ) @ SY1084 ) @ SV488 ) ) )
= $false )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(3500,plain,
! [SV700: $i,SV732: $i] :
( ( ( ~ ( element @ SV732 @ SV700 ) )
= $true )
| ( ( in @ SV732 @ SV700 )
= $true )
| ( ( empty @ SV700 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3418]) ).
thf(3501,plain,
! [SV701: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV701 ) )
= $true )
| ( ( element @ SV733 @ SV701 )
= $true )
| ( ( empty @ SV701 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3419]) ).
thf(3502,plain,
! [SV702: $i,SV745: $i] :
( ( ( ~ ( element @ SV745 @ SV702 )
| ( empty @ SV745 ) )
= $true )
| ( ( empty @ SV702 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(3503,plain,
! [SV703: $i,SV746: $i] :
( ( ( ~ ( empty @ SV746 )
| ( element @ SV746 @ SV703 ) )
= $true )
| ( ( empty @ SV703 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(3504,plain,
! [SV747: $i,SV704: $i] :
( ( ( subset @ SV704 @ ( singleton @ SV747 ) )
= $true )
| ( ( SV704 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(3505,plain,
! [SV723: $i,SV705: $i] :
( ( ( SV705
= ( singleton @ SV723 ) )
= $false )
| ( ( subset @ SV705 @ ( singleton @ SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3506,plain,
! [SV748: $i,SV734: $i,SV600: $i] :
( ( ( ( ( sK48_B @ SV600 )
!= ( ordered_pair @ SV734 @ SV748 ) ) )
= $true )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(3507,plain,
! [SV491: $i,SV673: $i,SV648: $i] :
( ( ( in @ SV648 @ SV673 )
= $false )
| ( ( in @ SV491 @ SV673 )
= $false )
| ( ( subset @ ( unordered_pair @ SV491 @ SV648 ) @ SV673 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3508,plain,
! [SV735: $i,SV724: $i,SV491: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV491 @ SV724 ) @ SV735 ) )
= $true )
| ( ( in @ SV491 @ SV735 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3428]) ).
thf(3509,plain,
! [SV736: $i,SV725: $i,SV491: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV491 @ SV725 ) @ SV736 ) )
= $true )
| ( ( in @ SV725 @ SV736 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3429]) ).
thf(3510,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) ) ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3430]) ).
thf(3511,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV492 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV649 ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3431]) ).
thf(3512,plain,
! [SV650: $i,SV492: $i,SV675: $i] :
( ( ( ~ ! [SY1052: $i] :
( ~ ( in @ SY1052 @ SV675 )
| ( SY1052 = SV492 )
| ( SY1052 = SV650 ) ) )
= $false )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3513,plain,
! [SV650: $i,SV675: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) )
| ~ ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) ) )
= $false )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3514,plain,
! [SV708: $i,SV547: $i,SV676: $i,SV493: $i] :
( ( ( in @ SV493 @ SV676 )
= $false )
| ( ( ~ ( in @ SV547 @ SV708 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV676 @ SV708 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3515,plain,
! [SV737: $i,SV547: $i,SV493: $i] :
( ( ( ! [SY1107: $i] :
~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV737 @ SY1107 ) ) )
= $true )
| ( ( in @ SV493 @ SV737 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3434]) ).
thf(3516,plain,
! [SV749: $i,SV738: $i,SV547: $i,SV493: $i] :
( ( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV738 @ SV749 ) )
| ( in @ SV547 @ SV749 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3517,plain,
! [SV677: $i,SV651: $i,SV494: $i] :
( ( ( in @ ( ordered_pair @ SV494 @ SV651 ) @ SV677 )
= $false )
| ( ( in @ SV494 @ ( relation_dom @ SV677 ) )
= $true )
| ( ( relation @ SV677 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3518,plain,
! [SV678: $i,SV652: $i,SV494: $i] :
( ( ( in @ ( ordered_pair @ SV494 @ SV652 ) @ SV678 )
= $false )
| ( ( in @ SV652 @ ( relation_rng @ SV678 ) )
= $true )
| ( ( relation @ SV678 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3519,plain,
! [SV604: $i,SV655: $i] :
( ( ( ( ( sK29_C @ SV655 @ SV604 )
!= SV604 ) )
= $true )
| ( ( ~ ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) )
= $true )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3439]) ).
thf(3520,plain,
! [SV604: $i,SV655: $i] :
( ( ( ( sK29_C @ SV655 @ SV604 )
= SV604 )
= $true )
| ( ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 )
= $true )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3440]) ).
thf(3521,plain,
! [SV656: $i,SV605: $i] :
( ( ( ! [SY1028: $i] :
( ( SY1028 != SV605 )
| ( in @ SY1028 @ SV656 ) ) )
= $true )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3441]) ).
thf(3522,plain,
! [SV605: $i,SV656: $i] :
( ( ( ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV656 )
| ( SY1029 = SV605 ) ) )
= $true )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3442]) ).
thf(3523,plain,
! [SV726: $i,SV710: $i] :
( ( ( proper_subset @ SV710 @ SV726 )
= $false )
| ( ( ( SV710 != SV726 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3524,plain,
! [SV727: $i,SV711: $i] :
( ( ( proper_subset @ SV711 @ SV727 )
= $false )
| ( ( subset @ SV711 @ SV727 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3525,plain,
! [SV679: $i,SV658: $i,SV495: $i] :
( ( ( ! [SY1056: $i,SY1057: $i] :
( ~ ( in @ SY1056 @ SV495 )
| ~ ( in @ SY1057 @ SV658 )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SY1056 @ SY1057 ) ) )
| ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3445]) ).
thf(3526,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) ) )
| ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3446]) ).
thf(3527,plain,
! [SV680: $i,SV659: $i,SV495: $i] :
( ( ( ~ ! [SY1058: $i] :
( ! [SY1035: $i,SY1036: $i] :
( ~ ( in @ SY1035 @ SV495 )
| ~ ( in @ SY1036 @ SV659 )
| ( SY1058
!= ( ordered_pair @ SY1035 @ SY1036 ) ) )
| ( in @ SY1058 @ SV680 ) ) )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3447]) ).
thf(3528,plain,
! [SV495: $i,SV659: $i,SV680: $i] :
( ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV680 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SY1061
!= ( ordered_pair @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) ) ) ) ) )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3447]) ).
thf(3529,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3448]) ).
thf(3530,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) ) )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3449]) ).
thf(3531,plain,
! [SV682: $i,SV663: $i,SV497: $i] :
( ( ( ~ ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV497 )
| ( in @ SY1062 @ SV663 )
| ( in @ SY1062 @ SV682 ) ) )
= $false )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3450]) ).
thf(3532,plain,
! [SV663: $i,SV497: $i,SV682: $i] :
( ( ( ~ ~ ( ~ ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) )
| ~ ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) ) )
= $false )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3450]) ).
thf(3533,plain,
! [SV498: $i,SV712: $i] :
( ( ( ~ ( ! [SY1093: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SY1093 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) ) )
= $false )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3451]) ).
thf(3534,plain,
! [SV498: $i,SV712: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ ( sK41_SY326 @ SV712 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) ) )
= $false )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3451]) ).
thf(3535,plain,
! [SV713: $i,SV498: $i] :
( ( ( ~ ! [SY1094: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY1094 @ SY909 ) @ SV498 )
| ( in @ SY1094 @ SV713 ) )
| ~ ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV713 )
| ( in @ ( ordered_pair @ SY1096 @ ( sK39_D @ SY1096 @ SV713 @ SV498 ) ) @ SV498 ) ) )
= $false )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3536,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( relation @ SV739 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY1109: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SY1109 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1109 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) ) )
| ( SV739
= ( relation_composition @ SV477 @ SV564 ) ) )
= $true )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3455]) ).
thf(3537,plain,
! [SV564: $i,SV477: $i,SV740: $i] :
( ( ( ~ ( relation @ SV740 ) )
= $true )
| ( ( ( SV740
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY1110: $i,SY1111: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY1110 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY1111 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY1110 @ SY1111 ) @ SV740 ) )
| ~ ! [SY1113: $i,SY1114: $i] :
( ~ ( in @ ( ordered_pair @ SY1113 @ SY1114 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1113 @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) @ SY1114 ) @ SV564 ) ) ) ) )
= $true )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3456]) ).
thf(3538,plain,
! [SV478: $i,SV714: $i] :
( ( ( ~ ! [SY1097: $i] :
( ~ ( subset @ SY1097 @ SV714 )
| ( in @ SY1097 @ ( sK3_SY300 @ SV714 @ SV478 ) ) ) )
= $false )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3539,plain,
! [SV478: $i,SV714: $i] :
( ( ( ~ ( in @ ( sK3_SY300 @ SV714 @ SV478 ) @ ( sK2_B @ SV478 ) ) )
= $false )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3540,plain,
! [SV478: $i,SV750: $i] :
( ( ! [SY1115: $i] :
( ~ ( in @ SV750 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SY1115 @ SV750 )
| ( in @ SY1115 @ ( sK2_B @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(3541,plain,
! [SV481: $i,SV686: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) ) )
= $false )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3542,plain,
! [SV481: $i,SV687: $i] :
( ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( ~ ( ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1068 @ SY1067 ) @ SV481 ) )
| ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1070 @ SY1069 ) @ SV481 )
| ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV687 ) ) ) )
= $true )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3543,plain,
! [SV668: $i,SV482: $i,SV688: $i,SV544: $i] :
( ( ( in @ SV544 @ SV688 )
= $false )
| ( ( in @ SV482 @ SV668 )
= $false )
| ( ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV668 @ SV688 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3544,plain,
! [SV751: $i,SV728: $i,SV544: $i,SV482: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV728 @ SV751 ) ) )
= $true )
| ( ( in @ SV482 @ SV728 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(3545,plain,
! [SV742: $i,SV729: $i,SV544: $i,SV482: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV729 @ SV742 ) ) )
= $true )
| ( ( in @ SV544 @ SV742 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(3546,plain,
! [SV691: $i,SV484: $i] :
( ( ( subset @ SV484 @ SV691 )
= $false )
| ( ( subset @ ( relation_dom @ SV484 ) @ ( relation_dom @ SV691 ) )
= $true )
| ( ( relation @ SV691 )
= $false )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3469]) ).
thf(3547,plain,
! [SV692: $i,SV484: $i] :
( ( ( subset @ SV484 @ SV692 )
= $false )
| ( ( subset @ ( relation_rng @ SV484 ) @ ( relation_rng @ SV692 ) )
= $true )
| ( ( relation @ SV692 )
= $false )
| ( ( relation @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3470]) ).
thf(3548,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) )
= $false )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3473]) ).
thf(3549,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
= $true )
| ( ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 )
| ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3474]) ).
thf(3550,plain,
! [SV629: $i,SV485: $i,SV670: $i] :
( ( ( ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV670 )
| ( in @ SY1046 @ SV485 )
| ( in @ SY1046 @ SV629 ) ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3475]) ).
thf(3551,plain,
! [SV629: $i,SV670: $i,SV485: $i] :
( ( ( ~ ( ~ ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) )
| ~ ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3476]) ).
thf(3552,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) )
| ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
| ~ ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV693 )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SY1102 ) )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) ) )
= $false )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3477]) ).
