TSTP Solution File: SEU186+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU186+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 : n007.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 12:07:49 EDT 2022
% Result : Theorem 9.91s 10.09s
% Output : CNFRefutation 11.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 222
% Syntax : Number of formulae : 2299 (1125 unt; 79 typ; 0 def)
% Number of atoms : 16021 (5745 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 35822 (5926 ~;5586 |; 363 &;23645 @)
% ( 98 <=>; 204 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 150 ( 150 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 79 usr; 8 con; 0-5 aty)
% Number of variables : 6779 ( 0 ^6745 !; 34 ?;6779 :)
% 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_C,type,
sK10_C: $i > $i > $i ).
thf(tp_sK11_A,type,
sK11_A: $i ).
thf(tp_sK12_A,type,
sK12_A: $i ).
thf(tp_sK13_F,type,
sK13_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_D,type,
sK14_D: $i > $i > $i > $i ).
thf(tp_sK15_SY349,type,
sK15_SY349: $i > $i > $i > $i ).
thf(tp_sK16_SY353,type,
sK16_SY353: $i > $i > $i > $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_SY354,type,
sK18_SY354: $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_SY356,type,
sK21_SY356: $i > $i > $i ).
thf(tp_sK22_D,type,
sK22_D: $i > $i > $i > $i ).
thf(tp_sK23_D,type,
sK23_D: $i > $i > $i > $i ).
thf(tp_sK24_C,type,
sK24_C: $i > $i > $i ).
thf(tp_sK25_SY358,type,
sK25_SY358: $i > $i > $i ).
thf(tp_sK26_D,type,
sK26_D: $i > $i > $i > $i ).
thf(tp_sK27_C,type,
sK27_C: $i > $i > $i ).
thf(tp_sK28_SY360,type,
sK28_SY360: $i > $i > $i ).
thf(tp_sK29_D,type,
sK29_D: $i > $i > $i > $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(tp_sK30_C,type,
sK30_C: $i > $i > $i ).
thf(tp_sK31_E,type,
sK31_E: $i > $i > $i > $i > $i ).
thf(tp_sK32_SY361,type,
sK32_SY361: $i > $i > $i > $i > $i ).
thf(tp_sK33_D,type,
sK33_D: $i > $i > $i > $i ).
thf(tp_sK34_SY364,type,
sK34_SY364: $i > $i > $i > $i ).
thf(tp_sK35_SY366,type,
sK35_SY366: $i > $i > $i > $i ).
thf(tp_sK36_D,type,
sK36_D: $i > $i > $i > $i ).
thf(tp_sK37_D,type,
sK37_D: $i > $i > $i > $i ).
thf(tp_sK38_C,type,
sK38_C: $i > $i > $i ).
thf(tp_sK39_B,type,
sK39_B: $i > $i ).
thf(tp_sK3_B,type,
sK3_B: $i > $i ).
thf(tp_sK40_C,type,
sK40_C: $i > $i > $i ).
thf(tp_sK41_D,type,
sK41_D: $i > $i > $i > $i ).
thf(tp_sK42_C,type,
sK42_C: $i > $i > $i ).
thf(tp_sK43_SY367,type,
sK43_SY367: $i > $i > $i ).
thf(tp_sK44_C,type,
sK44_C: $i > $i > $i ).
thf(tp_sK45_SY369,type,
sK45_SY369: $i > $i > $i ).
thf(tp_sK46_B,type,
sK46_B: $i > $i ).
thf(tp_sK47_C,type,
sK47_C: $i > $i > $i ).
thf(tp_sK48_C,type,
sK48_C: $i > $i > $i ).
thf(tp_sK49_C,type,
sK49_C: $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK8_B,type,
sK8_B: $i > $i ).
thf(tp_sK9_SY344,type,
sK9_SY344: $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(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
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(27,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(28,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(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,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(33,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(35,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(37,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(38,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(39,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(40,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(41,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(42,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(48,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(51,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(59,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(66,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(68,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(69,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(70,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(71,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(72,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(73,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(74,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(75,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(76,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(78,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(79,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(80,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(81,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(82,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(83,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(84,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(85,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(86,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(87,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(88,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(89,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(90,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(91,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(92,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(93,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(94,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(97,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(98,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(100,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(101,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(102,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(103,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(105,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(106,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(107,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(108,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(110,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(111,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(112,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(115,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(116,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(117,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(118,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(119,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(120,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(121,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(122,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
thf(123,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(124,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(125,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(126,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(127,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(128,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(129,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(130,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(131,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(132,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(133,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(134,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(135,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(136,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(138,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(139,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(140,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(141,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(142,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(143,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(144,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(145,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(146,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(147,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(148,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(149,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(150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(151,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(152,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(153,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(154,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(155,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(156,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(157,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(158,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(159,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(161,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(162,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(163,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(164,conjecture,
! [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(165,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[164]) ).
thf(166,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[165]) ).
thf(167,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(168,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(169,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(170,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(171,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(172,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(173,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(175,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(176,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(177,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(178,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(187,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(188,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(189,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(191,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(192,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(195,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(196,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(197,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(198,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(202,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(203,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(204,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(205,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(206,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)],[101]) ).
thf(207,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(208,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(209,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(210,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(211,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(212,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(213,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(214,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(216,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)],[115]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(218,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)],[118]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(220,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)],[120]) ).
thf(221,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)],[121]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(225,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)],[131]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(227,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)],[134]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(229,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)],[138]) ).
thf(230,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)],[139]) ).
thf(231,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(232,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(233,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)],[144]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(235,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)],[146]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(237,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)],[148]) ).
thf(238,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)],[149]) ).
thf(239,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(240,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)],[156]) ).
thf(241,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(242,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(243,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(244,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(245,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(246,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(247,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(249,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(250,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(251,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(252,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(253,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(254,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(255,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(258,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(260,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(261,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)],[68]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(263,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)],[70]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(265,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)],[74]) ).
thf(266,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)],[75]) ).
thf(267,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)],[76]) ).
thf(268,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)],[78]) ).
thf(269,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)],[79]) ).
thf(270,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(271,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)],[81]) ).
thf(272,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)],[82]) ).
thf(273,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)],[83]) ).
thf(274,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)],[84]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(276,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(278,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)],[88]) ).
thf(279,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)],[89]) ).
thf(280,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(281,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(282,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(284,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)],[111]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(286,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(287,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)],[125]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(289,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)],[128]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(291,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(292,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)],[133]) ).
thf(293,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)],[135]) ).
thf(294,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(295,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)],[141]) ).
thf(296,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(297,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)],[151]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(299,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)],[153]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(303,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(305,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(307,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(308,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(309,plain,
( ( ( relation @ sK1_A )
=> ( ! [SY336: $i,SY337: $i] :
~ ( in @ ( ordered_pair @ SY336 @ SY337 ) @ sK1_A )
=> ( sK1_A = empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[166]) ).
thf(310,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[309]) ).
thf(311,plain,
( ( ! [SY336: $i,SY337: $i] :
~ ( in @ ( ordered_pair @ SY336 @ SY337 ) @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[309]) ).
thf(312,plain,
( ( sK1_A = empty_set )
= $false ),
inference(standard_cnf,[status(thm)],[309]) ).
thf(313,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[312]) ).
thf(314,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(315,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(316,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)],[169]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(318,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(319,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(321,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(322,plain,
( ( ~ ( empty @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(323,plain,
( ( ! [A: $i] :
( ( element @ ( sK3_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK3_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(324,plain,
( ( empty @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(325,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(327,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(328,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(329,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(331,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(332,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(333,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(335,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[192]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[193]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(339,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)],[196]) ).
thf(340,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[197]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(342,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)],[199]) ).
thf(343,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[203]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(345,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[206]) ).
thf(346,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[207]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[209]) ).
thf(348,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[212]) ).
thf(350,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[213]) ).
thf(351,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[214]) ).
thf(352,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)],[216]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[217]) ).
thf(354,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)],[218]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[219]) ).
thf(356,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)],[220]) ).
thf(357,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)],[221]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[222]) ).
thf(359,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)],[225]) ).
thf(360,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)],[227]) ).
thf(361,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[228]) ).
thf(362,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)],[229]) ).
thf(363,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)],[230]) ).
thf(364,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[231]) ).
thf(365,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[232]) ).
thf(366,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)],[233]) ).
thf(367,plain,
( ( ! [A: $i] :
( ! [SY338: $i] :
( ~ ( subset @ SY338 @ ( sK7_B @ A ) )
| ( are_equipotent @ SY338 @ ( sK7_B @ A ) )
| ( in @ SY338 @ ( sK7_B @ A ) ) )
& ! [SY339: $i] :
( ~ ( in @ SY339 @ ( sK7_B @ A ) )
| ( in @ ( powerset @ SY339 ) @ ( sK7_B @ A ) ) )
& ! [SY340: $i,SY341: $i] :
( ~ ( in @ SY340 @ ( sK7_B @ A ) )
| ~ ( subset @ SY341 @ SY340 )
| ( in @ SY341 @ ( sK7_B @ A ) ) )
& ( in @ A @ ( sK7_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[235]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[236]) ).
thf(369,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)],[237]) ).
thf(370,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)],[238]) ).
thf(371,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[239]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(373,plain,
( ( ! [A: $i] :
( ! [SY342: $i] :
( ~ ( subset @ SY342 @ ( sK8_B @ A ) )
| ( are_equipotent @ SY342 @ ( sK8_B @ A ) )
| ( in @ SY342 @ ( sK8_B @ A ) ) )
& ! [SY343: $i] :
( ( ! [SY348: $i] :
( ~ ( subset @ SY348 @ SY343 )
| ( in @ SY348 @ ( sK9_SY344 @ SY343 @ A ) ) )
& ( in @ ( sK9_SY344 @ SY343 @ A ) @ ( sK8_B @ A ) ) )
| ~ ( in @ SY343 @ ( sK8_B @ A ) ) )
& ! [SY346: $i,SY347: $i] :
( ~ ( in @ SY346 @ ( sK8_B @ A ) )
| ~ ( subset @ SY347 @ SY346 )
| ( in @ SY347 @ ( sK8_B @ A ) ) )
& ( in @ A @ ( sK8_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[241]) ).
thf(374,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[242]) ).
thf(375,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[243]) ).
thf(376,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[244]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK10_C @ B @ A ) @ A )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( in @ ( sK10_C @ B @ A ) @ A )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(378,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(379,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(380,plain,
( ( ~ ( empty @ sK11_A )
& ( relation @ sK11_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(381,plain,
( ( ( empty @ sK12_A )
& ( relation @ sK12_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(382,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[254]) ).
thf(383,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[256]) ).
thf(384,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(385,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[260]) ).
thf(386,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY352: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ SY352 ) @ A )
| ~ ( in @ ( ordered_pair @ SY352 @ ( sK15_SY349 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY349 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK16_SY353 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK16_SY353 @ C @ B @ A ) @ ( sK15_SY349 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY349 @ 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 @ ( sK13_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK13_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[261]) ).
thf(387,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)],[262]) ).
thf(388,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY354 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ B @ A ) @ ( sK17_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY354 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ B @ A ) @ ( sK17_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)],[263]) ).
thf(389,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY355: $i] :
~ ( in @ ( ordered_pair @ SY355 @ ( sK20_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK20_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK21_SY356 @ B @ A ) @ ( sK20_C @ B @ A ) ) @ A )
| ( in @ ( sK20_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 @ ( sK19_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(390,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ( in @ ( sK22_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)],[266]) ).