thf(3553,plain,
! [SV694: $i,SV731: $i] :
( ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( ~ ( ~ ! [SY1103: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SY1103 @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) ) )
| ( in @ SY1103 @ SV731 ) )
| ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV731 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV694 )
| ( in @ SY1104 @ SY1078 ) ) ) ) )
= $true )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(3554,plain,
! [SV695: $i,SV743: $i] :
( ( ( ( SV743
!= ( set_meet @ SV695 ) ) )
= $true )
| ( ( SV743 = empty_set )
= $true )
| ( ( SV695 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3479]) ).
thf(3555,plain,
! [SV696: $i,SV744: $i] :
( ( ( ( SV744 != empty_set ) )
= $true )
| ( ( SV744
= ( set_meet @ SV696 ) )
= $true )
| ( ( SV696 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3480]) ).
thf(3556,plain,
! [SV752: $i,SV577: $i,SV632: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV752 )
| ~ ( in @ SV752 @ SV577 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(3557,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) )
| ~ ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 ) )
= $false )
| ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3558,plain,
! [SV633: $i,SV578: $i,SV753: $i] :
( ( ( ! [SY1116: $i] :
( ~ ( in @ SV753 @ SY1116 )
| ~ ( in @ SY1116 @ SV578 ) )
| ( in @ SV753 @ SV633 ) )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(3559,plain,
! [SV578: $i,SV633: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ SV633 )
| ~ ( ~ ( in @ SV754 @ ( sK16_D @ SV754 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SV754 @ SV633 @ SV578 ) @ SV578 ) ) )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(3560,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3485]) ).
thf(3561,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
| ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) )
= $false )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3486]) ).
thf(3562,plain,
! [SV672: $i,SV635: $i,SV486: $i] :
( ( ( ! [SY1049: $i] :
( ~ ( in @ SY1049 @ SV486 )
| ~ ( in @ SY1049 @ SV635 )
| ( in @ SY1049 @ SV672 ) ) )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3487]) ).
thf(3563,plain,
! [SV635: $i,SV486: $i,SV672: $i] :
( ( ( ~ ( ~ ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) )
| ~ ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) ) )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3488]) ).
thf(3564,plain,
! [SV487: $i,SV755: $i] :
( ( ! [SY1117: $i] :
( ~ ( in @ SV755 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SY1117 @ SV755 )
| ( in @ SY1117 @ ( sK32_B @ SV487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(3565,plain,
! [SV583: $i,SV637: $i] :
( ( ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
= $false )
| ( ( ~ ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 ) )
= $true )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3492]) ).
thf(3566,plain,
! [SV584: $i,SV638: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV638 )
| ( subset @ SV756 @ SV584 ) )
= $true )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(3567,plain,
! [SV638: $i,SV584: $i,SV757: $i] :
( ( ( ~ ( subset @ SV757 @ SV584 )
| ( in @ SV757 @ SV638 ) )
= $true )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(3568,plain,
! [SV697: $i,SV640: $i,SV586: $i] :
( ( ( disjoint @ SV586 @ SV640 )
= $false )
| ( ( in @ SV697 @ SV586 )
= $false )
| ( ( in @ SV697 @ SV640 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3496]) ).
thf(3569,plain,
! [SV488: $i,SV698: $i] :
( ( ( ! [SY1081: $i] :
~ ( in @ ( ordered_pair @ SY1081 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ~ ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) )
= $true )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3497]) ).
thf(3570,plain,
! [SV488: $i,SV698: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV698 @ SV488 ) @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
| ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) )
= $true )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3498]) ).
thf(3571,plain,
! [SV699: $i,SV488: $i] :
( ( ( ~ ! [SY1082: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY1082 ) @ SV488 )
| ( in @ SY1082 @ SV699 ) ) )
= $false )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3499]) ).
thf(3572,plain,
! [SV488: $i,SV699: $i] :
( ( ( ~ ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV699 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY1084 @ SV699 @ SV488 ) @ SY1084 ) @ SV488 ) ) )
= $false )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3499]) ).
thf(3573,plain,
! [SV700: $i,SV732: $i] :
( ( ( element @ SV732 @ SV700 )
= $false )
| ( ( in @ SV732 @ SV700 )
= $true )
| ( ( empty @ SV700 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3500]) ).
thf(3574,plain,
! [SV701: $i,SV733: $i] :
( ( ( in @ SV733 @ SV701 )
= $false )
| ( ( element @ SV733 @ SV701 )
= $true )
| ( ( empty @ SV701 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3575,plain,
! [SV702: $i,SV745: $i] :
( ( ( ~ ( element @ SV745 @ SV702 ) )
= $true )
| ( ( empty @ SV745 )
= $true )
| ( ( empty @ SV702 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(3576,plain,
! [SV703: $i,SV746: $i] :
( ( ( ~ ( empty @ SV746 ) )
= $true )
| ( ( element @ SV746 @ SV703 )
= $true )
| ( ( empty @ SV703 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3503]) ).
thf(3577,plain,
! [SV748: $i,SV734: $i,SV600: $i] :
( ( ( ( sK48_B @ SV600 )
= ( ordered_pair @ SV734 @ SV748 ) )
= $false )
| ( ( relation @ SV600 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3578,plain,
! [SV735: $i,SV724: $i,SV491: $i] :
( ( ( subset @ ( unordered_pair @ SV491 @ SV724 ) @ SV735 )
= $false )
| ( ( in @ SV491 @ SV735 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3508]) ).
thf(3579,plain,
! [SV736: $i,SV725: $i,SV491: $i] :
( ( ( subset @ ( unordered_pair @ SV491 @ SV725 ) @ SV736 )
= $false )
| ( ( in @ SV725 @ SV736 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3509]) ).
thf(3580,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) ) )
= $false )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(3581,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
= $true )
| ( ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV492 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV649 ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3582,plain,
! [SV650: $i,SV492: $i,SV675: $i] :
( ( ( ! [SY1052: $i] :
( ~ ( in @ SY1052 @ SV675 )
| ( SY1052 = SV492 )
| ( SY1052 = SV650 ) ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3512]) ).
thf(3583,plain,
! [SV650: $i,SV675: $i,SV492: $i] :
( ( ( ~ ( ~ ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) )
| ~ ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3513]) ).
thf(3584,plain,
! [SV676: $i,SV493: $i,SV708: $i,SV547: $i] :
( ( ( in @ SV547 @ SV708 )
= $false )
| ( ( in @ SV493 @ SV676 )
= $false )
| ( ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV676 @ SV708 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(3585,plain,
! [SV758: $i,SV737: $i,SV547: $i,SV493: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV737 @ SV758 ) ) )
= $true )
| ( ( in @ SV493 @ SV737 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(3586,plain,
! [SV749: $i,SV738: $i,SV547: $i,SV493: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV738 @ SV749 ) ) )
= $true )
| ( ( in @ SV547 @ SV749 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(3587,plain,
! [SV604: $i,SV655: $i] :
( ( ( ( sK29_C @ SV655 @ SV604 )
= SV604 )
= $false )
| ( ( ~ ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 ) )
= $true )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3588,plain,
! [SV656: $i,SV605: $i,SV759: $i] :
( ( ( ( SV759 != SV605 )
| ( in @ SV759 @ SV656 ) )
= $true )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(3589,plain,
! [SV605: $i,SV656: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV656 )
| ( SV760 = SV605 ) )
= $true )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(3590,plain,
! [SV726: $i,SV710: $i] :
( ( ( SV710 = SV726 )
= $false )
| ( ( proper_subset @ SV710 @ SV726 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3591,plain,
! [SV679: $i,SV658: $i,SV495: $i] :
( ( ( ! [SY1056: $i,SY1057: $i] :
( ~ ( in @ SY1056 @ SV495 )
| ~ ( in @ SY1057 @ SV658 )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SY1056 @ SY1057 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3525]) ).
thf(3592,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3526]) ).
thf(3593,plain,
! [SV680: $i,SV659: $i,SV495: $i] :
( ( ( ! [SY1058: $i] :
( ! [SY1035: $i,SY1036: $i] :
( ~ ( in @ SY1035 @ SV495 )
| ~ ( in @ SY1036 @ SV659 )
| ( SY1058
!= ( ordered_pair @ SY1035 @ SY1036 ) ) )
| ( in @ SY1058 @ SV680 ) ) )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3527]) ).
thf(3594,plain,
! [SV495: $i,SV659: $i,SV680: $i] :
( ( ( ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV680 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SY1061
!= ( ordered_pair @ ( sK21_E @ SY1061 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SY1061 @ SV680 @ SV659 @ SV495 ) ) ) ) ) )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3528]) ).
thf(3595,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3529]) ).
thf(3596,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) )
= $false )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3597,plain,
! [SV682: $i,SV663: $i,SV497: $i] :
( ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV497 )
| ( in @ SY1062 @ SV663 )
| ( in @ SY1062 @ SV682 ) ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3531]) ).
thf(3598,plain,
! [SV663: $i,SV497: $i,SV682: $i] :
( ( ( ~ ( ~ ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) )
| ~ ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3532]) ).
thf(3599,plain,
! [SV498: $i,SV712: $i] :
( ( ( ! [SY1093: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SY1093 ) @ SV498 )
| ~ ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) )
= $true )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3533]) ).
thf(3600,plain,
! [SV498: $i,SV712: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ ( sK41_SY326 @ SV712 @ SV498 ) ) @ SV498 )
| ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) )
= $true )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3534]) ).
thf(3601,plain,
! [SV713: $i,SV498: $i] :
( ( ( ~ ! [SY1094: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY1094 @ SY909 ) @ SV498 )
| ( in @ SY1094 @ SV713 ) ) )
= $false )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3535]) ).
thf(3602,plain,
! [SV498: $i,SV713: $i] :
( ( ( ~ ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV713 )
| ( in @ ( ordered_pair @ SY1096 @ ( sK39_D @ SY1096 @ SV713 @ SV498 ) ) @ SV498 ) ) )
= $false )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3535]) ).
thf(3603,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( relation @ SV739 )
= $false )
| ( ( ~ ( ~ ( ! [SY1109: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SY1109 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1109 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) ) )
| ( SV739
= ( relation_composition @ SV477 @ SV564 ) ) )
= $true )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3604,plain,
! [SV564: $i,SV477: $i,SV740: $i] :
( ( ( relation @ SV740 )
= $false )
| ( ( ( SV740
!= ( relation_composition @ SV477 @ SV564 ) )
| ~ ( ~ ! [SY1110: $i,SY1111: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY1110 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY1111 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY1110 @ SY1111 ) @ SV740 ) )
| ~ ! [SY1113: $i,SY1114: $i] :
( ~ ( in @ ( ordered_pair @ SY1113 @ SY1114 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1113 @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) @ SY1114 ) @ SV564 ) ) ) ) )
= $true )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3537]) ).
thf(3605,plain,
! [SV478: $i,SV714: $i] :
( ( ( ! [SY1097: $i] :
( ~ ( subset @ SY1097 @ SV714 )
| ( in @ SY1097 @ ( sK3_SY300 @ SV714 @ SV478 ) ) ) )
= $true )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3538]) ).
thf(3606,plain,
! [SV478: $i,SV714: $i] :
( ( ( in @ ( sK3_SY300 @ SV714 @ SV478 ) @ ( sK2_B @ SV478 ) )
= $true )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3539]) ).
thf(3607,plain,
! [SV761: $i,SV478: $i,SV750: $i] :
( ( ~ ( in @ SV750 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SV761 @ SV750 )
| ( in @ SV761 @ ( sK2_B @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(3608,plain,
! [SV481: $i,SV686: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) ) )
= $false )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3541]) ).