thf(391,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY357: $i] :
( ~ ( in @ ( sK24_C @ B @ A ) @ SY357 )
| ~ ( in @ SY357 @ A ) )
| ~ ( in @ ( sK24_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK24_C @ B @ A ) @ ( sK25_SY358 @ B @ A ) )
& ( in @ ( sK25_SY358 @ B @ A ) @ A ) )
| ( in @ ( sK24_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 @ ( sK23_D @ C @ B @ A ) )
& ( in @ ( sK23_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(392,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY359: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ B @ A ) @ SY359 ) @ A )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK27_C @ B @ A ) @ ( sK28_SY360 @ B @ A ) ) @ A )
| ( in @ ( sK27_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 @ ( sK26_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(393,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK29_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK29_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK29_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK29_D @ C @ B @ A ) @ A )
| ( in @ ( sK29_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK29_D @ C @ B @ A ) @ B )
| ( in @ ( sK29_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)],[269]) ).
thf(394,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK30_C @ B @ A ) @ A )
& ~ ( in @ ( sK30_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)],[270]) ).
thf(395,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY362: $i,SY363: $i] :
( ~ ( in @ SY362 @ A )
| ~ ( in @ SY363 @ B )
| ( ( sK33_D @ C @ B @ A )
!= ( ordered_pair @ SY362 @ SY363 ) ) )
| ~ ( in @ ( sK33_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK34_SY364 @ C @ B @ A ) @ A )
& ( in @ ( sK35_SY366 @ C @ B @ A ) @ B )
& ( ( sK33_D @ C @ B @ A )
= ( ordered_pair @ ( sK34_SY364 @ C @ B @ A ) @ ( sK35_SY366 @ C @ B @ A ) ) ) )
| ( in @ ( sK33_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 @ ( sK31_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK32_SY361 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK31_E @ D @ C @ B @ A ) @ ( sK32_SY361 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[271]) ).
thf(396,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK36_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK36_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK36_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK36_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK36_D @ C @ B @ A ) @ C )
| ( in @ ( sK36_D @ C @ B @ A ) @ A )
| ( in @ ( sK36_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)],[272]) ).
thf(397,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ( ( sK37_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ( ( sK37_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ( ( sK37_D @ C @ B @ A )
= A )
| ( ( sK37_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)],[273]) ).
thf(398,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)],[274]) ).
thf(399,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK38_C @ B @ A ) @ B )
| ~ ( subset @ ( sK38_C @ B @ A ) @ A ) )
& ( ( in @ ( sK38_C @ B @ A ) @ B )
| ( subset @ ( sK38_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)],[275]) ).
thf(400,plain,
( ( ! [A: $i] :
( ( in @ ( sK39_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK40_C @ B @ A )
!= A )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( ( sK40_C @ B @ A )
= A )
| ( in @ ( sK40_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)],[277]) ).
thf(402,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK43_SY367 @ B @ A ) @ A )
& ~ ( in @ ( sK42_C @ B @ A ) @ ( sK43_SY367 @ B @ A ) ) )
| ~ ( in @ ( sK42_C @ B @ A ) @ B ) )
& ( ! [SY368: $i] :
( ~ ( in @ SY368 @ A )
| ( in @ ( sK42_C @ B @ A ) @ SY368 ) )
| ( in @ ( sK42_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK41_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK41_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)],[278]) ).
thf(403,plain,
( ( ! [A: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ( sK46_B @ A )
!= ( ordered_pair @ SY370 @ SY371 ) )
& ( in @ ( sK46_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY369 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[279]) ).
thf(404,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(407,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)],[283]) ).
thf(408,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK47_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)],[284]) ).
thf(409,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(410,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(411,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK48_C @ B @ A ) @ A )
& ( in @ ( sK48_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)],[287]) ).
thf(412,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)],[288]) ).
thf(413,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)],[289]) ).
thf(414,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)],[290]) ).
thf(415,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)],[291]) ).
thf(416,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)],[292]) ).
thf(417,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)],[293]) ).
thf(418,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)],[295]) ).
thf(419,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)],[297]) ).
thf(420,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK49_C @ B @ A ) @ A )
& ~ ( in @ ( sK49_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[298]) ).
thf(421,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)],[299]) ).
thf(422,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(423,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(424,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[302]) ).
thf(425,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)],[303]) ).
thf(426,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)],[304]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[305]) ).
thf(428,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[306]) ).
thf(429,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[307]) ).
thf(430,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[308]) ).
thf(431,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(432,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(433,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(435,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)],[426]) ).
thf(436,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)],[425]) ).
thf(437,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(438,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)],[423]) ).
thf(439,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(440,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)],[421]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK49_C @ B @ A ) @ A )
& ~ ( in @ ( sK49_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(442,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)],[419]) ).
thf(443,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(444,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)],[418]) ).
thf(445,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(446,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)],[417]) ).
thf(447,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)],[416]) ).
thf(448,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)],[415]) ).
thf(449,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)],[414]) ).
thf(450,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)],[413]) ).
thf(451,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)],[412]) ).
thf(452,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK48_C @ B @ A ) @ A )
& ( in @ ( sK48_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(453,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(454,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK47_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)],[408]) ).
thf(456,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)],[407]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(458,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(459,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(460,plain,
( ( ! [A: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ( sK46_B @ A )
!= ( ordered_pair @ SY370 @ SY371 ) )
& ( in @ ( sK46_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY369 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(461,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK43_SY367 @ B @ A ) @ A )
& ~ ( in @ ( sK42_C @ B @ A ) @ ( sK43_SY367 @ B @ A ) ) )
| ~ ( in @ ( sK42_C @ B @ A ) @ B ) )
& ( ! [SY368: $i] :
( ~ ( in @ SY368 @ A )
| ( in @ ( sK42_C @ B @ A ) @ SY368 ) )
| ( in @ ( sK42_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK41_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK41_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)],[402]) ).
thf(462,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK40_C @ B @ A )
!= A )
| ~ ( in @ ( sK40_C @ B @ A ) @ B ) )
& ( ( ( sK40_C @ B @ A )
= A )
| ( in @ ( sK40_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)],[401]) ).
thf(463,plain,
( ( ! [A: $i] :
( ( in @ ( sK39_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK38_C @ B @ A ) @ B )
| ~ ( subset @ ( sK38_C @ B @ A ) @ A ) )
& ( ( in @ ( sK38_C @ B @ A ) @ B )
| ( subset @ ( sK38_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)],[399]) ).
thf(465,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)],[398]) ).
thf(466,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ( ( sK37_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ( ( sK37_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ( ( sK37_D @ C @ B @ A )
= A )
| ( ( sK37_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)],[397]) ).
thf(467,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK36_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK36_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK36_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK36_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK36_D @ C @ B @ A ) @ C )
| ( in @ ( sK36_D @ C @ B @ A ) @ A )
| ( in @ ( sK36_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)],[396]) ).
thf(468,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY362: $i,SY363: $i] :
( ~ ( in @ SY362 @ A )
| ~ ( in @ SY363 @ B )
| ( ( sK33_D @ C @ B @ A )
!= ( ordered_pair @ SY362 @ SY363 ) ) )
| ~ ( in @ ( sK33_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK34_SY364 @ C @ B @ A ) @ A )
& ( in @ ( sK35_SY366 @ C @ B @ A ) @ B )
& ( ( sK33_D @ C @ B @ A )
= ( ordered_pair @ ( sK34_SY364 @ C @ B @ A ) @ ( sK35_SY366 @ C @ B @ A ) ) ) )
| ( in @ ( sK33_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 @ ( sK31_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK32_SY361 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK31_E @ D @ C @ B @ A ) @ ( sK32_SY361 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(469,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK30_C @ B @ A ) @ A )
& ~ ( in @ ( sK30_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)],[394]) ).
thf(470,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK29_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK29_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK29_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK29_D @ C @ B @ A ) @ A )
| ( in @ ( sK29_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK29_D @ C @ B @ A ) @ B )
| ( in @ ( sK29_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)],[393]) ).
thf(471,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY359: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ B @ A ) @ SY359 ) @ A )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK27_C @ B @ A ) @ ( sK28_SY360 @ B @ A ) ) @ A )
| ( in @ ( sK27_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 @ ( sK26_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(472,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY357: $i] :
( ~ ( in @ ( sK24_C @ B @ A ) @ SY357 )
| ~ ( in @ SY357 @ A ) )
| ~ ( in @ ( sK24_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK24_C @ B @ A ) @ ( sK25_SY358 @ B @ A ) )
& ( in @ ( sK25_SY358 @ B @ A ) @ A ) )
| ( in @ ( sK24_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 @ ( sK23_D @ C @ B @ A ) )
& ( in @ ( sK23_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(473,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ( in @ ( sK22_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)],[390]) ).
thf(474,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY355: $i] :
~ ( in @ ( ordered_pair @ SY355 @ ( sK20_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK20_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK21_SY356 @ B @ A ) @ ( sK20_C @ B @ A ) ) @ A )
| ( in @ ( sK20_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 @ ( sK19_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(475,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(476,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY354 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ B @ A ) @ ( sK17_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY354 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ B @ A ) @ ( sK17_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)],[388]) ).
thf(477,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)],[387]) ).
thf(478,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY352: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ SY352 ) @ A )
| ~ ( in @ ( ordered_pair @ SY352 @ ( sK15_SY349 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY349 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK16_SY353 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK16_SY353 @ C @ B @ A ) @ ( sK15_SY349 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY349 @ 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 @ ( sK13_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK13_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(479,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(481,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(482,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(484,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(485,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(486,plain,
( ( ( empty @ sK12_A )
& ( relation @ sK12_A ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(487,plain,
( ( ~ ( empty @ sK11_A )
& ( relation @ sK11_A ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(488,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(489,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(490,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(491,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK10_C @ B @ A ) @ A )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( in @ ( sK10_C @ B @ A ) @ A )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(493,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(494,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(495,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(496,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(498,plain,
( ( ! [A: $i] :
( ! [SY342: $i] :
( ~ ( subset @ SY342 @ ( sK8_B @ A ) )
| ( are_equipotent @ SY342 @ ( sK8_B @ A ) )
| ( in @ SY342 @ ( sK8_B @ A ) ) )
& ! [SY343: $i] :
( ( ! [SY348: $i] :
( ~ ( subset @ SY348 @ SY343 )
| ( in @ SY348 @ ( sK9_SY344 @ SY343 @ A ) ) )
& ( in @ ( sK9_SY344 @ SY343 @ A ) @ ( sK8_B @ A ) ) )
| ~ ( in @ SY343 @ ( sK8_B @ A ) ) )
& ! [SY346: $i,SY347: $i] :
( ~ ( in @ SY346 @ ( sK8_B @ A ) )
| ~ ( subset @ SY347 @ SY346 )
| ( in @ SY347 @ ( sK8_B @ A ) ) )
& ( in @ A @ ( sK8_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(500,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(501,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)],[370]) ).
thf(502,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)],[369]) ).
thf(503,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(504,plain,
( ( ! [A: $i] :
( ! [SY338: $i] :
( ~ ( subset @ SY338 @ ( sK7_B @ A ) )
| ( are_equipotent @ SY338 @ ( sK7_B @ A ) )
| ( in @ SY338 @ ( sK7_B @ A ) ) )
& ! [SY339: $i] :
( ~ ( in @ SY339 @ ( sK7_B @ A ) )
| ( in @ ( powerset @ SY339 ) @ ( sK7_B @ A ) ) )
& ! [SY340: $i,SY341: $i] :
( ~ ( in @ SY340 @ ( sK7_B @ A ) )
| ~ ( subset @ SY341 @ SY340 )
| ( in @ SY341 @ ( sK7_B @ A ) ) )
& ( in @ A @ ( sK7_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(505,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(506,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(507,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(508,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(509,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)],[363]) ).
thf(510,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(511,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(514,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)],[359]) ).
thf(515,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(517,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(518,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(519,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(520,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(521,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)],[354]) ).
thf(522,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(523,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)],[352]) ).
thf(524,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(525,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(526,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(527,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(528,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(529,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(530,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(533,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(534,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(535,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(536,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(537,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(540,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)],[342]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(542,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(543,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)],[339]) ).