thf(3609,plain,
! [SV481: $i,SV686: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) ) )
= $false )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3541]) ).
thf(3610,plain,
! [SV481: $i,SV687: $i] :
( ( ( ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1068 @ SY1067 ) @ SV481 ) )
| ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1070 @ SY1069 ) @ SV481 )
| ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV687 ) ) )
= $false )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3542]) ).
thf(3611,plain,
! [SV751: $i,SV728: $i,SV544: $i,SV482: $i] :
( ( ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV728 @ SV751 ) )
= $false )
| ( ( in @ SV482 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3544]) ).
thf(3612,plain,
! [SV742: $i,SV729: $i,SV544: $i,SV482: $i] :
( ( ( in @ ( ordered_pair @ SV482 @ SV544 ) @ ( cartesian_product2 @ SV729 @ SV742 ) )
= $false )
| ( ( in @ SV544 @ SV742 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3545]) ).
thf(3613,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) ) )
= $false )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3548]) ).
thf(3614,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) ) )
= $false )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3548]) ).
thf(3615,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 )
= $true )
| ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 )
= $true )
| ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3549]) ).
thf(3616,plain,
! [SV629: $i,SV485: $i,SV670: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV670 )
| ( in @ SV762 @ SV485 )
| ( in @ SV762 @ SV629 ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(3617,plain,
! [SV629: $i,SV670: $i,SV485: $i] :
( ( ( ~ ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) )
| ~ ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) )
= $false )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3551]) ).
thf(3618,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) )
| ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) ) )
= $false )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3552]) ).
thf(3619,plain,
! [SV730: $i,SV693: $i] :
( ( ( ~ ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV693 )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SY1102 ) )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) ) )
= $false )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3552]) ).
thf(3620,plain,
! [SV694: $i,SV731: $i] :
( ( ( ~ ! [SY1103: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SY1103 @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) ) )
| ( in @ SY1103 @ SV731 ) )
| ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV731 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV694 )
| ( in @ SY1104 @ SY1078 ) ) ) )
= $false )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3553]) ).
thf(3621,plain,
! [SV695: $i,SV743: $i] :
( ( ( SV743
= ( set_meet @ SV695 ) )
= $false )
| ( ( SV743 = empty_set )
= $true )
| ( ( SV695 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3554]) ).
thf(3622,plain,
! [SV696: $i,SV744: $i] :
( ( ( SV744 = empty_set )
= $false )
| ( ( SV744
= ( set_meet @ SV696 ) )
= $true )
| ( ( SV696 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3623,plain,
! [SV752: $i,SV577: $i,SV632: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV752 ) )
= $true )
| ( ( ~ ( in @ SV752 @ SV577 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3556]) ).
thf(3624,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) ) )
= $false )
| ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3557]) ).
thf(3625,plain,
! [SV577: $i,SV632: $i] :
( ( ( ~ ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 ) )
= $false )
| ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3557]) ).
thf(3626,plain,
! [SV633: $i,SV578: $i,SV753: $i] :
( ( ( ! [SY1116: $i] :
( ~ ( in @ SV753 @ SY1116 )
| ~ ( in @ SY1116 @ SV578 ) ) )
= $true )
| ( ( in @ SV753 @ SV633 )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3558]) ).
thf(3627,plain,
! [SV578: $i,SV633: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ SV633 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV754 @ ( sK16_D @ SV754 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SV754 @ SV633 @ SV578 ) @ SV578 ) ) )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(3628,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(3629,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) )
= $false )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3561]) ).
thf(3630,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) ) )
= $false )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3561]) ).
thf(3631,plain,
! [SV672: $i,SV635: $i,SV486: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV486 )
| ~ ( in @ SV763 @ SV635 )
| ( in @ SV763 @ SV672 ) )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(3632,plain,
! [SV635: $i,SV486: $i,SV672: $i] :
( ( ( ~ ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) )
| ~ ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) )
= $false )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3633,plain,
! [SV764: $i,SV487: $i,SV755: $i] :
( ( ~ ( in @ SV755 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SV764 @ SV755 )
| ( in @ SV764 @ ( sK32_B @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(3634,plain,
! [SV583: $i,SV637: $i] :
( ( ( subset @ ( sK28_C @ SV637 @ SV583 ) @ SV583 )
= $false )
| ( ( in @ ( sK28_C @ SV637 @ SV583 ) @ SV637 )
= $false )
| ( ( SV637
= ( powerset @ SV583 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3565]) ).
thf(3635,plain,
! [SV584: $i,SV638: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV638 ) )
= $true )
| ( ( subset @ SV756 @ SV584 )
= $true )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(3636,plain,
! [SV638: $i,SV584: $i,SV757: $i] :
( ( ( ~ ( subset @ SV757 @ SV584 ) )
= $true )
| ( ( in @ SV757 @ SV638 )
= $true )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3567]) ).
thf(3637,plain,
! [SV488: $i,SV698: $i] :
( ( ( ! [SY1081: $i] :
~ ( in @ ( ordered_pair @ SY1081 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 ) )
= $true )
| ( ( ~ ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) )
= $true )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3569]) ).
thf(3638,plain,
! [SV488: $i,SV698: $i] :
( ( ( in @ ( ordered_pair @ ( sK38_SY324 @ SV698 @ SV488 ) @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
= $true )
| ( ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 )
= $true )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(3639,plain,
! [SV699: $i,SV488: $i] :
( ( ( ! [SY1082: $i] :
( ! [SY861: $i] :
~ ( in @ ( ordered_pair @ SY861 @ SY1082 ) @ SV488 )
| ( in @ SY1082 @ SV699 ) ) )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3571]) ).
thf(3640,plain,
! [SV488: $i,SV699: $i] :
( ( ( ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV699 )
| ( in @ ( ordered_pair @ ( sK36_D @ SY1084 @ SV699 @ SV488 ) @ SY1084 ) @ SV488 ) ) )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3572]) ).
thf(3641,plain,
! [SV702: $i,SV745: $i] :
( ( ( element @ SV745 @ SV702 )
= $false )
| ( ( empty @ SV745 )
= $true )
| ( ( empty @ SV702 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3575]) ).
thf(3642,plain,
! [SV703: $i,SV746: $i] :
( ( ( empty @ SV746 )
= $false )
| ( ( element @ SV746 @ SV703 )
= $true )
| ( ( empty @ SV703 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3643,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) ) )
= $false )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3580]) ).
thf(3644,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) ) )
= $false )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3580]) ).
thf(3645,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV492 )
= $true )
| ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV649 )
= $true )
| ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3646,plain,
! [SV650: $i,SV492: $i,SV675: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ SV675 )
| ( SV765 = SV492 )
| ( SV765 = SV650 ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(3647,plain,
! [SV650: $i,SV675: $i,SV492: $i] :
( ( ( ~ ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) )
| ~ ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) )
= $false )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3583]) ).
thf(3648,plain,
! [SV758: $i,SV737: $i,SV547: $i,SV493: $i] :
( ( ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV737 @ SV758 ) )
= $false )
| ( ( in @ SV493 @ SV737 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3585]) ).
thf(3649,plain,
! [SV749: $i,SV738: $i,SV547: $i,SV493: $i] :
( ( ( in @ ( ordered_pair @ SV493 @ SV547 ) @ ( cartesian_product2 @ SV738 @ SV749 ) )
= $false )
| ( ( in @ SV547 @ SV749 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3650,plain,
! [SV604: $i,SV655: $i] :
( ( ( in @ ( sK29_C @ SV655 @ SV604 ) @ SV655 )
= $false )
| ( ( ( sK29_C @ SV655 @ SV604 )
= SV604 )
= $false )
| ( ( SV655
= ( singleton @ SV604 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3587]) ).
thf(3651,plain,
! [SV656: $i,SV605: $i,SV759: $i] :
( ( ( ( SV759 != SV605 ) )
= $true )
| ( ( in @ SV759 @ SV656 )
= $true )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3588]) ).
thf(3652,plain,
! [SV605: $i,SV656: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV656 ) )
= $true )
| ( ( SV760 = SV605 )
= $true )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3589]) ).
thf(3653,plain,
! [SV679: $i,SV658: $i,SV495: $i,SV766: $i] :
( ( ( ! [SY1118: $i] :
( ~ ( in @ SV766 @ SV495 )
| ~ ( in @ SY1118 @ SV658 )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SV766 @ SY1118 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(3654,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(3655,plain,
! [SV680: $i,SV767: $i,SV659: $i,SV495: $i] :
( ( ( ! [SY1119: $i,SY1120: $i] :
( ~ ( in @ SY1119 @ SV495 )
| ~ ( in @ SY1120 @ SV659 )
| ( SV767
!= ( ordered_pair @ SY1119 @ SY1120 ) ) )
| ( in @ SV767 @ SV680 ) )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(3656,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ SV680 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SV768
!= ( ordered_pair @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) ) ) ) )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3594]) ).
thf(3657,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 ) )
= $true )
| ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(3658,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) )
= $false )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3596]) ).
thf(3659,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) ) )
= $false )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3596]) ).
thf(3660,plain,
! [SV682: $i,SV663: $i,SV497: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV497 )
| ( in @ SV769 @ SV663 )
| ( in @ SV769 @ SV682 ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3597]) ).
thf(3661,plain,
! [SV663: $i,SV497: $i,SV682: $i] :
( ( ( ~ ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) )
| ~ ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) )
= $false )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3598]) ).
thf(3662,plain,
! [SV498: $i,SV712: $i] :
( ( ( ! [SY1093: $i] :
~ ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SY1093 ) @ SV498 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) )
= $true )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3599]) ).
thf(3663,plain,
! [SV498: $i,SV712: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ ( sK41_SY326 @ SV712 @ SV498 ) ) @ SV498 )
= $true )
| ( ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 )
= $true )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3600]) ).
thf(3664,plain,
! [SV713: $i,SV498: $i] :
( ( ( ! [SY1094: $i] :
( ! [SY909: $i] :
~ ( in @ ( ordered_pair @ SY1094 @ SY909 ) @ SV498 )
| ( in @ SY1094 @ SV713 ) ) )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3601]) ).
thf(3665,plain,
! [SV498: $i,SV713: $i] :
( ( ( ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV713 )
| ( in @ ( ordered_pair @ SY1096 @ ( sK39_D @ SY1096 @ SV713 @ SV498 ) ) @ SV498 ) ) )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3602]) ).
thf(3666,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( ~ ( ! [SY1109: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SY1109 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1109 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) ) ) )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3603]) ).
thf(3667,plain,
! [SV564: $i,SV477: $i,SV740: $i] :
( ( ( ( SV740
!= ( relation_composition @ SV477 @ SV564 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1110: $i,SY1111: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY1110 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY1111 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY1110 @ SY1111 ) @ SV740 ) )
| ~ ! [SY1113: $i,SY1114: $i] :
( ~ ( in @ ( ordered_pair @ SY1113 @ SY1114 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1113 @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) @ SY1114 ) @ SV564 ) ) ) ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3604]) ).
thf(3668,plain,
! [SV478: $i,SV714: $i,SV770: $i] :
( ( ( ~ ( subset @ SV770 @ SV714 )
| ( in @ SV770 @ ( sK3_SY300 @ SV714 @ SV478 ) ) )
= $true )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(3669,plain,
! [SV478: $i,SV714: $i] :
( ( ( in @ SV714 @ ( sK2_B @ SV478 ) )
= $false )
| ( ( in @ ( sK3_SY300 @ SV714 @ SV478 ) @ ( sK2_B @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3670,plain,
! [SV761: $i,SV478: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ ( sK2_B @ SV478 ) )
| ~ ( subset @ SV761 @ SV750 ) )
= $true )
| ( ( in @ SV761 @ ( sK2_B @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(3671,plain,
! [SV481: $i,SV686: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
= $true )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3608]) ).
thf(3672,plain,
! [SV481: $i,SV686: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
| ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
= $true )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3609]) ).
thf(3673,plain,
! [SV481: $i,SV687: $i] :
( ( ( ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1068 @ SY1067 ) @ SV481 ) ) )
= $false )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3610]) ).
thf(3674,plain,
! [SV687: $i,SV481: $i] :
( ( ( ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1070 @ SY1069 ) @ SV481 )
| ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV687 ) ) )
= $false )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3610]) ).
thf(3675,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3613]) ).
thf(3676,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
| ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3614]) ).
thf(3677,plain,
! [SV629: $i,SV485: $i,SV670: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV670 ) )
= $true )
| ( ( ( in @ SV762 @ SV485 )
| ( in @ SV762 @ SV629 ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(3678,plain,
! [SV629: $i,SV670: $i,SV485: $i] :
( ( ( ~ ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) ) )
= $false )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3617]) ).
thf(3679,plain,
! [SV485: $i,SV670: $i,SV629: $i] :
( ( ( ~ ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) )
= $false )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3617]) ).
thf(3680,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) )
| ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3618]) ).
thf(3681,plain,
! [SV730: $i,SV693: $i] :
( ( ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV693 )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SY1102 ) )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3619]) ).
thf(3682,plain,
! [SV694: $i,SV731: $i] :
( ( ( ~ ! [SY1103: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SY1103 @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) ) )
| ( in @ SY1103 @ SV731 ) ) )
= $false )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3620]) ).
thf(3683,plain,
! [SV694: $i,SV731: $i] :
( ( ( ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV731 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV694 )
| ( in @ SY1104 @ SY1078 ) ) ) )
= $false )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3620]) ).
thf(3684,plain,
! [SV752: $i,SV577: $i,SV632: $i] :
( ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV752 )
= $false )
| ( ( ~ ( in @ SV752 @ SV577 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3623]) ).
thf(3685,plain,
! [SV577: $i,SV632: $i] :
( ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ ( sK18_SY312 @ SV632 @ SV577 ) )
= $true )
| ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3624]) ).
thf(3686,plain,
! [SV577: $i,SV632: $i] :
( ( ( in @ ( sK18_SY312 @ SV632 @ SV577 ) @ SV577 )
= $true )
| ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3625]) ).
thf(3687,plain,
! [SV633: $i,SV578: $i,SV771: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ SV771 )
| ~ ( in @ SV771 @ SV578 ) )
= $true )
| ( ( in @ SV753 @ SV633 )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(3688,plain,
! [SV578: $i,SV633: $i,SV754: $i] :
( ( ( in @ SV754 @ SV633 )
= $false )
| ( ( ~ ( ~ ( in @ SV754 @ ( sK16_D @ SV754 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SV754 @ SV633 @ SV578 ) @ SV578 ) ) )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3689,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3628]) ).
thf(3690,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3629]) ).
thf(3691,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
| ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3630]) ).
thf(3692,plain,
! [SV672: $i,SV635: $i,SV486: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV486 )
| ~ ( in @ SV763 @ SV635 ) )
= $true )
| ( ( in @ SV763 @ SV672 )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(3693,plain,
! [SV635: $i,SV486: $i,SV672: $i] :
( ( ( ~ ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) ) )
= $false )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3632]) ).
thf(3694,plain,
! [SV486: $i,SV635: $i,SV672: $i] :
( ( ( ~ ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) )
= $false )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3632]) ).
thf(3695,plain,
! [SV764: $i,SV487: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ ( sK32_B @ SV487 ) )
| ~ ( subset @ SV764 @ SV755 ) )
= $true )
| ( ( in @ SV764 @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(3696,plain,
! [SV584: $i,SV638: $i,SV756: $i] :
( ( ( in @ SV756 @ SV638 )
= $false )
| ( ( subset @ SV756 @ SV584 )
= $true )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(3697,plain,
! [SV638: $i,SV584: $i,SV757: $i] :
( ( ( subset @ SV757 @ SV584 )
= $false )
| ( ( in @ SV757 @ SV638 )
= $true )
| ( ( SV638
= ( powerset @ SV584 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3636]) ).
thf(3698,plain,
! [SV488: $i,SV698: $i,SV772: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV772 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 ) )
= $true )
| ( ( ~ ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) )
= $true )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(3699,plain,
! [SV699: $i,SV488: $i,SV773: $i] :
( ( ( ! [SY1121: $i] :
~ ( in @ ( ordered_pair @ SY1121 @ SV773 ) @ SV488 )
| ( in @ SV773 @ SV699 ) )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(3700,plain,
! [SV488: $i,SV699: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV699 )
| ( in @ ( ordered_pair @ ( sK36_D @ SV774 @ SV699 @ SV488 ) @ SV774 ) @ SV488 ) )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(3701,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3643]) ).
thf(3702,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
| ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3644]) ).
thf(3703,plain,
! [SV650: $i,SV492: $i,SV675: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ SV675 ) )
= $true )
| ( ( ( SV765 = SV492 )
| ( SV765 = SV650 ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3646]) ).
thf(3704,plain,
! [SV650: $i,SV675: $i,SV492: $i] :
( ( ( ~ ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) ) )
= $false )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3647]) ).
thf(3705,plain,
! [SV492: $i,SV675: $i,SV650: $i] :
( ( ( ~ ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) )
= $false )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3647]) ).
thf(3706,plain,
! [SV656: $i,SV605: $i,SV759: $i] :
( ( ( SV759 = SV605 )
= $false )
| ( ( in @ SV759 @ SV656 )
= $true )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3651]) ).
thf(3707,plain,
! [SV605: $i,SV656: $i,SV760: $i] :
( ( ( in @ SV760 @ SV656 )
= $false )
| ( ( SV760 = SV605 )
= $true )
| ( ( SV656
= ( singleton @ SV605 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3708,plain,
! [SV679: $i,SV658: $i,SV775: $i,SV495: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV495 )
| ~ ( in @ SV775 @ SV658 )
| ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SV766 @ SV775 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(3709,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3654]) ).
thf(3710,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3654]) ).
thf(3711,plain,
! [SV680: $i,SV767: $i,SV659: $i,SV495: $i] :
( ( ( ! [SY1119: $i,SY1120: $i] :
( ~ ( in @ SY1119 @ SV495 )
| ~ ( in @ SY1120 @ SV659 )
| ( SV767
!= ( ordered_pair @ SY1119 @ SY1120 ) ) ) )
= $true )
| ( ( in @ SV767 @ SV680 )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(3712,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ SV680 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SV768
!= ( ordered_pair @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) ) ) ) )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(3713,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
= $false )
| ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3714,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3658]) ).
thf(3715,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
| ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 ) )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3659]) ).
thf(3716,plain,
! [SV682: $i,SV663: $i,SV497: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV497 )
| ( in @ SV769 @ SV663 ) )
= $true )
| ( ( in @ SV769 @ SV682 )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3660]) ).
thf(3717,plain,
! [SV663: $i,SV497: $i,SV682: $i] :
( ( ( ~ ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) ) )
= $false )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3661]) ).
thf(3718,plain,
! [SV497: $i,SV663: $i,SV682: $i] :
( ( ( ~ ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) )
= $false )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3661]) ).
thf(3719,plain,
! [SV776: $i,SV498: $i,SV712: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SV776 ) @ SV498 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) )
= $true )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(3720,plain,
! [SV713: $i,SV498: $i,SV777: $i] :
( ( ( ! [SY1122: $i] :
~ ( in @ ( ordered_pair @ SV777 @ SY1122 ) @ SV498 )
| ( in @ SV777 @ SV713 ) )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(3721,plain,
! [SV498: $i,SV713: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ SV713 )
| ( in @ ( ordered_pair @ SV778 @ ( sK39_D @ SV778 @ SV713 @ SV498 ) ) @ SV498 ) )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(3722,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( ! [SY1109: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SY1109 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1109 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) ) )
= $false )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3666]) ).
thf(3723,plain,
! [SV564: $i,SV477: $i,SV740: $i] :
( ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( ~ ( ~ ! [SY1110: $i,SY1111: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY1110 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY1111 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY1110 @ SY1111 ) @ SV740 ) )
| ~ ! [SY1113: $i,SY1114: $i] :
( ~ ( in @ ( ordered_pair @ SY1113 @ SY1114 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1113 @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) @ SY1114 ) @ SV564 ) ) ) ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3667]) ).
thf(3724,plain,
! [SV478: $i,SV714: $i,SV770: $i] :
( ( ( ~ ( subset @ SV770 @ SV714 ) )
= $true )
| ( ( in @ SV770 @ ( sK3_SY300 @ SV714 @ SV478 ) )
= $true )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(3725,plain,
! [SV761: $i,SV478: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ ( sK2_B @ SV478 ) ) )
= $true )
| ( ( ~ ( subset @ SV761 @ SV750 ) )
= $true )
| ( ( in @ SV761 @ ( sK2_B @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3670]) ).
thf(3726,plain,
! [SV481: $i,SV686: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
= $true )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3671]) ).
thf(3727,plain,
! [SV481: $i,SV686: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 )
= $true )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3672]) ).
thf(3728,plain,
! [SV481: $i,SV687: $i] :
( ( ( ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1068 @ SY1067 ) @ SV481 ) ) )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3673]) ).
thf(3729,plain,
! [SV687: $i,SV481: $i] :
( ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1070 @ SY1069 ) @ SV481 )
| ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV687 ) ) )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3674]) ).
thf(3730,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3675]) ).
thf(3731,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3676]) ).
thf(3732,plain,
! [SV629: $i,SV485: $i,SV670: $i,SV762: $i] :
( ( ( in @ SV762 @ SV670 )
= $false )
| ( ( ( in @ SV762 @ SV485 )
| ( in @ SV762 @ SV629 ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3677]) ).
thf(3733,plain,
! [SV629: $i,SV670: $i,SV485: $i] :
( ( ( ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV485 )
| ( in @ SY1047 @ SV670 ) ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(3734,plain,
! [SV485: $i,SV670: $i,SV629: $i] :
( ( ( ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV629 )
| ( in @ SY1048 @ SV670 ) ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3679]) ).
thf(3735,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(3736,plain,
! [SV730: $i,SV693: $i] :
( ( ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV693 )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SY1102 ) ) )
= $true )
| ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(3737,plain,
! [SV694: $i,SV731: $i] :
( ( ( ! [SY1103: $i] :
( ~ ( ~ ( in @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SY1103 @ ( sK43_D @ SY1103 @ SV731 @ SV694 ) ) )
| ( in @ SY1103 @ SV731 ) ) )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3682]) ).
thf(3738,plain,
! [SV694: $i,SV731: $i] :
( ( ( ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV731 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV694 )
| ( in @ SY1104 @ SY1078 ) ) ) )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3683]) ).
thf(3739,plain,
! [SV632: $i,SV577: $i,SV752: $i] :
( ( ( in @ SV752 @ SV577 )
= $false )
| ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV752 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 ) )
= $true )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(3740,plain,
! [SV633: $i,SV578: $i,SV771: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ SV771 ) )
= $true )
| ( ( ~ ( in @ SV771 @ SV578 ) )
= $true )
| ( ( in @ SV753 @ SV633 )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3687]) ).