thf(544,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(546,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(547,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(548,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(549,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(550,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(551,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(552,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(553,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(554,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(555,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(556,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(557,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(558,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(559,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(560,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(561,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(562,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(563,plain,
( ( ! [A: $i] :
( ( element @ ( sK3_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK3_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(564,plain,
( ( ~ ( empty @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(566,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(567,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(568,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(569,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(570,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)],[316]) ).
thf(571,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(572,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(573,plain,
( ( ! [SY336: $i,SY337: $i] :
~ ( in @ ( ordered_pair @ SY336 @ SY337 ) @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(574,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(575,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(576,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK30_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)],[469]) ).
thf(577,plain,
( ( ~ ( ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(578,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK47_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)],[455]) ).
thf(579,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK40_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK40_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK40_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)],[462]) ).
thf(580,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SX1 @ SX0 ) @ ( sK28_SY360 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK27_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 @ ( sK26_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(581,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY358 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK25_SY358 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK24_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 @ ( sK23_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(582,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK36_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK36_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK36_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK36_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK36_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK36_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)],[467]) ).
thf(583,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK22_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)],[473]) ).
thf(584,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)],[450]) ).
thf(585,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)],[436]) ).
thf(586,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)],[501]) ).
thf(587,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)],[435]) ).
thf(588,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)],[448]) ).
thf(589,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK7_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK7_B @ SX0 ) )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK7_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK7_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK7_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(590,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK15_SY349 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY349 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK16_SY353 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY349 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY349 @ 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 @ ( sK13_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(591,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)],[477]) ).
thf(592,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)],[532]) ).
thf(593,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK48_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK48_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)],[452]) ).
thf(594,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK38_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK38_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)],[464]) ).
thf(595,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)],[447]) ).
thf(596,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX2 )
| ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ( disjoint @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(597,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)],[509]) ).
thf(598,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY354 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SX1 @ SX0 ) @ ( sK17_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY354 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SX1 @ SX0 ) @ ( sK17_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)],[476]) ).
thf(599,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK29_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK29_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK29_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK29_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK29_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK29_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)],[470]) ).
thf(600,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)],[446]) ).
thf(601,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK8_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK8_B @ SX0 ) )
| ( in @ SX1 @ ( sK8_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK9_SY344 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK9_SY344 @ SX1 @ SX0 ) @ ( sK8_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK8_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK8_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK8_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK8_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(602,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)],[540]) ).
thf(603,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)],[449]) ).
thf(604,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)],[451]) ).
thf(605,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)],[442]) ).
thf(606,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK33_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK33_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK35_SY366 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK33_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK34_SY364 @ SX2 @ SX1 @ SX0 ) @ ( sK35_SY366 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK33_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 @ ( sK31_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK32_SY361 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK31_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK32_SY361 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(607,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)],[438]) ).
thf(608,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK37_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK37_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK37_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK37_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)],[466]) ).
thf(609,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)],[456]) ).
thf(610,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)],[440]) ).
thf(611,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)],[514]) ).
thf(612,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK5_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(613,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK39_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(614,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK20_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SX1 @ SX0 ) @ ( sK20_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK20_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 @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(615,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)],[444]) ).
thf(616,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)],[570]) ).
thf(617,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ ( sK43_SY367 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK41_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)],[461]) ).
thf(618,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)],[543]) ).
thf(619,plain,
( ( ~ ( ~ ~ ( empty @ sK11_A )
| ~ ( relation @ sK11_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(622,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK46_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK46_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY369 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(623,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK3_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK3_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(624,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(625,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)],[465]) ).
thf(626,plain,
! [SV1: $i] :
( ( ( ( singleton @ SV1 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(627,plain,
! [SV2: $i] :
( ( ! [SY372: $i] :
( ~ ( in @ SV2 @ SY372 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SY372 )
= SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(628,plain,
! [SV3: $i] :
( ( ! [SY373: $i] :
( ~ ( disjoint @ ( singleton @ SV3 ) @ SY373 )
| ~ ( in @ SV3 @ SY373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(629,plain,
! [SV4: $i] :
( ( ! [SY374: $i] :
( ( in @ SV4 @ SY374 )
| ( disjoint @ ( singleton @ SV4 ) @ SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(630,plain,
! [SV5: $i] :
( ( ! [SY375: $i] :
( ~ ( element @ SY375 @ ( powerset @ SV5 ) )
| ! [SY376: $i] :
( ~ ( in @ SY376 @ SY375 )
| ( in @ SY376 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(631,plain,
! [SV6: $i] :
( ( ! [SY377: $i] :
( ~ ( in @ SV6 @ SY377 )
| ( subset @ SV6 @ ( union @ SY377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(632,plain,
! [SV7: $i] :
( ( subset @ empty_set @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(633,plain,
! [SV8: $i] :
( ( ~ ( subset @ SV8 @ empty_set )
| ( SV8 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(634,plain,
! [SV9: $i] :
( ( ! [SY378: $i] :
( ~ ( in @ SV9 @ SY378 )
| ( ( set_union2 @ ( singleton @ SV9 ) @ SY378 )
= SY378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(635,plain,
! [SV10: $i] :
( ( ! [SY379: $i] :
( ~ ( in @ SV10 @ SY379 )
| ( subset @ SV10 @ ( union @ SY379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(636,plain,
! [SV11: $i] :
( ( ! [SY380: $i] :
( ~ ( in @ SV11 @ SY380 )
| ~ ( in @ SY380 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(637,plain,
! [SV12: $i] :
( ( ~ ( empty @ SV12 )
| ( relation @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(638,plain,
! [SV13: $i] :
( ( ! [SY381: $i] :
( ( ordered_pair @ SV13 @ SY381 )
= ( unordered_pair @ ( unordered_pair @ SV13 @ SY381 ) @ ( singleton @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(639,plain,
! [SV14: $i] :
( ( ~ ( relation @ SV14 )
| ( relation @ ( relation_inverse @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(640,plain,
! [SV15: $i] :
( ( ! [SY382: $i] :
( ~ ( relation @ SV15 )
| ~ ( relation @ SY382 )
| ( relation @ ( relation_composition @ SV15 @ SY382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(641,plain,
! [SV16: $i] :
( ( ! [SY383: $i] :
~ ( empty @ ( ordered_pair @ SV16 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(642,plain,
! [SV17: $i] :
( ( ! [SY384: $i] :
( ~ ( relation @ SV17 )
| ~ ( relation @ SY384 )
| ( relation @ ( set_union2 @ SV17 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(643,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ( ( relation_inverse @ ( relation_inverse @ SV18 ) )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(644,plain,
! [SV19: $i] :
( ( ( set_union2 @ SV19 @ empty_set )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(645,plain,
! [SV20: $i] :
( ( ! [SY385: $i] :
( ~ ( in @ SV20 @ SY385 )
| ( element @ SV20 @ SY385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(646,plain,
! [SV21: $i] :
( ( ( set_intersection2 @ SV21 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(647,plain,
! [SV22: $i] :
( ( ! [SY386: $i] :
( ~ ( element @ SV22 @ SY386 )
| ( empty @ SY386 )
| ( in @ SV22 @ SY386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(648,plain,
! [SV23: $i] :
( ( ( set_difference @ SV23 @ empty_set )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(649,plain,
! [SV24: $i] :
( ( ( set_difference @ empty_set @ SV24 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(650,plain,
! [SV25: $i] :
( ( ! [SY387: $i,SY388: $i] :
( ~ ( element @ SY387 @ ( powerset @ SY388 ) )
| ~ ( in @ SV25 @ SY387 )
| ( element @ SV25 @ SY388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(651,plain,
! [SV26: $i] :
( ( ~ ( empty @ SV26 )
| ( SV26 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(652,plain,
! [SV27: $i] :
( ( ! [SY389: $i] :
( ~ ( empty @ SY389 )
| ~ ( in @ SV27 @ SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(653,plain,
! [SV28: $i] :
( ( ! [SY390: $i] :
( ~ ( subset @ SV28 @ SY390 )
| ! [SY391: $i] :
( ( in @ SY391 @ SV28 )
| ( subset @ SV28 @ ( set_difference @ SY390 @ ( singleton @ SY391 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(654,plain,
! [SV29: $i] :
( ( ! [SY392: $i,SY393: $i,SY394: $i] :
( ( SV29 = SY394 )
| ( SV29 = SY393 )
| ( ( unordered_pair @ SV29 @ SY392 )
!= ( unordered_pair @ SY393 @ SY394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(655,plain,
! [SV30: $i] :
( ( ! [SY395: $i,SY396: $i,SY397: $i] :
( ~ ( subset @ SV30 @ SY395 )
| ~ ( subset @ SY396 @ SY397 )
| ( subset @ ( cartesian_product2 @ SV30 @ SY396 ) @ ( cartesian_product2 @ SY395 @ SY397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(656,plain,
! [SV31: $i] :
( ( ! [SY398: $i] :
( ~ ( subset @ SV31 @ SY398 )
| ( ( set_union2 @ SV31 @ SY398 )
= SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(657,plain,
! [SV32: $i] :
( ( ! [SY399: $i] : ( subset @ ( set_intersection2 @ SV32 @ SY399 ) @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(658,plain,
! [SV33: $i] :
( ( ! [SY400: $i,SY401: $i] :
( ~ ( subset @ SV33 @ SY400 )
| ~ ( subset @ SV33 @ SY401 )
| ( subset @ SV33 @ ( set_intersection2 @ SY400 @ SY401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(659,plain,
! [SV34: $i] :
( ( ! [SY402: $i,SY403: $i] :
( ~ ( subset @ SV34 @ SY402 )
| ~ ( subset @ SY402 @ SY403 )
| ( subset @ SV34 @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(660,plain,
! [SV35: $i] :
( ( ~ ( relation @ SV35 )
| ( subset @ SV35 @ ( cartesian_product2 @ ( relation_dom @ SV35 ) @ ( relation_rng @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(661,plain,
! [SV36: $i] :
( ( ! [SY404: $i] :
( ~ ( subset @ SV36 @ SY404 )
| ! [SY405: $i] : ( subset @ ( set_intersection2 @ SV36 @ SY405 ) @ ( set_intersection2 @ SY404 @ SY405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(662,plain,
! [SV37: $i] :
( ( ! [SY406: $i] :
( ~ ( subset @ SV37 @ SY406 )
| ( ( set_intersection2 @ SV37 @ SY406 )
= SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(663,plain,
! [SV38: $i] :
( ( ! [SY407: $i] :
( ~ ( subset @ SV38 @ SY407 )
| ! [SY408: $i] : ( subset @ ( set_difference @ SV38 @ SY408 ) @ ( set_difference @ SY407 @ SY408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(664,plain,
! [SV39: $i] :
( ( ! [SY409: $i] : ( subset @ ( set_difference @ SV39 @ SY409 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(665,plain,
! [SV40: $i] :
( ( ! [SY410: $i] :
( ( set_union2 @ SV40 @ ( set_difference @ SY410 @ SV40 ) )
= ( set_union2 @ SV40 @ SY410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(666,plain,
! [SV41: $i] :
( ( ! [SY411: $i] :
( ( set_difference @ ( set_union2 @ SV41 @ SY411 ) @ SY411 )
= ( set_difference @ SV41 @ SY411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(667,plain,
! [SV42: $i] :
( ( ~ ( relation @ SV42 )
| ! [SY412: $i] :
( ~ ( relation @ SY412 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV42 @ SY412 ) ) @ ( relation_dom @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(668,plain,
! [SV43: $i] :
( ( ~ ( relation @ SV43 )
| ! [SY413: $i] :
( ~ ( relation @ SY413 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV43 @ SY413 ) ) @ ( relation_rng @ SY413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(669,plain,
! [SV44: $i] :
( ( ! [SY414: $i] :
( ~ ( subset @ SV44 @ SY414 )
| ( SY414
= ( set_union2 @ SV44 @ ( set_difference @ SY414 @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(670,plain,
! [SV45: $i] :
( ( ~ ( relation @ SV45 )
| ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( subset @ ( relation_rng @ SV45 ) @ ( relation_dom @ SY415 ) )
| ( ( relation_dom @ ( relation_composition @ SV45 @ SY415 ) )
= ( relation_dom @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(671,plain,
! [SV46: $i] :
( ( ! [SY416: $i] :
( ~ ( element @ SY416 @ ( powerset @ ( powerset @ SV46 ) ) )
| ( SY416 = empty_set )
| ( ( complements_of_subsets @ SV46 @ SY416 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(672,plain,
! [SV47: $i] :
( ( ~ ( relation @ SV47 )
| ! [SY417: $i] :
( ~ ( relation @ SY417 )
| ~ ( subset @ ( relation_dom @ SV47 ) @ ( relation_rng @ SY417 ) )
| ( ( relation_rng @ ( relation_composition @ SY417 @ SV47 ) )
= ( relation_rng @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(673,plain,
! [SV48: $i] :
( ( ! [SY418: $i] :
( ( set_difference @ SV48 @ ( set_difference @ SV48 @ SY418 ) )
= ( set_intersection2 @ SV48 @ SY418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(674,plain,
! [SV49: $i] :
( ( ( SV49 = empty_set )
| ! [SY419: $i] :
( ~ ( element @ SY419 @ ( powerset @ SV49 ) )
| ! [SY420: $i] :
( ~ ( element @ SY420 @ SV49 )
| ( in @ SY420 @ SY419 )
| ( in @ SY420 @ ( subset_complement @ SV49 @ SY419 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(675,plain,
! [SV50: $i] :
( ( ! [SY421: $i,SY422: $i] :
( ~ ( element @ SY422 @ ( powerset @ SV50 ) )
| ~ ( in @ SY421 @ ( subset_complement @ SV50 @ SY422 ) )
| ~ ( in @ SY421 @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(676,plain,
! [SV51: $i] :
( ( ! [SY423: $i] :
( ~ ( proper_subset @ SY423 @ SV51 )
| ~ ( subset @ SV51 @ SY423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(677,plain,
! [SV52: $i] :
( ( ! [SY424: $i,SY425: $i] :
( ~ ( disjoint @ SY424 @ SY425 )
| ~ ( subset @ SV52 @ SY424 )
| ( disjoint @ SV52 @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(678,plain,
! [SV53: $i] :
( ( ( unordered_pair @ SV53 @ SV53 )
= ( singleton @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(679,plain,
! [SV54: $i] :
( ( ! [SY426: $i] :
( ~ ( subset @ ( singleton @ SV54 ) @ ( singleton @ SY426 ) )
| ( SV54 = SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(680,plain,
! [SV55: $i] :
( ( ! [SY427: $i] : ( subset @ SV55 @ ( set_union2 @ SV55 @ SY427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(681,plain,
! [SV56: $i] :
( ( ! [SY428: $i,SY429: $i] :
( ~ ( subset @ SV56 @ SY428 )
| ~ ( subset @ SY429 @ SY428 )
| ( subset @ ( set_union2 @ SV56 @ SY429 ) @ SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(682,plain,
! [SV57: $i] :
( ( ! [SY430: $i] :
( ! [SY431: $i] :
( ( singleton @ SV57 )
!= ( unordered_pair @ SY430 @ SY431 ) )
| ( SV57 = SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(683,plain,
! [SV58: $i] :
( ( ( union @ ( powerset @ SV58 ) )
= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(684,plain,
! [SV59: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ( ( singleton @ SV59 )
!= ( unordered_pair @ SY432 @ SY433 ) )
| ( SY432 = SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(685,plain,
! [SV60: $i] :
( ( ! [SY434: $i] :
( ( unordered_pair @ SV60 @ SY434 )
= ( unordered_pair @ SY434 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(686,plain,
! [SV61: $i] :
( ( ! [SY435: $i] :
( ( set_union2 @ SV61 @ SY435 )
= ( set_union2 @ SY435 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(687,plain,
! [SV62: $i] :
( ( ! [SY436: $i] :
( ( set_intersection2 @ SV62 @ SY436 )
= ( set_intersection2 @ SY436 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(688,plain,
! [SV63: $i] :
( ( ! [SY437: $i] :
( ~ ( element @ SY437 @ ( powerset @ SV63 ) )
| ( ( subset_complement @ SV63 @ SY437 )
= ( set_difference @ SV63 @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(689,plain,
! [SV64: $i] :
( ( ~ ( relation @ SV64 )
| ( ( relation_field @ SV64 )
= ( set_union2 @ ( relation_dom @ SV64 ) @ ( relation_rng @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(690,plain,
! [SV65: $i] :
( ( element @ ( cast_to_subset @ SV65 ) @ ( powerset @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(691,plain,
! [SV66: $i] :
( ( ! [SY438: $i] :
( ~ ( element @ SY438 @ ( powerset @ SV66 ) )
| ( element @ ( subset_complement @ SV66 @ SY438 ) @ ( powerset @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(692,plain,
! [SV67: $i] :
( ( ! [SY439: $i] :
( ~ ( element @ SY439 @ ( powerset @ ( powerset @ SV67 ) ) )
| ( element @ ( union_of_subsets @ SV67 @ SY439 ) @ ( powerset @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(693,plain,
! [SV68: $i] :
( ( ! [SY440: $i] :
( ~ ( element @ SY440 @ ( powerset @ ( powerset @ SV68 ) ) )
| ( element @ ( meet_of_subsets @ SV68 @ SY440 ) @ ( powerset @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(694,plain,
! [SV69: $i] :
( ( ! [SY441: $i,SY442: $i] :
( ~ ( element @ SY441 @ ( powerset @ SV69 ) )
| ~ ( element @ SY442 @ ( powerset @ SV69 ) )
| ( element @ ( subset_difference @ SV69 @ SY441 @ SY442 ) @ ( powerset @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(695,plain,
! [SV70: $i] :
( ( ! [SY443: $i] :
( ~ ( element @ SY443 @ ( powerset @ ( powerset @ SV70 ) ) )
| ( element @ ( complements_of_subsets @ SV70 @ SY443 ) @ ( powerset @ ( powerset @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(696,plain,
! [SV71: $i] :
( ( element @ ( sK6_B @ SV71 ) @ SV71 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(697,plain,
! [SV72: $i] :
( ( ~ ( empty @ ( powerset @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(698,plain,
! [SV73: $i] :
( ( ~ ( empty @ ( singleton @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(699,plain,
! [SV74: $i] :
( ( ( empty @ SV74 )
| ! [SY444: $i] :
~ ( empty @ ( set_union2 @ SV74 @ SY444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(700,plain,
! [SV75: $i] :
( ( ! [SY445: $i] :
~ ( empty @ ( unordered_pair @ SV75 @ SY445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(701,plain,
! [SV76: $i] :
( ( ( empty @ SV76 )
| ! [SY446: $i] :
~ ( empty @ ( set_union2 @ SY446 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(702,plain,
! [SV77: $i] :
( ( ! [SY447: $i] :
( ( empty @ SV77 )
| ( empty @ SY447 )
| ~ ( empty @ ( cartesian_product2 @ SV77 @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(703,plain,
! [SV78: $i] :
( ( ( set_union2 @ SV78 @ SV78 )
= SV78 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(704,plain,
! [SV79: $i] :
( ( ( set_intersection2 @ SV79 @ SV79 )
= SV79 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(705,plain,
! [SV80: $i] :
( ( ! [SY448: $i] :
( ~ ( element @ SY448 @ ( powerset @ SV80 ) )
| ( ( subset_complement @ SV80 @ ( subset_complement @ SV80 @ SY448 ) )
= SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(706,plain,
! [SV81: $i] :
( ( ! [SY449: $i] :
( ~ ( element @ SY449 @ ( powerset @ ( powerset @ SV81 ) ) )
| ( ( complements_of_subsets @ SV81 @ ( complements_of_subsets @ SV81 @ SY449 ) )
= SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(707,plain,
( ( empty @ sK2_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(708,plain,
! [SV82: $i] :
( ( ! [SY450: $i] :
( ~ ( element @ SY450 @ ( powerset @ ( powerset @ SV82 ) ) )
| ( ( union_of_subsets @ SV82 @ SY450 )
= ( union @ SY450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(709,plain,
! [SV83: $i] :
( ( ! [SY451: $i] :
( ~ ( element @ SY451 @ ( powerset @ ( powerset @ SV83 ) ) )
| ( ( meet_of_subsets @ SV83 @ SY451 )
= ( set_meet @ SY451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(710,plain,
! [SV84: $i] :
( ( ! [SY452: $i,SY453: $i] :
( ~ ( element @ SY452 @ ( powerset @ SV84 ) )
| ~ ( element @ SY453 @ ( powerset @ SV84 ) )
| ( ( subset_difference @ SV84 @ SY452 @ SY453 )
= ( set_difference @ SY452 @ SY453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(711,plain,
! [SV85: $i] :
( ( subset @ SV85 @ SV85 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(712,plain,
! [SV86: $i] :
( ( ! [SY454: $i] :
( ~ ( disjoint @ SV86 @ SY454 )
| ( disjoint @ SY454 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(713,plain,
! [SV87: $i] :
( ( ! [SY455: $i,SY456: $i] :
( ~ ( element @ SY455 @ ( powerset @ SY456 ) )
| ~ ( in @ SV87 @ SY455 )
| ~ ( empty @ SY456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(714,plain,
! [SV88: $i] :
( ( ! [SY457: $i] :
( ( SV88 = SY457 )
| ~ ( empty @ SV88 )
| ~ ( empty @ SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(715,plain,
! [SV89: $i] :
( ( ! [SY458: $i] :
~ ( in @ ( ordered_pair @ SV89 @ SY458 ) @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(716,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(717,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK30_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)],[576]) ).
thf(718,plain,
( ( ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(719,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK47_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)],[578]) ).
thf(720,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK40_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK40_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK40_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)],[579]) ).
thf(721,plain,
! [SV90: $i] :
( ( ~ ( relation @ SV90 )
| ~ ( ~ ! [SY459: $i] :
( ~ ( ~ ( ! [SY460: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ SY460 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ ( sK28_SY360 @ SY459 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) ) )
| ( SY459
= ( relation_dom @ SV90 ) ) )
| ~ ! [SY461: $i] :
( ( SY461
!= ( relation_dom @ SV90 ) )
| ~ ( ~ ! [SY462: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY462 @ SY463 ) @ SV90 )
| ( in @ SY462 @ SY461 ) )
| ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SY461 )
| ( in @ ( ordered_pair @ SY464 @ ( sK26_D @ SY464 @ SY461 @ SV90 ) ) @ SV90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(722,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY358 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK25_SY358 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK24_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 @ ( sK23_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(723,plain,
! [SV91: $i] :
( ( ~ ( ~ ! [SY465: $i,SY466: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY465 ) ) )
| ~ ( ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY465 ) ) )
| ( SY466
= ( set_union2 @ SV91 @ SY465 ) ) )
| ~ ! [SY467: $i,SY468: $i] :
( ( SY468
!= ( set_union2 @ SV91 @ SY467 ) )
| ~ ( ~ ! [SY469: $i] :
( ~ ( in @ SY469 @ SY468 )
| ( in @ SY469 @ SV91 )
| ( in @ SY469 @ SY467 ) )
| ~ ~ ( ~ ! [SY470: $i] :
( ~ ( in @ SY470 @ SV91 )
| ( in @ SY470 @ SY468 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY467 )
| ( in @ SX3 @ SY468 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(724,plain,
! [SV92: $i] :
( ( ~ ( ~ ! [SY472: $i,SY473: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY472 )
| ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY472 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) ) ) )
| ( SY473
= ( set_difference @ SV92 @ SY472 ) ) )
| ~ ! [SY474: $i,SY475: $i] :
( ( SY475
!= ( set_difference @ SV92 @ SY474 ) )
| ~ ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV92 )
| ( in @ SY476 @ SY474 )
| ( in @ SY476 @ SY475 ) )
| ~ ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY475 )
| ( in @ SY477 @ SV92 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY475 )
| ~ ( in @ SX3 @ SY474 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(725,plain,
! [SV93: $i] :
( ( ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( in @ SV93 @ SY480 )
| ~ ( in @ SY479 @ SY480 )
| ( subset @ ( unordered_pair @ SV93 @ SY479 ) @ SY480 ) )
| ~ ~ ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY481 ) @ SY482 )
| ( in @ SV93 @ SY482 ) )
| ~ ! [SY483: $i,SY484: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY483 ) @ SY484 )
| ( in @ SY483 @ SY484 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(726,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)],[585]) ).