thf(3741,plain,
! [SV578: $i,SV633: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( sK16_D @ SV754 @ SV633 @ SV578 ) )
| ~ ( in @ ( sK16_D @ SV754 @ SV633 @ SV578 ) @ SV578 ) )
= $false )
| ( ( in @ SV754 @ SV633 )
= $false )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3688]) ).
thf(3742,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
= $false )
| ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 ) )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3689]) ).
thf(3743,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
= $true )
| ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3690]) ).
thf(3744,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
= $true )
| ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 )
= $true )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3691]) ).
thf(3745,plain,
! [SV672: $i,SV635: $i,SV486: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV486 ) )
= $true )
| ( ( ~ ( in @ SV763 @ SV635 ) )
= $true )
| ( ( in @ SV763 @ SV672 )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(3746,plain,
! [SV635: $i,SV486: $i,SV672: $i] :
( ( ( ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV672 )
| ( in @ SY1050 @ SV486 ) ) )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3693]) ).
thf(3747,plain,
! [SV486: $i,SV635: $i,SV672: $i] :
( ( ( ! [SY1051: $i] :
( ~ ( in @ SY1051 @ SV672 )
| ( in @ SY1051 @ SV635 ) ) )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3694]) ).
thf(3748,plain,
! [SV764: $i,SV487: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ ( sK32_B @ SV487 ) ) )
= $true )
| ( ( ~ ( subset @ SV764 @ SV755 ) )
= $true )
| ( ( in @ SV764 @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(3749,plain,
! [SV488: $i,SV698: $i,SV772: $i] :
( ( ( in @ ( ordered_pair @ SV772 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
= $false )
| ( ( ~ ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 ) )
= $true )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3750,plain,
! [SV699: $i,SV488: $i,SV773: $i] :
( ( ( ! [SY1121: $i] :
~ ( in @ ( ordered_pair @ SY1121 @ SV773 ) @ SV488 ) )
= $true )
| ( ( in @ SV773 @ SV699 )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3699]) ).
thf(3751,plain,
! [SV488: $i,SV699: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV699 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK36_D @ SV774 @ SV699 @ SV488 ) @ SV774 ) @ SV488 )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3700]) ).
thf(3752,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 ) )
= $true )
| ( ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(3753,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 ) )
= $true )
| ( ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3702]) ).
thf(3754,plain,
! [SV650: $i,SV492: $i,SV675: $i,SV765: $i] :
( ( ( in @ SV765 @ SV675 )
= $false )
| ( ( ( SV765 = SV492 )
| ( SV765 = SV650 ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(3755,plain,
! [SV650: $i,SV675: $i,SV492: $i] :
( ( ( ! [SY1053: $i] :
( ( SY1053 != SV492 )
| ( in @ SY1053 @ SV675 ) ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3704]) ).
thf(3756,plain,
! [SV492: $i,SV675: $i,SV650: $i] :
( ( ( ! [SY1054: $i] :
( ( SY1054 != SV650 )
| ( in @ SY1054 @ SV675 ) ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3705]) ).
thf(3757,plain,
! [SV679: $i,SV658: $i,SV775: $i,SV495: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV495 )
| ~ ( in @ SV775 @ SV658 ) )
= $true )
| ( ( ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SV766 @ SV775 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3708]) ).
thf(3758,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3709]) ).
thf(3759,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ( sK23_D @ SV679 @ SV658 @ SV495 )
= ( ordered_pair @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3710]) ).
thf(3760,plain,
! [SV680: $i,SV767: $i,SV659: $i,SV495: $i,SV779: $i] :
( ( ( ! [SY1123: $i] :
( ~ ( in @ SV779 @ SV495 )
| ~ ( in @ SY1123 @ SV659 )
| ( SV767
!= ( ordered_pair @ SV779 @ SY1123 ) ) ) )
= $true )
| ( ( in @ SV767 @ SV680 )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(3761,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( in @ SV768 @ SV680 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SV768
!= ( ordered_pair @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) ) ) ) )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(3762,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 )
= $false )
| ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
= $true )
| ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
= $false )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3763,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV497 )
= $true )
| ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3714]) ).
thf(3764,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 ) )
= $true )
| ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3715]) ).
thf(3765,plain,
! [SV682: $i,SV663: $i,SV497: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV497 ) )
= $true )
| ( ( in @ SV769 @ SV663 )
= $true )
| ( ( in @ SV769 @ SV682 )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3716]) ).
thf(3766,plain,
! [SV663: $i,SV497: $i,SV682: $i] :
( ( ( ! [SY1063: $i] :
( ~ ( in @ SY1063 @ SV682 )
| ( in @ SY1063 @ SV497 ) ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3717]) ).
thf(3767,plain,
! [SV497: $i,SV663: $i,SV682: $i] :
( ( ( ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV682 )
| ~ ( in @ SY1064 @ SV663 ) ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3718]) ).
thf(3768,plain,
! [SV776: $i,SV498: $i,SV712: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SV776 ) @ SV498 )
= $false )
| ( ( ~ ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 ) )
= $true )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3719]) ).
thf(3769,plain,
! [SV713: $i,SV498: $i,SV777: $i] :
( ( ( ! [SY1122: $i] :
~ ( in @ ( ordered_pair @ SV777 @ SY1122 ) @ SV498 ) )
= $true )
| ( ( in @ SV777 @ SV713 )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3720]) ).
thf(3770,plain,
! [SV498: $i,SV713: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ SV713 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV778 @ ( sK39_D @ SV778 @ SV713 @ SV498 ) ) @ SV498 )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3721]) ).
thf(3771,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( ! [SY1109: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SY1109 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1109 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) ) )
= $false )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3722]) ).
thf(3772,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) ) )
= $false )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3722]) ).
thf(3773,plain,
! [SV740: $i,SV564: $i,SV477: $i] :
( ( ( ~ ! [SY1110: $i,SY1111: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY1110 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY1111 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY1110 @ SY1111 ) @ SV740 ) )
| ~ ! [SY1113: $i,SY1114: $i] :
( ~ ( in @ ( ordered_pair @ SY1113 @ SY1114 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1113 @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) @ SY1114 ) @ SV564 ) ) ) )
= $false )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3723]) ).
thf(3774,plain,
! [SV478: $i,SV714: $i,SV770: $i] :
( ( ( subset @ SV770 @ SV714 )
= $false )
| ( ( in @ SV770 @ ( sK3_SY300 @ SV714 @ SV478 ) )
= $true )
| ( ( ~ ( in @ SV714 @ ( sK2_B @ SV478 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3724]) ).
thf(3775,plain,
! [SV761: $i,SV478: $i,SV750: $i] :
( ( ( in @ SV750 @ ( sK2_B @ SV478 ) )
= $false )
| ( ( ~ ( subset @ SV761 @ SV750 ) )
= $true )
| ( ( in @ SV761 @ ( sK2_B @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(3776,plain,
! [SV481: $i,SV686: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 ) )
= $true )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3726]) ).
thf(3777,plain,
! [SV481: $i,SV687: $i,SV780: $i] :
( ( ( ! [SY1124: $i] :
( ~ ( in @ ( ordered_pair @ SV780 @ SY1124 ) @ SV687 )
| ( in @ ( ordered_pair @ SY1124 @ SV780 ) @ SV481 ) ) )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(3778,plain,
! [SV687: $i,SV481: $i,SV781: $i] :
( ( ( ! [SY1125: $i] :
( ~ ( in @ ( ordered_pair @ SY1125 @ SV781 ) @ SV481 )
| ( in @ ( ordered_pair @ SV781 @ SY1125 ) @ SV687 ) ) )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(3779,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3730]) ).
thf(3780,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 ) )
= $true )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3731]) ).
thf(3781,plain,
! [SV670: $i,SV629: $i,SV485: $i,SV762: $i] :
( ( ( in @ SV762 @ SV485 )
= $true )
| ( ( in @ SV762 @ SV629 )
= $true )
| ( ( in @ SV762 @ SV670 )
= $false )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3732]) ).
thf(3782,plain,
! [SV629: $i,SV670: $i,SV485: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ SV485 )
| ( in @ SV782 @ SV670 ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(3783,plain,
! [SV485: $i,SV670: $i,SV629: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ SV629 )
| ( in @ SV783 @ SV670 ) )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(3784,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
| ~ ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3735]) ).
thf(3785,plain,
! [SV730: $i,SV693: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ SV693 )
| ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV784 ) )
= $true )
| ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(3786,plain,
! [SV694: $i,SV731: $i,SV785: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_D @ SV785 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SV785 @ ( sK43_D @ SV785 @ SV731 @ SV694 ) ) )
| ( in @ SV785 @ SV731 ) )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(3787,plain,
! [SV694: $i,SV731: $i,SV786: $i] :
( ( ( ~ ( in @ SV786 @ SV731 )
| ! [SY1126: $i] :
( ~ ( in @ SY1126 @ SV694 )
| ( in @ SV786 @ SY1126 ) ) )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(3788,plain,
! [SV752: $i,SV577: $i,SV632: $i] :
( ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV632 )
= $false )
| ( ( in @ ( sK17_C @ SV632 @ SV577 ) @ SV752 )
= $false )
| ( ( in @ SV752 @ SV577 )
= $false )
| ( ( SV632
= ( union @ SV577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3739]) ).
thf(3789,plain,
! [SV633: $i,SV578: $i,SV771: $i,SV753: $i] :
( ( ( in @ SV753 @ SV771 )
= $false )
| ( ( ~ ( in @ SV771 @ SV578 ) )
= $true )
| ( ( in @ SV753 @ SV633 )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3740]) ).
thf(3790,plain,
! [SV578: $i,SV633: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( sK16_D @ SV754 @ SV633 @ SV578 ) ) )
= $false )
| ( ( in @ SV754 @ SV633 )
= $false )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3741]) ).
thf(3791,plain,
! [SV578: $i,SV633: $i,SV754: $i] :
( ( ( ~ ( in @ ( sK16_D @ SV754 @ SV633 @ SV578 ) @ SV578 ) )
= $false )
| ( ( in @ SV754 @ SV633 )
= $false )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3741]) ).
thf(3792,plain,
! [SV486: $i,SV634: $i,SV671: $i] :
( ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV671 )
= $false )
| ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV486 )
= $false )
| ( ( in @ ( sK19_D @ SV671 @ SV634 @ SV486 ) @ SV634 )
= $false )
| ( ( SV671
= ( set_intersection2 @ SV486 @ SV634 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3742]) ).
thf(3793,plain,
! [SV672: $i,SV635: $i,SV486: $i,SV763: $i] :
( ( ( in @ SV763 @ SV486 )
= $false )
| ( ( ~ ( in @ SV763 @ SV635 ) )
= $true )
| ( ( in @ SV763 @ SV672 )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(3794,plain,
! [SV635: $i,SV486: $i,SV672: $i,SV787: $i] :
( ( ( ~ ( in @ SV787 @ SV672 )
| ( in @ SV787 @ SV486 ) )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(3795,plain,
! [SV486: $i,SV635: $i,SV672: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ SV672 )
| ( in @ SV788 @ SV635 ) )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(3796,plain,
! [SV764: $i,SV487: $i,SV755: $i] :
( ( ( in @ SV755 @ ( sK32_B @ SV487 ) )
= $false )
| ( ( ~ ( subset @ SV764 @ SV755 ) )
= $true )
| ( ( in @ SV764 @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3748]) ).
thf(3797,plain,
! [SV772: $i,SV488: $i,SV698: $i] :
( ( ( in @ ( sK37_C @ SV698 @ SV488 ) @ SV698 )
= $false )
| ( ( in @ ( ordered_pair @ SV772 @ ( sK37_C @ SV698 @ SV488 ) ) @ SV488 )
= $false )
| ( ( SV698
= ( relation_rng @ SV488 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(3798,plain,
! [SV699: $i,SV488: $i,SV773: $i,SV789: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV789 @ SV773 ) @ SV488 ) )
= $true )
| ( ( in @ SV773 @ SV699 )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3750]) ).
thf(3799,plain,
! [SV488: $i,SV699: $i,SV774: $i] :
( ( ( in @ SV774 @ SV699 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK36_D @ SV774 @ SV699 @ SV488 ) @ SV774 ) @ SV488 )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(3800,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
= $false )
| ( ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV492 ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3801,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
= $false )
| ( ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
!= SV649 ) )
= $true )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(3802,plain,
! [SV675: $i,SV650: $i,SV492: $i,SV765: $i] :
( ( ( SV765 = SV492 )
= $true )
| ( ( SV765 = SV650 )
= $true )
| ( ( in @ SV765 @ SV675 )
= $false )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3754]) ).
thf(3803,plain,
! [SV650: $i,SV675: $i,SV492: $i,SV790: $i] :
( ( ( ( SV790 != SV492 )
| ( in @ SV790 @ SV675 ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3755]) ).
thf(3804,plain,
! [SV492: $i,SV675: $i,SV650: $i,SV791: $i] :
( ( ( ( SV791 != SV650 )
| ( in @ SV791 @ SV675 ) )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3756]) ).
thf(3805,plain,
! [SV679: $i,SV658: $i,SV775: $i,SV495: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV495 ) )
= $true )
| ( ( ~ ( in @ SV775 @ SV658 ) )
= $true )
| ( ( ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SV766 @ SV775 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(3806,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
= $false )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(3807,plain,
! [SV680: $i,SV767: $i,SV659: $i,SV792: $i,SV495: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ SV495 )
| ~ ( in @ SV792 @ SV659 )
| ( SV767
!= ( ordered_pair @ SV779 @ SV792 ) ) )
= $true )
| ( ( in @ SV767 @ SV680 )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(3808,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
| ( SV768
!= ( ordered_pair @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) ) ) )
= $false )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3809,plain,
! [SV497: $i,SV662: $i,SV681: $i] :
( ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV662 )
= $false )
| ( ( in @ ( sK15_D @ SV681 @ SV662 @ SV497 ) @ SV681 )
= $true )
| ( ( SV681
= ( set_difference @ SV497 @ SV662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(3810,plain,
! [SV682: $i,SV663: $i,SV497: $i,SV769: $i] :
( ( ( in @ SV769 @ SV497 )
= $false )
| ( ( in @ SV769 @ SV663 )
= $true )
| ( ( in @ SV769 @ SV682 )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3765]) ).
thf(3811,plain,
! [SV663: $i,SV497: $i,SV682: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ SV682 )
| ( in @ SV793 @ SV497 ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3766]) ).
thf(3812,plain,
! [SV497: $i,SV663: $i,SV682: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV682 )
| ~ ( in @ SV794 @ SV663 ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(3813,plain,
! [SV776: $i,SV498: $i,SV712: $i] :
( ( ( in @ ( sK40_C @ SV712 @ SV498 ) @ SV712 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK40_C @ SV712 @ SV498 ) @ SV776 ) @ SV498 )
= $false )
| ( ( SV712
= ( relation_dom @ SV498 ) )
= $true )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(3814,plain,
! [SV713: $i,SV498: $i,SV795: $i,SV777: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV777 @ SV795 ) @ SV498 ) )
= $true )
| ( ( in @ SV777 @ SV713 )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3769]) ).
thf(3815,plain,
! [SV498: $i,SV713: $i,SV778: $i] :
( ( ( in @ SV778 @ SV713 )
= $false )
| ( ( in @ ( ordered_pair @ SV778 @ ( sK39_D @ SV778 @ SV713 @ SV498 ) ) @ SV498 )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3816,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ! [SY1109: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SY1109 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1109 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3771]) ).
thf(3817,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3772]) ).
thf(3818,plain,
! [SV740: $i,SV564: $i,SV477: $i] :
( ( ( ~ ! [SY1110: $i,SY1111: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY1110 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY1111 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY1110 @ SY1111 ) @ SV740 ) ) )
= $false )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3773]) ).
thf(3819,plain,
! [SV477: $i,SV564: $i,SV740: $i] :
( ( ( ~ ! [SY1113: $i,SY1114: $i] :
( ~ ( in @ ( ordered_pair @ SY1113 @ SY1114 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1113 @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) @ SY1114 ) @ SV564 ) ) ) )
= $false )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3773]) ).
thf(3820,plain,
! [SV770: $i,SV478: $i,SV714: $i] :
( ( ( in @ SV714 @ ( sK2_B @ SV478 ) )
= $false )
| ( ( in @ SV770 @ ( sK3_SY300 @ SV714 @ SV478 ) )
= $true )
| ( ( subset @ SV770 @ SV714 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(3821,plain,
! [SV478: $i,SV750: $i,SV761: $i] :
( ( ( subset @ SV761 @ SV750 )
= $false )
| ( ( in @ SV750 @ ( sK2_B @ SV478 ) )
= $false )
| ( ( in @ SV761 @ ( sK2_B @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(3822,plain,
! [SV481: $i,SV686: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY310 @ SV686 @ SV481 ) @ ( sK13_C @ SV686 @ SV481 ) ) @ SV481 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_C @ SV686 @ SV481 ) @ ( sK14_SY310 @ SV686 @ SV481 ) ) @ SV686 )
= $false )
| ( ( SV686
= ( relation_inverse @ SV481 ) )
= $true )
| ( ( relation @ SV686 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3823,plain,
! [SV481: $i,SV687: $i,SV796: $i,SV780: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV780 @ SV796 ) @ SV687 )
| ( in @ ( ordered_pair @ SV796 @ SV780 ) @ SV481 ) )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3777]) ).
thf(3824,plain,
! [SV687: $i,SV481: $i,SV781: $i,SV797: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV797 @ SV781 ) @ SV481 )
| ( in @ ( ordered_pair @ SV781 @ SV797 ) @ SV687 ) )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3778]) ).
thf(3825,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV485 )
= $false )
| ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
= $false )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3779]) ).
thf(3826,plain,
! [SV485: $i,SV628: $i,SV669: $i] :
( ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV628 )
= $false )
| ( ( in @ ( sK26_D @ SV669 @ SV628 @ SV485 ) @ SV669 )
= $false )
| ( ( SV669
= ( set_union2 @ SV485 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3780]) ).
thf(3827,plain,
! [SV629: $i,SV670: $i,SV485: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ SV485 ) )
= $true )
| ( ( in @ SV782 @ SV670 )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3782]) ).
thf(3828,plain,
! [SV485: $i,SV670: $i,SV629: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ SV629 ) )
= $true )
| ( ( in @ SV783 @ SV670 )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3783]) ).
thf(3829,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3784]) ).
thf(3830,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3784]) ).
thf(3831,plain,
! [SV730: $i,SV693: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ SV693 ) )
= $true )
| ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV784 )
= $true )
| ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(3832,plain,
! [SV694: $i,SV731: $i,SV785: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_D @ SV785 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SV785 @ ( sK43_D @ SV785 @ SV731 @ SV694 ) ) ) )
= $true )
| ( ( in @ SV785 @ SV731 )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3786]) ).
thf(3833,plain,
! [SV694: $i,SV731: $i,SV786: $i] :
( ( ( ~ ( in @ SV786 @ SV731 ) )
= $true )
| ( ( ! [SY1126: $i] :
( ~ ( in @ SY1126 @ SV694 )
| ( in @ SV786 @ SY1126 ) ) )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3787]) ).
thf(3834,plain,
! [SV633: $i,SV753: $i,SV578: $i,SV771: $i] :
( ( ( in @ SV771 @ SV578 )
= $false )
| ( ( in @ SV753 @ SV771 )
= $false )
| ( ( in @ SV753 @ SV633 )
= $true )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(3835,plain,
! [SV578: $i,SV633: $i,SV754: $i] :
( ( ( in @ SV754 @ ( sK16_D @ SV754 @ SV633 @ SV578 ) )
= $true )
| ( ( in @ SV754 @ SV633 )
= $false )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3790]) ).
thf(3836,plain,
! [SV578: $i,SV633: $i,SV754: $i] :
( ( ( in @ ( sK16_D @ SV754 @ SV633 @ SV578 ) @ SV578 )
= $true )
| ( ( in @ SV754 @ SV633 )
= $false )
| ( ( SV633
= ( union @ SV578 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3791]) ).
thf(3837,plain,
! [SV672: $i,SV486: $i,SV635: $i,SV763: $i] :
( ( ( in @ SV763 @ SV635 )
= $false )
| ( ( in @ SV763 @ SV486 )
= $false )
| ( ( in @ SV763 @ SV672 )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(3838,plain,
! [SV635: $i,SV486: $i,SV672: $i,SV787: $i] :
( ( ( ~ ( in @ SV787 @ SV672 ) )
= $true )
| ( ( in @ SV787 @ SV486 )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3794]) ).
thf(3839,plain,
! [SV486: $i,SV635: $i,SV672: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ SV672 ) )
= $true )
| ( ( in @ SV788 @ SV635 )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3795]) ).
thf(3840,plain,
! [SV487: $i,SV755: $i,SV764: $i] :
( ( ( subset @ SV764 @ SV755 )
= $false )
| ( ( in @ SV755 @ ( sK32_B @ SV487 ) )
= $false )
| ( ( in @ SV764 @ ( sK32_B @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3796]) ).
thf(3841,plain,
! [SV699: $i,SV488: $i,SV773: $i,SV789: $i] :
( ( ( in @ ( ordered_pair @ SV789 @ SV773 ) @ SV488 )
= $false )
| ( ( in @ SV773 @ SV699 )
= $true )
| ( ( SV699
= ( relation_rng @ SV488 ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(3842,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV492 )
= $false )
| ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
= $false )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3800]) ).
thf(3843,plain,
! [SV492: $i,SV649: $i,SV674: $i] :
( ( ( ( sK27_D @ SV674 @ SV649 @ SV492 )
= SV649 )
= $false )
| ( ( in @ ( sK27_D @ SV674 @ SV649 @ SV492 ) @ SV674 )
= $false )
| ( ( SV674
= ( unordered_pair @ SV492 @ SV649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(3844,plain,
! [SV650: $i,SV675: $i,SV492: $i,SV790: $i] :
( ( ( ( SV790 != SV492 ) )
= $true )
| ( ( in @ SV790 @ SV675 )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(3845,plain,
! [SV492: $i,SV675: $i,SV650: $i,SV791: $i] :
( ( ( ( SV791 != SV650 ) )
= $true )
| ( ( in @ SV791 @ SV675 )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3804]) ).
thf(3846,plain,
! [SV679: $i,SV658: $i,SV775: $i,SV495: $i,SV766: $i] :
( ( ( in @ SV766 @ SV495 )
= $false )
| ( ( ~ ( in @ SV775 @ SV658 ) )
= $true )
| ( ( ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SV766 @ SV775 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(3847,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 ) )
= $false )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3806]) ).