thf(727,plain,
! [SV94: $i] :
( ( ~ ( ~ ! [SY485: $i] :
( ~ ( subset @ SV94 @ SY485 )
| ! [SY486: $i] : ( subset @ ( cartesian_product2 @ SV94 @ SY486 ) @ ( cartesian_product2 @ SY485 @ SY486 ) ) )
| ~ ! [SY487: $i] :
( ~ ( subset @ SV94 @ SY487 )
| ! [SY488: $i] : ( subset @ ( cartesian_product2 @ SY488 @ SV94 ) @ ( cartesian_product2 @ SY488 @ SY487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(728,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)],[587]) ).
thf(729,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)],[588]) ).
thf(730,plain,
! [SV95: $i] :
( ( ~ ( ~ ! [SY489: $i] :
( ~ ( subset @ SY489 @ ( sK7_B @ SV95 ) )
| ( are_equipotent @ SY489 @ ( sK7_B @ SV95 ) )
| ( in @ SY489 @ ( sK7_B @ SV95 ) ) )
| ~ ~ ( ~ ! [SY490: $i] :
( ~ ( in @ SY490 @ ( sK7_B @ SV95 ) )
| ( in @ ( powerset @ SY490 ) @ ( sK7_B @ SV95 ) ) )
| ~ ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) )
| ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(731,plain,
! [SV96: $i] :
( ( ~ ( relation @ SV96 )
| ! [SY493: $i] :
( ~ ( relation @ SY493 )
| ~ ( ~ ! [SY494: $i] :
( ~ ( relation @ SY494 )
| ~ ( ~ ( ! [SY495: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ SY495 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY495 @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY493 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY494 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK16_SY353 @ SY494 @ SY493 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY493 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY494 ) ) )
| ( SY494
= ( relation_composition @ SV96 @ SY493 ) ) )
| ~ ! [SY496: $i] :
( ~ ( relation @ SY496 )
| ( SY496
!= ( relation_composition @ SV96 @ SY493 ) )
| ~ ( ~ ! [SY497: $i,SY498: $i] :
( ! [SY499: $i] :
( ~ ( in @ ( ordered_pair @ SY497 @ SY499 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY499 @ SY498 ) @ SY493 ) )
| ( in @ ( ordered_pair @ SY497 @ SY498 ) @ SY496 ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( in @ ( ordered_pair @ SY500 @ SY501 ) @ SY496 )
| ~ ( ~ ( in @ ( ordered_pair @ SY500 @ ( sK13_F @ SY501 @ SY500 @ SY496 @ SY493 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY501 @ SY500 @ SY496 @ SY493 @ SV96 ) @ SY501 ) @ SY493 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(732,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)],[591]) ).
thf(733,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)],[592]) ).
thf(734,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK48_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK48_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)],[593]) ).
thf(735,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK38_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK38_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)],[594]) ).
thf(736,plain,
! [SV97: $i] :
( ( ! [SY502: $i] :
~ ( ~ ! [SY503: $i] :
( ! [SY504: $i] :
( ( ordered_pair @ SV97 @ SY502 )
!= ( ordered_pair @ SY503 @ SY504 ) )
| ( SV97 = SY503 ) )
| ~ ! [SY505: $i,SY506: $i] :
( ( ( ordered_pair @ SV97 @ SY502 )
!= ( ordered_pair @ SY505 @ SY506 ) )
| ( SY502 = SY506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(737,plain,
! [SV98: $i] :
( ( ! [SY507: $i] :
( ~ ( element @ SY507 @ ( powerset @ SV98 ) )
| ~ ( ~ ! [SY508: $i] :
( ~ ( element @ SY508 @ ( powerset @ SV98 ) )
| ~ ( disjoint @ SY507 @ SY508 )
| ( subset @ SY507 @ ( subset_complement @ SV98 @ SY508 ) ) )
| ~ ! [SY509: $i] :
( ~ ( element @ SY509 @ ( powerset @ SV98 ) )
| ~ ( subset @ SY507 @ ( subset_complement @ SV98 @ SY509 ) )
| ( disjoint @ SY507 @ SY509 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(738,plain,
! [SV99: $i] :
( ( ~ ( relation @ SV99 )
| ~ ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV99 @ SY510 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SY510 ) ) )
| ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV99 @ SY511 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SY511 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(739,plain,
! [SV100: $i] :
( ( ~ ( relation @ SV100 )
| ~ ( ~ ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) ) )
| ( SY512
= ( relation_inverse @ SV100 ) ) )
| ~ ! [SY513: $i] :
( ~ ( relation @ SY513 )
| ( SY513
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( in @ ( ordered_pair @ SY514 @ SY515 ) @ SY513 )
| ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV100 ) )
| ~ ! [SY516: $i,SY517: $i] :
( ~ ( in @ ( ordered_pair @ SY517 @ SY516 ) @ SV100 )
| ( in @ ( ordered_pair @ SY516 @ SY517 ) @ SY513 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(740,plain,
! [SV101: $i] :
( ( ~ ( ~ ! [SY518: $i,SY519: $i] :
( ~ ( ~ ( ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY518 )
| ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) )
| ~ ( ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY518 )
| ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) ) ) )
| ( SY519
= ( set_intersection2 @ SV101 @ SY518 ) ) )
| ~ ! [SY520: $i,SY521: $i] :
( ( SY521
!= ( set_intersection2 @ SV101 @ SY520 ) )
| ~ ( ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ SV101 )
| ~ ( in @ SY522 @ SY520 )
| ( in @ SY522 @ SY521 ) )
| ~ ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY521 )
| ( in @ SY523 @ SV101 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY521 )
| ( in @ SX3 @ SY520 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(741,plain,
! [SV102: $i] :
( ( ~ ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( relation @ SY526 )
| ~ ( in @ ( ordered_pair @ SV102 @ SY525 ) @ SY526 )
| ( in @ SV102 @ ( relation_field @ SY526 ) ) )
| ~ ! [SY527: $i,SY528: $i] :
( ~ ( relation @ SY528 )
| ~ ( in @ ( ordered_pair @ SV102 @ SY527 ) @ SY528 )
| ( in @ SY527 @ ( relation_field @ SY528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(742,plain,
! [SV103: $i] :
( ( ~ ( ~ ! [SY529: $i] :
( ~ ( subset @ SY529 @ ( sK8_B @ SV103 ) )
| ( are_equipotent @ SY529 @ ( sK8_B @ SV103 ) )
| ( in @ SY529 @ ( sK8_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( ~ ! [SY531: $i] :
( ~ ( subset @ SY531 @ SY530 )
| ( in @ SY531 @ ( sK9_SY344 @ SY530 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SY530 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SY530 @ ( sK8_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(743,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)],[602]) ).
thf(744,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)],[603]) ).
thf(745,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)],[604]) ).
thf(746,plain,
! [SV104: $i] :
( ( ! [SY534: $i] :
~ ( ~ ! [SY535: $i,SY536: $i] :
( ~ ( in @ SV104 @ SY535 )
| ~ ( in @ SY534 @ SY536 )
| ( in @ ( ordered_pair @ SV104 @ SY534 ) @ ( cartesian_product2 @ SY535 @ SY536 ) ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SY534 ) @ ( cartesian_product2 @ SY537 @ SY538 ) )
| ( in @ SV104 @ SY537 ) )
| ~ ! [SY539: $i,SY540: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SY534 ) @ ( cartesian_product2 @ SY539 @ SY540 ) )
| ( in @ SY534 @ SY540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(747,plain,
! [SV105: $i] :
( ( ~ ( ~ ! [SY541: $i,SY542: $i] :
( ~ ( ~ ( ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ SV105 )
| ~ ( in @ SY544 @ SY541 )
| ( ( sK33_D @ SY542 @ SY541 @ SV105 )
!= ( ordered_pair @ SY543 @ SY544 ) ) )
| ~ ( in @ ( sK33_D @ SY542 @ SY541 @ SV105 ) @ SY542 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SY542 @ SY541 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SY542 @ SY541 @ SV105 ) @ SY541 ) )
| ( ( sK33_D @ SY542 @ SY541 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SY542 @ SY541 @ SV105 ) @ ( sK35_SY366 @ SY542 @ SY541 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SY542 @ SY541 @ SV105 ) @ SY542 ) ) )
| ( SY542
= ( cartesian_product2 @ SV105 @ SY541 ) ) )
| ~ ! [SY545: $i,SY546: $i] :
( ( SY546
!= ( cartesian_product2 @ SV105 @ SY545 ) )
| ~ ( ~ ! [SY547: $i] :
( ! [SY548: $i,SY549: $i] :
( ~ ( in @ SY548 @ SV105 )
| ~ ( in @ SY549 @ SY545 )
| ( SY547
!= ( ordered_pair @ SY548 @ SY549 ) ) )
| ( in @ SY547 @ SY546 ) )
| ~ ! [SY550: $i] :
( ~ ( in @ SY550 @ SY546 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY550 @ SY546 @ SY545 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY550 @ SY546 @ SY545 @ SV105 ) @ SY545 ) )
| ( SY550
!= ( ordered_pair @ ( sK31_E @ SY550 @ SY546 @ SY545 @ SV105 ) @ ( sK32_SY361 @ SY550 @ SY546 @ SY545 @ SV105 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(748,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)],[607]) ).
thf(749,plain,
! [SV106: $i] :
( ( ~ ( ~ ! [SY551: $i,SY552: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
!= SY551 ) ) )
| ~ ( ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
= SV106 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
= SY551 ) ) )
| ( SY552
= ( unordered_pair @ SV106 @ SY551 ) ) )
| ~ ! [SY553: $i,SY554: $i] :
( ( SY554
!= ( unordered_pair @ SV106 @ SY553 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SY554 )
| ( SY555 = SV106 )
| ( SY555 = SY553 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ( SY556 != SV106 )
| ( in @ SY556 @ SY554 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY553 )
| ( in @ SX3 @ SY554 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(750,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)],[609]) ).
thf(751,plain,
! [SV107: $i] :
( ( ! [SY558: $i] :
~ ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( in @ SV107 @ SY559 )
| ~ ( in @ SY558 @ SY560 )
| ( in @ ( ordered_pair @ SV107 @ SY558 ) @ ( cartesian_product2 @ SY559 @ SY560 ) ) )
| ~ ~ ( ~ ! [SY561: $i] :
( ! [SY562: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SY558 ) @ ( cartesian_product2 @ SY561 @ SY562 ) )
| ( in @ SV107 @ SY561 ) )
| ~ ! [SY563: $i,SY564: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SY558 ) @ ( cartesian_product2 @ SY563 @ SY564 ) )
| ( in @ SY558 @ SY564 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(752,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)],[611]) ).