thf(3848,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( ~ ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 ) )
= $false )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3806]) ).
thf(3849,plain,
! [SV680: $i,SV767: $i,SV659: $i,SV792: $i,SV495: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ SV495 )
| ~ ( in @ SV792 @ SV659 ) )
= $true )
| ( ( ( SV767
!= ( ordered_pair @ SV779 @ SV792 ) ) )
= $true )
| ( ( in @ SV767 @ SV680 )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(3850,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 ) ) )
= $false )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3808]) ).
thf(3851,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ( SV768
!= ( ordered_pair @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) ) ) )
= $false )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3808]) ).
thf(3852,plain,
! [SV663: $i,SV497: $i,SV682: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ SV682 ) )
= $true )
| ( ( in @ SV793 @ SV497 )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3811]) ).
thf(3853,plain,
! [SV497: $i,SV663: $i,SV682: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV682 ) )
= $true )
| ( ( ~ ( in @ SV794 @ SV663 ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3812]) ).
thf(3854,plain,
! [SV713: $i,SV498: $i,SV795: $i,SV777: $i] :
( ( ( in @ ( ordered_pair @ SV777 @ SV795 ) @ SV498 )
= $false )
| ( ( in @ SV777 @ SV713 )
= $true )
| ( ( SV713
= ( relation_dom @ SV498 ) )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(3855,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ! [SY1109: $i] :
( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SY1109 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1109 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3816]) ).
thf(3856,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(3857,plain,
! [SV740: $i,SV564: $i,SV477: $i] :
( ( ( ! [SY1110: $i,SY1111: $i] :
( ! [SY947: $i] :
( ~ ( in @ ( ordered_pair @ SY1110 @ SY947 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY947 @ SY1111 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SY1110 @ SY1111 ) @ SV740 ) ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3818]) ).
thf(3858,plain,
! [SV477: $i,SV564: $i,SV740: $i] :
( ( ( ! [SY1113: $i,SY1114: $i] :
( ~ ( in @ ( ordered_pair @ SY1113 @ SY1114 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1113 @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1114 @ SY1113 @ SV740 @ SV564 @ SV477 ) @ SY1114 ) @ SV564 ) ) ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3819]) ).
thf(3859,plain,
! [SV481: $i,SV687: $i,SV796: $i,SV780: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV780 @ SV796 ) @ SV687 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV796 @ SV780 ) @ SV481 )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3823]) ).
thf(3860,plain,
! [SV687: $i,SV481: $i,SV781: $i,SV797: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV797 @ SV781 ) @ SV481 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV781 @ SV797 ) @ SV687 )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(3861,plain,
! [SV629: $i,SV670: $i,SV485: $i,SV782: $i] :
( ( ( in @ SV782 @ SV485 )
= $false )
| ( ( in @ SV782 @ SV670 )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3827]) ).
thf(3862,plain,
! [SV485: $i,SV670: $i,SV629: $i,SV783: $i] :
( ( ( in @ SV783 @ SV629 )
= $false )
| ( ( in @ SV783 @ SV670 )
= $true )
| ( ( SV670
= ( set_union2 @ SV485 @ SV629 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(3863,plain,
! [SV693: $i,SV730: $i] :
( ( ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3829]) ).
thf(3864,plain,
! [SV693: $i,SV730: $i] :
( ( ( ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3830]) ).
thf(3865,plain,
! [SV730: $i,SV693: $i,SV784: $i] :
( ( ( in @ SV784 @ SV693 )
= $false )
| ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV784 )
= $true )
| ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(3866,plain,
! [SV694: $i,SV731: $i,SV785: $i] :
( ( ( ~ ( in @ ( sK43_D @ SV785 @ SV731 @ SV694 ) @ SV694 )
| ~ ~ ( in @ SV785 @ ( sK43_D @ SV785 @ SV731 @ SV694 ) ) )
= $false )
| ( ( in @ SV785 @ SV731 )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3832]) ).
thf(3867,plain,
! [SV694: $i,SV731: $i,SV786: $i] :
( ( ( in @ SV786 @ SV731 )
= $false )
| ( ( ! [SY1126: $i] :
( ~ ( in @ SY1126 @ SV694 )
| ( in @ SV786 @ SY1126 ) ) )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3833]) ).
thf(3868,plain,
! [SV635: $i,SV486: $i,SV672: $i,SV787: $i] :
( ( ( in @ SV787 @ SV672 )
= $false )
| ( ( in @ SV787 @ SV486 )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(3869,plain,
! [SV486: $i,SV635: $i,SV672: $i,SV788: $i] :
( ( ( in @ SV788 @ SV672 )
= $false )
| ( ( in @ SV788 @ SV635 )
= $true )
| ( ( SV672
= ( set_intersection2 @ SV486 @ SV635 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3839]) ).
thf(3870,plain,
! [SV650: $i,SV675: $i,SV492: $i,SV790: $i] :
( ( ( SV790 = SV492 )
= $false )
| ( ( in @ SV790 @ SV675 )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(3871,plain,
! [SV492: $i,SV675: $i,SV650: $i,SV791: $i] :
( ( ( SV791 = SV650 )
= $false )
| ( ( in @ SV791 @ SV675 )
= $true )
| ( ( SV675
= ( unordered_pair @ SV492 @ SV650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(3872,plain,
! [SV679: $i,SV495: $i,SV766: $i,SV658: $i,SV775: $i] :
( ( ( in @ SV775 @ SV658 )
= $false )
| ( ( in @ SV766 @ SV495 )
= $false )
| ( ( ( ( sK23_D @ SV679 @ SV658 @ SV495 )
!= ( ordered_pair @ SV766 @ SV775 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3846]) ).
thf(3873,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( in @ ( sK24_SY316 @ SV679 @ SV658 @ SV495 ) @ SV495 )
= $true )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3847]) ).
thf(3874,plain,
! [SV495: $i,SV658: $i,SV679: $i] :
( ( ( in @ ( sK25_SY318 @ SV679 @ SV658 @ SV495 ) @ SV658 )
= $true )
| ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3848]) ).
thf(3875,plain,
! [SV680: $i,SV767: $i,SV659: $i,SV792: $i,SV495: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ SV495 ) )
= $true )
| ( ( ~ ( in @ SV792 @ SV659 ) )
= $true )
| ( ( ( SV767
!= ( ordered_pair @ SV779 @ SV792 ) ) )
= $true )
| ( ( in @ SV767 @ SV680 )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3849]) ).
thf(3876,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 ) ) )
= $true )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3850]) ).
thf(3877,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( SV768
= ( ordered_pair @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) ) )
= $true )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3851]) ).
thf(3878,plain,
! [SV663: $i,SV497: $i,SV682: $i,SV793: $i] :
( ( ( in @ SV793 @ SV682 )
= $false )
| ( ( in @ SV793 @ SV497 )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(3879,plain,
! [SV497: $i,SV663: $i,SV682: $i,SV794: $i] :
( ( ( in @ SV794 @ SV682 )
= $false )
| ( ( ~ ( in @ SV794 @ SV663 ) )
= $true )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3853]) ).
thf(3880,plain,
! [SV798: $i,SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SV798 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SV798 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3855]) ).
thf(3881,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(3882,plain,
! [SV740: $i,SV564: $i,SV477: $i,SV799: $i] :
( ( ( ! [SY1127: $i] :
( ! [SY1128: $i] :
( ~ ( in @ ( ordered_pair @ SV799 @ SY1128 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1128 @ SY1127 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1127 ) @ SV740 ) ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(3883,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV800: $i] :
( ( ( ! [SY1129: $i] :
( ~ ( in @ ( ordered_pair @ SV800 @ SY1129 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SV800 @ ( sK9_F @ SY1129 @ SV800 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SY1129 @ SV800 @ SV740 @ SV564 @ SV477 ) @ SY1129 ) @ SV564 ) ) ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3858]) ).
thf(3884,plain,
! [SV481: $i,SV687: $i,SV796: $i,SV780: $i] :
( ( ( in @ ( ordered_pair @ SV780 @ SV796 ) @ SV687 )
= $false )
| ( ( in @ ( ordered_pair @ SV796 @ SV780 ) @ SV481 )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3859]) ).
thf(3885,plain,
! [SV687: $i,SV481: $i,SV781: $i,SV797: $i] :
( ( ( in @ ( ordered_pair @ SV797 @ SV781 ) @ SV481 )
= $false )
| ( ( in @ ( ordered_pair @ SV781 @ SV797 ) @ SV687 )
= $true )
| ( ( SV687
= ( relation_inverse @ SV481 ) )
= $false )
| ( ( relation @ SV687 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(3886,plain,
! [SV693: $i,SV730: $i] :
( ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 )
= $false )
| ( ( in @ ( sK45_SY327 @ SV730 @ SV693 ) @ SV693 )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(3887,plain,
! [SV693: $i,SV730: $i] :
( ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 ) )
= $true )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3864]) ).
thf(3888,plain,
! [SV694: $i,SV731: $i,SV785: $i] :
( ( ( ~ ( in @ ( sK43_D @ SV785 @ SV731 @ SV694 ) @ SV694 ) )
= $false )
| ( ( in @ SV785 @ SV731 )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3866]) ).
thf(3889,plain,
! [SV694: $i,SV731: $i,SV785: $i] :
( ( ( ~ ~ ( in @ SV785 @ ( sK43_D @ SV785 @ SV731 @ SV694 ) ) )
= $false )
| ( ( in @ SV785 @ SV731 )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3866]) ).
thf(3890,plain,
! [SV731: $i,SV786: $i,SV694: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV694 )
| ( in @ SV786 @ SV801 ) )
= $true )
| ( ( in @ SV786 @ SV731 )
= $false )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(3891,plain,
! [SV775: $i,SV766: $i,SV495: $i,SV658: $i,SV679: $i] :
( ( ( ( sK23_D @ SV679 @ SV658 @ SV495 )
= ( ordered_pair @ SV766 @ SV775 ) )
= $false )
| ( ( in @ SV766 @ SV495 )
= $false )
| ( ( in @ SV775 @ SV658 )
= $false )
| ( ( ~ ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 ) )
= $true )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3872]) ).
thf(3892,plain,
! [SV680: $i,SV767: $i,SV659: $i,SV792: $i,SV495: $i,SV779: $i] :
( ( ( in @ SV779 @ SV495 )
= $false )
| ( ( ~ ( in @ SV792 @ SV659 ) )
= $true )
| ( ( ( SV767
!= ( ordered_pair @ SV779 @ SV792 ) ) )
= $true )
| ( ( in @ SV767 @ SV680 )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(3893,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 )
| ~ ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
= $false )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(3894,plain,
! [SV497: $i,SV682: $i,SV663: $i,SV794: $i] :
( ( ( in @ SV794 @ SV663 )
= $false )
| ( ( in @ SV794 @ SV682 )
= $false )
| ( ( SV682
= ( set_difference @ SV497 @ SV663 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3879]) ).
thf(3895,plain,
! [SV798: $i,SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SV798 ) @ SV477 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV798 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(3896,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3881]) ).
thf(3897,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3881]) ).
thf(3898,plain,
! [SV740: $i,SV564: $i,SV802: $i,SV477: $i,SV799: $i] :
( ( ( ! [SY1130: $i] :
( ~ ( in @ ( ordered_pair @ SV799 @ SY1130 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1130 @ SV802 ) @ SV564 ) )
| ( in @ ( ordered_pair @ SV799 @ SV802 ) @ SV740 ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3882]) ).