thf(753,plain,
! [SV108: $i] :
( ( ( empty @ SV108 )
| ~ ( ~ ( element @ ( sK5_B @ SV108 ) @ ( powerset @ SV108 ) )
| ~ ~ ( empty @ ( sK5_B @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(754,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK39_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(755,plain,
! [SV109: $i] :
( ( ~ ( relation @ SV109 )
| ~ ( ~ ! [SY565: $i] :
( ~ ( ~ ( ! [SY566: $i] :
~ ( in @ ( ordered_pair @ SY566 @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SY565 @ SV109 ) @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) ) )
| ( SY565
= ( relation_rng @ SV109 ) ) )
| ~ ! [SY567: $i] :
( ( SY567
!= ( relation_rng @ SV109 ) )
| ~ ( ~ ! [SY568: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY568 ) @ SV109 )
| ( in @ SY568 @ SY567 ) )
| ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ SY567 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY570 @ SY567 @ SV109 ) @ SY570 ) @ SV109 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(756,plain,
! [SV110: $i] :
( ( ~ ( ~ ! [SY571: $i,SY572: $i] :
( ~ ( relation @ SY572 )
| ~ ( in @ ( ordered_pair @ SV110 @ SY571 ) @ SY572 )
| ( in @ SV110 @ ( relation_dom @ SY572 ) ) )
| ~ ! [SY573: $i,SY574: $i] :
( ~ ( relation @ SY574 )
| ~ ( in @ ( ordered_pair @ SV110 @ SY573 ) @ SY574 )
| ( in @ SY573 @ ( relation_rng @ SY574 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(757,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)],[616]) ).
thf(758,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ ( sK43_SY367 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK41_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)],[617]) ).
thf(759,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)],[618]) ).
thf(760,plain,
( ( ~ ~ ( empty @ sK11_A )
| ~ ( relation @ sK11_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(761,plain,
! [SV111: $i] :
( ( ! [SY575: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_C @ SY575 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK10_C @ SY575 @ SV111 ) @ SY575 ) )
| ~ ( ( in @ ( sK10_C @ SY575 @ SV111 ) @ SV111 )
| ( in @ ( sK10_C @ SY575 @ SV111 ) @ SY575 ) ) )
| ( SV111 = SY575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(762,plain,
! [SV112: $i] :
( ( ! [SY576: $i] :
( ~ ( ~ ( in @ ( sK49_C @ SY576 @ SV112 ) @ SV112 )
| ~ ~ ( in @ ( sK49_C @ SY576 @ SV112 ) @ SY576 ) )
| ( element @ SV112 @ ( powerset @ SY576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(763,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK46_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK46_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY369 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(764,plain,
! [SV113: $i] :
( ( ~ ( ~ ( element @ ( sK3_B @ SV113 ) @ ( powerset @ SV113 ) )
| ~ ( empty @ ( sK3_B @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(765,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(766,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)],[625]) ).
thf(767,plain,
! [SV1: $i] :
( ( ( singleton @ SV1 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(768,plain,
! [SV114: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV114 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SV114 )
= SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(769,plain,
! [SV115: $i,SV3: $i] :
( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV115 )
| ~ ( in @ SV3 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(770,plain,
! [SV116: $i,SV4: $i] :
( ( ( in @ SV4 @ SV116 )
| ( disjoint @ ( singleton @ SV4 ) @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(771,plain,
! [SV5: $i,SV117: $i] :
( ( ~ ( element @ SV117 @ ( powerset @ SV5 ) )
| ! [SY577: $i] :
( ~ ( in @ SY577 @ SV117 )
| ( in @ SY577 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(772,plain,
! [SV118: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV118 )
| ( subset @ SV6 @ ( union @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(773,plain,
! [SV8: $i] :
( ( ( ~ ( subset @ SV8 @ empty_set ) )
= $true )
| ( ( SV8 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(774,plain,
! [SV119: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ SV119 )
| ( ( set_union2 @ ( singleton @ SV9 ) @ SV119 )
= SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(775,plain,
! [SV120: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ SV120 )
| ( subset @ SV10 @ ( union @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(776,plain,
! [SV121: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV121 )
| ~ ( in @ SV121 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(777,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(778,plain,
! [SV122: $i,SV13: $i] :
( ( ( ordered_pair @ SV13 @ SV122 )
= ( unordered_pair @ ( unordered_pair @ SV13 @ SV122 ) @ ( singleton @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(779,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(780,plain,
! [SV123: $i,SV15: $i] :
( ( ~ ( relation @ SV15 )
| ~ ( relation @ SV123 )
| ( relation @ ( relation_composition @ SV15 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(781,plain,
! [SV124: $i,SV16: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV16 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(782,plain,
! [SV125: $i,SV17: $i] :
( ( ~ ( relation @ SV17 )
| ~ ( relation @ SV125 )
| ( relation @ ( set_union2 @ SV17 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(783,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV18 ) )
= SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(784,plain,
! [SV126: $i,SV20: $i] :
( ( ~ ( in @ SV20 @ SV126 )
| ( element @ SV20 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(785,plain,
! [SV127: $i,SV22: $i] :
( ( ~ ( element @ SV22 @ SV127 )
| ( empty @ SV127 )
| ( in @ SV22 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(786,plain,
! [SV25: $i,SV128: $i] :
( ( ! [SY578: $i] :
( ~ ( element @ SV128 @ ( powerset @ SY578 ) )
| ~ ( in @ SV25 @ SV128 )
| ( element @ SV25 @ SY578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(787,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(788,plain,
! [SV27: $i,SV129: $i] :
( ( ~ ( empty @ SV129 )
| ~ ( in @ SV27 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(789,plain,
! [SV130: $i,SV28: $i] :
( ( ~ ( subset @ SV28 @ SV130 )
| ! [SY579: $i] :
( ( in @ SY579 @ SV28 )
| ( subset @ SV28 @ ( set_difference @ SV130 @ ( singleton @ SY579 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(790,plain,
! [SV131: $i,SV29: $i] :
( ( ! [SY580: $i,SY581: $i] :
( ( SV29 = SY581 )
| ( SV29 = SY580 )
| ( ( unordered_pair @ SV29 @ SV131 )
!= ( unordered_pair @ SY580 @ SY581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(791,plain,
! [SV132: $i,SV30: $i] :
( ( ! [SY582: $i,SY583: $i] :
( ~ ( subset @ SV30 @ SV132 )
| ~ ( subset @ SY582 @ SY583 )
| ( subset @ ( cartesian_product2 @ SV30 @ SY582 ) @ ( cartesian_product2 @ SV132 @ SY583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(792,plain,
! [SV133: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV133 )
| ( ( set_union2 @ SV31 @ SV133 )
= SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(793,plain,
! [SV134: $i,SV32: $i] :
( ( subset @ ( set_intersection2 @ SV32 @ SV134 ) @ SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(794,plain,
! [SV135: $i,SV33: $i] :
( ( ! [SY584: $i] :
( ~ ( subset @ SV33 @ SV135 )
| ~ ( subset @ SV33 @ SY584 )
| ( subset @ SV33 @ ( set_intersection2 @ SV135 @ SY584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(795,plain,
! [SV136: $i,SV34: $i] :
( ( ! [SY585: $i] :
( ~ ( subset @ SV34 @ SV136 )
| ~ ( subset @ SV136 @ SY585 )
| ( subset @ SV34 @ SY585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(796,plain,
! [SV35: $i] :
( ( ( ~ ( relation @ SV35 ) )
= $true )
| ( ( subset @ SV35 @ ( cartesian_product2 @ ( relation_dom @ SV35 ) @ ( relation_rng @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(797,plain,
! [SV137: $i,SV36: $i] :
( ( ~ ( subset @ SV36 @ SV137 )
| ! [SY586: $i] : ( subset @ ( set_intersection2 @ SV36 @ SY586 ) @ ( set_intersection2 @ SV137 @ SY586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(798,plain,
! [SV138: $i,SV37: $i] :
( ( ~ ( subset @ SV37 @ SV138 )
| ( ( set_intersection2 @ SV37 @ SV138 )
= SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(799,plain,
! [SV139: $i,SV38: $i] :
( ( ~ ( subset @ SV38 @ SV139 )
| ! [SY587: $i] : ( subset @ ( set_difference @ SV38 @ SY587 ) @ ( set_difference @ SV139 @ SY587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(800,plain,
! [SV140: $i,SV39: $i] :
( ( subset @ ( set_difference @ SV39 @ SV140 ) @ SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(801,plain,
! [SV141: $i,SV40: $i] :
( ( ( set_union2 @ SV40 @ ( set_difference @ SV141 @ SV40 ) )
= ( set_union2 @ SV40 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(802,plain,
! [SV142: $i,SV41: $i] :
( ( ( set_difference @ ( set_union2 @ SV41 @ SV142 ) @ SV142 )
= ( set_difference @ SV41 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(803,plain,
! [SV42: $i] :
( ( ( ~ ( relation @ SV42 ) )
= $true )
| ( ( ! [SY412: $i] :
( ~ ( relation @ SY412 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV42 @ SY412 ) ) @ ( relation_dom @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(804,plain,
! [SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ! [SY413: $i] :
( ~ ( relation @ SY413 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV43 @ SY413 ) ) @ ( relation_rng @ SY413 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(805,plain,
! [SV143: $i,SV44: $i] :
( ( ~ ( subset @ SV44 @ SV143 )
| ( SV143
= ( set_union2 @ SV44 @ ( set_difference @ SV143 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(806,plain,
! [SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( subset @ ( relation_rng @ SV45 ) @ ( relation_dom @ SY415 ) )
| ( ( relation_dom @ ( relation_composition @ SV45 @ SY415 ) )
= ( relation_dom @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(807,plain,
! [SV46: $i,SV144: $i] :
( ( ~ ( element @ SV144 @ ( powerset @ ( powerset @ SV46 ) ) )
| ( SV144 = empty_set )
| ( ( complements_of_subsets @ SV46 @ SV144 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(808,plain,
! [SV47: $i] :
( ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( ! [SY417: $i] :
( ~ ( relation @ SY417 )
| ~ ( subset @ ( relation_dom @ SV47 ) @ ( relation_rng @ SY417 ) )
| ( ( relation_rng @ ( relation_composition @ SY417 @ SV47 ) )
= ( relation_rng @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(809,plain,
! [SV145: $i,SV48: $i] :
( ( ( set_difference @ SV48 @ ( set_difference @ SV48 @ SV145 ) )
= ( set_intersection2 @ SV48 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(810,plain,
! [SV49: $i] :
( ( ( SV49 = empty_set )
= $true )
| ( ( ! [SY419: $i] :
( ~ ( element @ SY419 @ ( powerset @ SV49 ) )
| ! [SY420: $i] :
( ~ ( element @ SY420 @ SV49 )
| ( in @ SY420 @ SY419 )
| ( in @ SY420 @ ( subset_complement @ SV49 @ SY419 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(811,plain,
! [SV146: $i,SV50: $i] :
( ( ! [SY588: $i] :
( ~ ( element @ SY588 @ ( powerset @ SV50 ) )
| ~ ( in @ SV146 @ ( subset_complement @ SV50 @ SY588 ) )
| ~ ( in @ SV146 @ SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(812,plain,
! [SV51: $i,SV147: $i] :
( ( ~ ( proper_subset @ SV147 @ SV51 )
| ~ ( subset @ SV51 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(813,plain,
! [SV52: $i,SV148: $i] :
( ( ! [SY589: $i] :
( ~ ( disjoint @ SV148 @ SY589 )
| ~ ( subset @ SV52 @ SV148 )
| ( disjoint @ SV52 @ SY589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(814,plain,
! [SV149: $i,SV54: $i] :
( ( ~ ( subset @ ( singleton @ SV54 ) @ ( singleton @ SV149 ) )
| ( SV54 = SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(815,plain,
! [SV150: $i,SV55: $i] :
( ( subset @ SV55 @ ( set_union2 @ SV55 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(816,plain,
! [SV151: $i,SV56: $i] :
( ( ! [SY590: $i] :
( ~ ( subset @ SV56 @ SV151 )
| ~ ( subset @ SY590 @ SV151 )
| ( subset @ ( set_union2 @ SV56 @ SY590 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(817,plain,
! [SV152: $i,SV57: $i] :
( ( ! [SY591: $i] :
( ( singleton @ SV57 )
!= ( unordered_pair @ SV152 @ SY591 ) )
| ( SV57 = SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(818,plain,
! [SV153: $i,SV59: $i] :
( ( ! [SY592: $i] :
( ( ( singleton @ SV59 )
!= ( unordered_pair @ SV153 @ SY592 ) )
| ( SV153 = SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(819,plain,
! [SV154: $i,SV60: $i] :
( ( ( unordered_pair @ SV60 @ SV154 )
= ( unordered_pair @ SV154 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(820,plain,
! [SV155: $i,SV61: $i] :
( ( ( set_union2 @ SV61 @ SV155 )
= ( set_union2 @ SV155 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(821,plain,
! [SV156: $i,SV62: $i] :
( ( ( set_intersection2 @ SV62 @ SV156 )
= ( set_intersection2 @ SV156 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(822,plain,
! [SV63: $i,SV157: $i] :
( ( ~ ( element @ SV157 @ ( powerset @ SV63 ) )
| ( ( subset_complement @ SV63 @ SV157 )
= ( set_difference @ SV63 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(823,plain,
! [SV64: $i] :
( ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( ( relation_field @ SV64 )
= ( set_union2 @ ( relation_dom @ SV64 ) @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(824,plain,
! [SV66: $i,SV158: $i] :
( ( ~ ( element @ SV158 @ ( powerset @ SV66 ) )
| ( element @ ( subset_complement @ SV66 @ SV158 ) @ ( powerset @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(825,plain,
! [SV67: $i,SV159: $i] :
( ( ~ ( element @ SV159 @ ( powerset @ ( powerset @ SV67 ) ) )
| ( element @ ( union_of_subsets @ SV67 @ SV159 ) @ ( powerset @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(826,plain,
! [SV68: $i,SV160: $i] :
( ( ~ ( element @ SV160 @ ( powerset @ ( powerset @ SV68 ) ) )
| ( element @ ( meet_of_subsets @ SV68 @ SV160 ) @ ( powerset @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(827,plain,
! [SV69: $i,SV161: $i] :
( ( ! [SY593: $i] :
( ~ ( element @ SV161 @ ( powerset @ SV69 ) )
| ~ ( element @ SY593 @ ( powerset @ SV69 ) )
| ( element @ ( subset_difference @ SV69 @ SV161 @ SY593 ) @ ( powerset @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(828,plain,
! [SV70: $i,SV162: $i] :
( ( ~ ( element @ SV162 @ ( powerset @ ( powerset @ SV70 ) ) )
| ( element @ ( complements_of_subsets @ SV70 @ SV162 ) @ ( powerset @ ( powerset @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(829,plain,
! [SV72: $i] :
( ( empty @ ( powerset @ SV72 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(830,plain,
! [SV73: $i] :
( ( empty @ ( singleton @ SV73 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(831,plain,
! [SV74: $i] :
( ( ( empty @ SV74 )
= $true )
| ( ( ! [SY444: $i] :
~ ( empty @ ( set_union2 @ SV74 @ SY444 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(832,plain,
! [SV163: $i,SV75: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV75 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(833,plain,
! [SV76: $i] :
( ( ( empty @ SV76 )
= $true )
| ( ( ! [SY446: $i] :
~ ( empty @ ( set_union2 @ SY446 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(834,plain,
! [SV164: $i,SV77: $i] :
( ( ( empty @ SV77 )
| ( empty @ SV164 )
| ~ ( empty @ ( cartesian_product2 @ SV77 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(835,plain,
! [SV80: $i,SV165: $i] :
( ( ~ ( element @ SV165 @ ( powerset @ SV80 ) )
| ( ( subset_complement @ SV80 @ ( subset_complement @ SV80 @ SV165 ) )
= SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(836,plain,
! [SV81: $i,SV166: $i] :
( ( ~ ( element @ SV166 @ ( powerset @ ( powerset @ SV81 ) ) )
| ( ( complements_of_subsets @ SV81 @ ( complements_of_subsets @ SV81 @ SV166 ) )
= SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(837,plain,
! [SV82: $i,SV167: $i] :
( ( ~ ( element @ SV167 @ ( powerset @ ( powerset @ SV82 ) ) )
| ( ( union_of_subsets @ SV82 @ SV167 )
= ( union @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(838,plain,
! [SV83: $i,SV168: $i] :
( ( ~ ( element @ SV168 @ ( powerset @ ( powerset @ SV83 ) ) )
| ( ( meet_of_subsets @ SV83 @ SV168 )
= ( set_meet @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(839,plain,
! [SV84: $i,SV169: $i] :
( ( ! [SY594: $i] :
( ~ ( element @ SV169 @ ( powerset @ SV84 ) )
| ~ ( element @ SY594 @ ( powerset @ SV84 ) )
| ( ( subset_difference @ SV84 @ SV169 @ SY594 )
= ( set_difference @ SV169 @ SY594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(840,plain,
! [SV170: $i,SV86: $i] :
( ( ~ ( disjoint @ SV86 @ SV170 )
| ( disjoint @ SV170 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(841,plain,
! [SV87: $i,SV171: $i] :
( ( ! [SY595: $i] :
( ~ ( element @ SV171 @ ( powerset @ SY595 ) )
| ~ ( in @ SV87 @ SV171 )
| ~ ( empty @ SY595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(842,plain,
! [SV172: $i,SV88: $i] :
( ( ( SV88 = SV172 )
| ~ ( empty @ SV88 )
| ~ ( empty @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(843,plain,
! [SV173: $i,SV89: $i] :
( ( ~ ( in @ ( ordered_pair @ SV89 @ SV173 ) @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(844,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(845,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(846,plain,
( ( ~ ( empty @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(847,plain,
( ( ~ ( relation @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(848,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK47_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[719]) ).
thf(849,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[719]) ).
thf(850,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK40_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK40_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(851,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)],[720]) ).
thf(852,plain,
! [SV90: $i] :
( ( ( ~ ( relation @ SV90 ) )
= $true )
| ( ( ~ ( ~ ! [SY459: $i] :
( ~ ( ~ ( ! [SY460: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ SY460 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ ( sK28_SY360 @ SY459 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) ) )
| ( SY459
= ( relation_dom @ SV90 ) ) )
| ~ ! [SY461: $i] :
( ( SY461
!= ( relation_dom @ SV90 ) )
| ~ ( ~ ! [SY462: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY462 @ SY463 ) @ SV90 )
| ( in @ SY462 @ SY461 ) )
| ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SY461 )
| ( in @ ( ordered_pair @ SY464 @ ( sK26_D @ SY464 @ SY461 @ SV90 ) ) @ SV90 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(853,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY358 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK25_SY358 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(854,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 @ ( sK23_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(855,plain,
! [SV91: $i] :
( ( ~ ! [SY465: $i,SY466: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY465 ) ) )
| ~ ( ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY465 ) ) )
| ( SY466
= ( set_union2 @ SV91 @ SY465 ) ) )
| ~ ! [SY467: $i,SY468: $i] :
( ( SY468
!= ( set_union2 @ SV91 @ SY467 ) )
| ~ ( ~ ! [SY469: $i] :
( ~ ( in @ SY469 @ SY468 )
| ( in @ SY469 @ SV91 )
| ( in @ SY469 @ SY467 ) )
| ~ ~ ( ~ ! [SY470: $i] :
( ~ ( in @ SY470 @ SV91 )
| ( in @ SY470 @ SY468 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY467 )
| ( in @ SX3 @ SY468 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(856,plain,
! [SV92: $i] :
( ( ~ ! [SY472: $i,SY473: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY472 )
| ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY472 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) ) ) )
| ( SY473
= ( set_difference @ SV92 @ SY472 ) ) )
| ~ ! [SY474: $i,SY475: $i] :
( ( SY475
!= ( set_difference @ SV92 @ SY474 ) )
| ~ ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV92 )
| ( in @ SY476 @ SY474 )
| ( in @ SY476 @ SY475 ) )
| ~ ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY475 )
| ( in @ SY477 @ SV92 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY475 )
| ~ ( in @ SX3 @ SY474 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(857,plain,
! [SV93: $i] :
( ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( in @ SV93 @ SY480 )
| ~ ( in @ SY479 @ SY480 )
| ( subset @ ( unordered_pair @ SV93 @ SY479 ) @ SY480 ) )
| ~ ~ ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY481 ) @ SY482 )
| ( in @ SV93 @ SY482 ) )
| ~ ! [SY483: $i,SY484: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY483 ) @ SY484 )
| ( in @ SY483 @ SY484 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(858,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(859,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(860,plain,
! [SV94: $i] :
( ( ~ ! [SY485: $i] :
( ~ ( subset @ SV94 @ SY485 )
| ! [SY486: $i] : ( subset @ ( cartesian_product2 @ SV94 @ SY486 ) @ ( cartesian_product2 @ SY485 @ SY486 ) ) )
| ~ ! [SY487: $i] :
( ~ ( subset @ SV94 @ SY487 )
| ! [SY488: $i] : ( subset @ ( cartesian_product2 @ SY488 @ SV94 ) @ ( cartesian_product2 @ SY488 @ SY487 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(861,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(862,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(863,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(864,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(865,plain,
! [SV95: $i] :
( ( ~ ! [SY489: $i] :
( ~ ( subset @ SY489 @ ( sK7_B @ SV95 ) )
| ( are_equipotent @ SY489 @ ( sK7_B @ SV95 ) )
| ( in @ SY489 @ ( sK7_B @ SV95 ) ) )
| ~ ~ ( ~ ! [SY490: $i] :
( ~ ( in @ SY490 @ ( sK7_B @ SV95 ) )
| ( in @ ( powerset @ SY490 ) @ ( sK7_B @ SV95 ) ) )
| ~ ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) )
| ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(866,plain,
! [SV96: $i] :
( ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ! [SY493: $i] :
( ~ ( relation @ SY493 )
| ~ ( ~ ! [SY494: $i] :
( ~ ( relation @ SY494 )
| ~ ( ~ ( ! [SY495: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ SY495 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY495 @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY493 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY494 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK16_SY353 @ SY494 @ SY493 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY493 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY494 ) ) )
| ( SY494
= ( relation_composition @ SV96 @ SY493 ) ) )
| ~ ! [SY496: $i] :
( ~ ( relation @ SY496 )
| ( SY496
!= ( relation_composition @ SV96 @ SY493 ) )
| ~ ( ~ ! [SY497: $i,SY498: $i] :
( ! [SY499: $i] :
( ~ ( in @ ( ordered_pair @ SY497 @ SY499 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY499 @ SY498 ) @ SY493 ) )
| ( in @ ( ordered_pair @ SY497 @ SY498 ) @ SY496 ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( in @ ( ordered_pair @ SY500 @ SY501 ) @ SY496 )
| ~ ( ~ ( in @ ( ordered_pair @ SY500 @ ( sK13_F @ SY501 @ SY500 @ SY496 @ SY493 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY501 @ SY500 @ SY496 @ SY493 @ SV96 ) @ SY501 ) @ SY493 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(867,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(868,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(869,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(870,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(871,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK48_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK48_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(872,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(873,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK38_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK38_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(874,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)],[735]) ).