thf(3899,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV803: $i,SV800: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV800 @ SV803 ) @ SV740 )
| ~ ( ~ ( in @ ( ordered_pair @ SV800 @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) @ SV803 ) @ SV564 ) ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(3900,plain,
! [SV693: $i,SV730: $i] :
( ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ SV730 )
= $false )
| ( ( in @ ( sK44_C @ SV730 @ SV693 ) @ ( sK45_SY327 @ SV730 @ SV693 ) )
= $false )
| ( ( SV730
= ( set_meet @ SV693 ) )
= $true )
| ( ( SV693 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3887]) ).
thf(3901,plain,
! [SV694: $i,SV731: $i,SV785: $i] :
( ( ( in @ ( sK43_D @ SV785 @ SV731 @ SV694 ) @ SV694 )
= $true )
| ( ( in @ SV785 @ SV731 )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3888]) ).
thf(3902,plain,
! [SV694: $i,SV731: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ ( sK43_D @ SV785 @ SV731 @ SV694 ) ) )
= $true )
| ( ( in @ SV785 @ SV731 )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3889]) ).
thf(3903,plain,
! [SV731: $i,SV786: $i,SV694: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV694 ) )
= $true )
| ( ( in @ SV786 @ SV801 )
= $true )
| ( ( in @ SV786 @ SV731 )
= $false )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(3904,plain,
! [SV766: $i,SV775: $i,SV495: $i,SV658: $i,SV679: $i] :
( ( ( in @ ( sK23_D @ SV679 @ SV658 @ SV495 ) @ SV679 )
= $false )
| ( ( in @ SV775 @ SV658 )
= $false )
| ( ( in @ SV766 @ SV495 )
= $false )
| ( ( ( sK23_D @ SV679 @ SV658 @ SV495 )
= ( ordered_pair @ SV766 @ SV775 ) )
= $false )
| ( ( SV679
= ( cartesian_product2 @ SV495 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3891]) ).
thf(3905,plain,
! [SV680: $i,SV767: $i,SV495: $i,SV779: $i,SV659: $i,SV792: $i] :
( ( ( in @ SV792 @ SV659 )
= $false )
| ( ( in @ SV779 @ SV495 )
= $false )
| ( ( ( SV767
!= ( ordered_pair @ SV779 @ SV792 ) ) )
= $true )
| ( ( in @ SV767 @ SV680 )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3892]) ).
thf(3906,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 ) )
= $false )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3893]) ).
thf(3907,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( ~ ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 ) )
= $false )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3893]) ).
thf(3908,plain,
! [SV798: $i,SV477: $i,SV564: $i,SV739: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SV798 ) @ SV477 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV798 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3895]) ).
thf(3909,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) ) @ SV477 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3896]) ).
thf(3910,plain,
! [SV477: $i,SV564: $i,SV739: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY309 @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3897]) ).
thf(3911,plain,
! [SV740: $i,SV564: $i,SV802: $i,SV477: $i,SV799: $i] :
( ( ( ! [SY1130: $i] :
( ~ ( in @ ( ordered_pair @ SV799 @ SY1130 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SY1130 @ SV802 ) @ SV564 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV799 @ SV802 ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3898]) ).
thf(3912,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV803: $i,SV800: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV800 @ SV803 ) @ SV740 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV800 @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) @ SV803 ) @ SV564 ) ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(3913,plain,
! [SV694: $i,SV731: $i,SV785: $i] :
( ( ( in @ SV785 @ ( sK43_D @ SV785 @ SV731 @ SV694 ) )
= $false )
| ( ( in @ SV785 @ SV731 )
= $true )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3902]) ).
thf(3914,plain,
! [SV731: $i,SV786: $i,SV694: $i,SV801: $i] :
( ( ( in @ SV801 @ SV694 )
= $false )
| ( ( in @ SV786 @ SV801 )
= $true )
| ( ( in @ SV786 @ SV731 )
= $false )
| ( ( SV731
= ( set_meet @ SV694 ) )
= $false )
| ( ( SV694 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3903]) ).
thf(3915,plain,
! [SV680: $i,SV659: $i,SV495: $i,SV792: $i,SV779: $i,SV767: $i] :
( ( ( SV767
= ( ordered_pair @ SV779 @ SV792 ) )
= $false )
| ( ( in @ SV779 @ SV495 )
= $false )
| ( ( in @ SV792 @ SV659 )
= $false )
| ( ( in @ SV767 @ SV680 )
= $true )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(3916,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( in @ ( sK21_E @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV495 )
= $true )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3906]) ).
thf(3917,plain,
! [SV495: $i,SV659: $i,SV680: $i,SV768: $i] :
( ( ( in @ ( sK22_SY313 @ SV768 @ SV680 @ SV659 @ SV495 ) @ SV659 )
= $true )
| ( ( in @ SV768 @ SV680 )
= $false )
| ( ( SV680
= ( cartesian_product2 @ SV495 @ SV659 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3907]) ).
thf(3918,plain,
! [SV477: $i,SV564: $i,SV739: $i,SV798: $i] :
( ( ( in @ ( ordered_pair @ SV798 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SV798 ) @ SV477 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 ) )
= $true )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(3919,plain,
! [SV740: $i,SV564: $i,SV802: $i,SV477: $i,SV804: $i,SV799: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV799 @ SV804 ) @ SV477 )
| ~ ( in @ ( ordered_pair @ SV804 @ SV802 ) @ SV564 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV799 @ SV802 ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(3920,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV803: $i,SV800: $i] :
( ( ( in @ ( ordered_pair @ SV800 @ SV803 ) @ SV740 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV800 @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) @ SV803 ) @ SV564 ) ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3912]) ).
thf(3921,plain,
! [SV798: $i,SV477: $i,SV564: $i,SV739: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV739 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV739 @ SV564 @ SV477 ) @ SV798 ) @ SV477 )
= $false )
| ( ( in @ ( ordered_pair @ SV798 @ ( sK11_SY305 @ SV739 @ SV564 @ SV477 ) ) @ SV564 )
= $false )
| ( ( SV739
= ( relation_composition @ SV477 @ SV564 ) )
= $true )
| ( ( relation @ SV739 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3918]) ).
thf(3922,plain,
! [SV740: $i,SV564: $i,SV802: $i,SV477: $i,SV804: $i,SV799: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV799 @ SV804 ) @ SV477 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV804 @ SV802 ) @ SV564 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV799 @ SV802 ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3919]) ).
thf(3923,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV803: $i,SV800: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV800 @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
| ~ ( in @ ( ordered_pair @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) @ SV803 ) @ SV564 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV800 @ SV803 ) @ SV740 )
= $false )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3920]) ).
thf(3924,plain,
! [SV740: $i,SV564: $i,SV802: $i,SV477: $i,SV804: $i,SV799: $i] :
( ( ( in @ ( ordered_pair @ SV799 @ SV804 ) @ SV477 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV804 @ SV802 ) @ SV564 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV799 @ SV802 ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3922]) ).
thf(3925,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV803: $i,SV800: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV800 @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) ) @ SV477 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV800 @ SV803 ) @ SV740 )
= $false )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3923]) ).
thf(3926,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV800: $i,SV803: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) @ SV803 ) @ SV564 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV800 @ SV803 ) @ SV740 )
= $false )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3923]) ).
thf(3927,plain,
! [SV740: $i,SV477: $i,SV799: $i,SV564: $i,SV802: $i,SV804: $i] :
( ( ( in @ ( ordered_pair @ SV804 @ SV802 ) @ SV564 )
= $false )
| ( ( in @ ( ordered_pair @ SV799 @ SV804 ) @ SV477 )
= $false )
| ( ( in @ ( ordered_pair @ SV799 @ SV802 ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3924]) ).
thf(3928,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV803: $i,SV800: $i] :
( ( ( in @ ( ordered_pair @ SV800 @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) ) @ SV477 )
= $true )
| ( ( in @ ( ordered_pair @ SV800 @ SV803 ) @ SV740 )
= $false )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3925]) ).
thf(3929,plain,
! [SV477: $i,SV564: $i,SV740: $i,SV800: $i,SV803: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_F @ SV803 @ SV800 @ SV740 @ SV564 @ SV477 ) @ SV803 ) @ SV564 )
= $true )
| ( ( in @ ( ordered_pair @ SV800 @ SV803 ) @ SV740 )
= $false )
| ( ( SV740
= ( relation_composition @ SV477 @ SV564 ) )
= $false )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV564 )
= $false )
| ( ( relation @ SV477 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3926]) ).
thf(3930,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[2178,3929,3928,3927,3921,3917,3916,3915,3914,3913,3910,3909,3904,3901,3900,3894,3886,3885,3884,3878,3877,3874,3873,3871,3870,3869,3868,3865,3862,3861,3854,3843,3842,3841,3840,3837,3836,3835,3834,3826,3825,3822,3821,3820,3815,3813,3810,3809,3802,3799,3797,3792,3788,3781,3763,3762,3759,3744,3743,3727,3707,3706,3697,3696,3686,3685,3669,3663,3650,3649,3648,3645,3642,3641,3638,3634,3622,3621,3615,3612,3611,3590,3584,3579,3578,3577,3574,3573,3568,3547,3546,3543,3524,3520,3518,3517,3507,3505,3504,3493,3491,3489,3472,3471,3468,3467,3461,3460,3459,3454,3453,3438,3426,3424,3414,3413,3389,3384,3378,3377,3359,3343,3340,3339,3338,3335,3320,3303,3290,3289,3288,3285,3280,3279,3278,3277,3272,3271,3249,3248,3247,3245,3244,3237,3236,3214,3213,3206,3201,3200,3194,3193,3178,3177,3176,3175,3174,3172,3163,3154,3136,3135,3116,3115,3111,3110,3092,3091,3065,3057,3055,3054,3051,3050,3042,3011,2945,2942,2941,2940,2939,2938,2935,2934,2933,2927,2926,2925,2903,2877,2876,2872,2820,2819,2817,2816,2813,2810,2807,2806,2804,2800,2798,2794,2789,2784,2783,2768,2766,2765,2734,2723,2722,2678,2676,2655,2652,2651,2646,2645,2644,2638,2637,2540,2538,2537,2536,2535,2529,2525,2522,2521,2520,2514,2489,2427,2426,2425,2424,2411,2405,2381,2380,2379,2378,2363,2305,2291,2204]) ).
thf(3931,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3930,2174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU189+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 12:16:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.40 ....
% 0.18/0.45
% 0.18/0.45 No.of.Axioms: 170
% 0.18/0.45
% 0.18/0.45 Length.of.Defs: 0
% 0.18/0.45
% 0.18/0.45 Contains.Choice.Funs: false
% 0.18/0.49 ..........
% 0.18/0.52 (rf:2,axioms:130,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:172,loop_count:0,foatp_calls:0,translation:fof_full)..........................................................................................................................................................................................................................................................................
% 1.66/1.97
% 1.66/1.97 ********************************
% 1.66/1.97 * All subproblems solved! *
% 1.66/1.97 ********************************
% 1.66/1.97 % 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:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3930,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.16/6.36
% 6.16/6.36 %**** Beginning of derivation protocol ****
% 6.16/6.36 % SZS output start CNFRefutation
% See solution above
% 6.16/6.38
% 6.16/6.38 %**** End of derivation protocol ****
% 6.16/6.38 %**** no. of clauses in derivation: 3891 ****
% 6.16/6.38 %**** clause counter: 3930 ****
% 6.16/6.38
% 6.16/6.38 % 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:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3930,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------