thf(875,plain,
! [SV174: $i,SV97: $i] :
( ( ~ ( ~ ! [SY596: $i] :
( ! [SY597: $i] :
( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SY596 @ SY597 ) )
| ( SV97 = SY596 ) )
| ~ ! [SY598: $i,SY599: $i] :
( ( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SY598 @ SY599 ) )
| ( SV174 = SY599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(876,plain,
! [SV98: $i,SV175: $i] :
( ( ~ ( element @ SV175 @ ( powerset @ SV98 ) )
| ~ ( ~ ! [SY600: $i] :
( ~ ( element @ SY600 @ ( powerset @ SV98 ) )
| ~ ( disjoint @ SV175 @ SY600 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SY600 ) ) )
| ~ ! [SY601: $i] :
( ~ ( element @ SY601 @ ( powerset @ SV98 ) )
| ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SY601 ) )
| ( disjoint @ SV175 @ SY601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(877,plain,
! [SV99: $i] :
( ( ( ~ ( relation @ SV99 ) )
= $true )
| ( ( ~ ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV99 @ SY510 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SY510 ) ) )
| ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV99 @ SY511 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SY511 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(878,plain,
! [SV100: $i] :
( ( ( ~ ( relation @ SV100 ) )
= $true )
| ( ( ~ ( ~ ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) ) )
| ( SY512
= ( relation_inverse @ SV100 ) ) )
| ~ ! [SY513: $i] :
( ~ ( relation @ SY513 )
| ( SY513
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( in @ ( ordered_pair @ SY514 @ SY515 ) @ SY513 )
| ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV100 ) )
| ~ ! [SY516: $i,SY517: $i] :
( ~ ( in @ ( ordered_pair @ SY517 @ SY516 ) @ SV100 )
| ( in @ ( ordered_pair @ SY516 @ SY517 ) @ SY513 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(879,plain,
! [SV101: $i] :
( ( ~ ! [SY518: $i,SY519: $i] :
( ~ ( ~ ( ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY518 )
| ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) )
| ~ ( ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY518 )
| ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) ) ) )
| ( SY519
= ( set_intersection2 @ SV101 @ SY518 ) ) )
| ~ ! [SY520: $i,SY521: $i] :
( ( SY521
!= ( set_intersection2 @ SV101 @ SY520 ) )
| ~ ( ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ SV101 )
| ~ ( in @ SY522 @ SY520 )
| ( in @ SY522 @ SY521 ) )
| ~ ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY521 )
| ( in @ SY523 @ SV101 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY521 )
| ( in @ SX3 @ SY520 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(880,plain,
! [SV102: $i] :
( ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( relation @ SY526 )
| ~ ( in @ ( ordered_pair @ SV102 @ SY525 ) @ SY526 )
| ( in @ SV102 @ ( relation_field @ SY526 ) ) )
| ~ ! [SY527: $i,SY528: $i] :
( ~ ( relation @ SY528 )
| ~ ( in @ ( ordered_pair @ SV102 @ SY527 ) @ SY528 )
| ( in @ SY527 @ ( relation_field @ SY528 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(881,plain,
! [SV103: $i] :
( ( ~ ! [SY529: $i] :
( ~ ( subset @ SY529 @ ( sK8_B @ SV103 ) )
| ( are_equipotent @ SY529 @ ( sK8_B @ SV103 ) )
| ( in @ SY529 @ ( sK8_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( ~ ! [SY531: $i] :
( ~ ( subset @ SY531 @ SY530 )
| ( in @ SY531 @ ( sK9_SY344 @ SY530 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SY530 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SY530 @ ( sK8_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(882,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(883,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)],[743]) ).
thf(884,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(885,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(886,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(887,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)],[745]) ).
thf(888,plain,
! [SV176: $i,SV104: $i] :
( ( ~ ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SV104 @ SY602 )
| ~ ( in @ SV176 @ SY603 )
| ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY602 @ SY603 ) ) )
| ~ ~ ( ~ ! [SY604: $i] :
( ! [SY605: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY604 @ SY605 ) )
| ( in @ SV104 @ SY604 ) )
| ~ ! [SY606: $i,SY607: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY606 @ SY607 ) )
| ( in @ SV176 @ SY607 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(889,plain,
! [SV105: $i] :
( ( ~ ! [SY541: $i,SY542: $i] :
( ~ ( ~ ( ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ SV105 )
| ~ ( in @ SY544 @ SY541 )
| ( ( sK33_D @ SY542 @ SY541 @ SV105 )
!= ( ordered_pair @ SY543 @ SY544 ) ) )
| ~ ( in @ ( sK33_D @ SY542 @ SY541 @ SV105 ) @ SY542 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SY542 @ SY541 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SY542 @ SY541 @ SV105 ) @ SY541 ) )
| ( ( sK33_D @ SY542 @ SY541 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SY542 @ SY541 @ SV105 ) @ ( sK35_SY366 @ SY542 @ SY541 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SY542 @ SY541 @ SV105 ) @ SY542 ) ) )
| ( SY542
= ( cartesian_product2 @ SV105 @ SY541 ) ) )
| ~ ! [SY545: $i,SY546: $i] :
( ( SY546
!= ( cartesian_product2 @ SV105 @ SY545 ) )
| ~ ( ~ ! [SY547: $i] :
( ! [SY548: $i,SY549: $i] :
( ~ ( in @ SY548 @ SV105 )
| ~ ( in @ SY549 @ SY545 )
| ( SY547
!= ( ordered_pair @ SY548 @ SY549 ) ) )
| ( in @ SY547 @ SY546 ) )
| ~ ! [SY550: $i] :
( ~ ( in @ SY550 @ SY546 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY550 @ SY546 @ SY545 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY550 @ SY546 @ SY545 @ SV105 ) @ SY545 ) )
| ( SY550
!= ( ordered_pair @ ( sK31_E @ SY550 @ SY546 @ SY545 @ SV105 ) @ ( sK32_SY361 @ SY550 @ SY546 @ SY545 @ SV105 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(890,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(891,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)],[748]) ).
thf(892,plain,
! [SV106: $i] :
( ( ~ ! [SY551: $i,SY552: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
!= SY551 ) ) )
| ~ ( ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
= SV106 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
= SY551 ) ) )
| ( SY552
= ( unordered_pair @ SV106 @ SY551 ) ) )
| ~ ! [SY553: $i,SY554: $i] :
( ( SY554
!= ( unordered_pair @ SV106 @ SY553 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SY554 )
| ( SY555 = SV106 )
| ( SY555 = SY553 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ( SY556 != SV106 )
| ( in @ SY556 @ SY554 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY553 )
| ( in @ SX3 @ SY554 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(893,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(894,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(895,plain,
! [SV177: $i,SV107: $i] :
( ( ~ ( ~ ! [SY608: $i,SY609: $i] :
( ~ ( in @ SV107 @ SY608 )
| ~ ( in @ SV177 @ SY609 )
| ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY608 @ SY609 ) ) )
| ~ ~ ( ~ ! [SY610: $i] :
( ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY610 @ SY611 ) )
| ( in @ SV107 @ SY610 ) )
| ~ ! [SY612: $i,SY613: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY612 @ SY613 ) )
| ( in @ SV177 @ SY613 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(896,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[752]) ).
thf(897,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[752]) ).
thf(898,plain,
! [SV108: $i] :
( ( ( empty @ SV108 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK5_B @ SV108 ) @ ( powerset @ SV108 ) )
| ~ ~ ( empty @ ( sK5_B @ SV108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(899,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK39_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(900,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(901,plain,
! [SV109: $i] :
( ( ( ~ ( relation @ SV109 ) )
= $true )
| ( ( ~ ( ~ ! [SY565: $i] :
( ~ ( ~ ( ! [SY566: $i] :
~ ( in @ ( ordered_pair @ SY566 @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SY565 @ SV109 ) @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) ) )
| ( SY565
= ( relation_rng @ SV109 ) ) )
| ~ ! [SY567: $i] :
( ( SY567
!= ( relation_rng @ SV109 ) )
| ~ ( ~ ! [SY568: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY568 ) @ SV109 )
| ( in @ SY568 @ SY567 ) )
| ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ SY567 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY570 @ SY567 @ SV109 ) @ SY570 ) @ SV109 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(902,plain,
! [SV110: $i] :
( ( ~ ! [SY571: $i,SY572: $i] :
( ~ ( relation @ SY572 )
| ~ ( in @ ( ordered_pair @ SV110 @ SY571 ) @ SY572 )
| ( in @ SV110 @ ( relation_dom @ SY572 ) ) )
| ~ ! [SY573: $i,SY574: $i] :
( ~ ( relation @ SY574 )
| ~ ( in @ ( ordered_pair @ SV110 @ SY573 ) @ SY574 )
| ( in @ SY573 @ ( relation_rng @ SY574 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(903,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(904,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(905,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ ( sK43_SY367 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK41_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)],[758]) ).
thf(906,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)],[758]) ).
thf(907,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(908,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)],[759]) ).
thf(909,plain,
( ( ~ ~ ( empty @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(910,plain,
( ( ~ ( relation @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(911,plain,
! [SV111: $i,SV178: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) )
| ~ ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) ) )
| ( SV111 = SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(912,plain,
! [SV112: $i,SV179: $i] :
( ( ~ ( ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV112 )
| ~ ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV179 ) )
| ( element @ SV112 @ ( powerset @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(913,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK46_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK46_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(914,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY369 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(915,plain,
! [SV113: $i] :
( ( ~ ( element @ ( sK3_B @ SV113 ) @ ( powerset @ SV113 ) )
| ~ ( empty @ ( sK3_B @ SV113 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(916,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(917,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(918,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)],[766]) ).
thf(919,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)],[766]) ).
thf(920,plain,
! [SV114: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV114 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV114 )
= SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(921,plain,
! [SV115: $i,SV3: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV115 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(922,plain,
! [SV116: $i,SV4: $i] :
( ( ( in @ SV4 @ SV116 )
= $true )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(923,plain,
! [SV5: $i,SV117: $i] :
( ( ( ~ ( element @ SV117 @ ( powerset @ SV5 ) ) )
= $true )
| ( ( ! [SY577: $i] :
( ~ ( in @ SY577 @ SV117 )
| ( in @ SY577 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(924,plain,
! [SV118: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV118 ) )
= $true )
| ( ( subset @ SV6 @ ( union @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(925,plain,
! [SV8: $i] :
( ( ( subset @ SV8 @ empty_set )
= $false )
| ( ( SV8 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(926,plain,
! [SV119: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV119 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV9 ) @ SV119 )
= SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(927,plain,
! [SV120: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV120 ) )
= $true )
| ( ( subset @ SV10 @ ( union @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(928,plain,
! [SV121: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV121 ) )
= $true )
| ( ( ~ ( in @ SV121 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(929,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
= $false )
| ( ( relation @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(930,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( relation @ ( relation_inverse @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(931,plain,
! [SV123: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 )
| ~ ( relation @ SV123 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV15 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(932,plain,
! [SV124: $i,SV16: $i] :
( ( empty @ ( ordered_pair @ SV16 @ SV124 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(933,plain,
! [SV125: $i,SV17: $i] :
( ( ( ~ ( relation @ SV17 )
| ~ ( relation @ SV125 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV17 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(934,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV18 ) )
= SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(935,plain,
! [SV126: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV126 ) )
= $true )
| ( ( element @ SV20 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(936,plain,
! [SV127: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ SV127 ) )
= $true )
| ( ( ( empty @ SV127 )
| ( in @ SV22 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(937,plain,
! [SV25: $i,SV180: $i,SV128: $i] :
( ( ~ ( element @ SV128 @ ( powerset @ SV180 ) )
| ~ ( in @ SV25 @ SV128 )
| ( element @ SV25 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(938,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(939,plain,
! [SV27: $i,SV129: $i] :
( ( ( ~ ( empty @ SV129 ) )
= $true )
| ( ( ~ ( in @ SV27 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(940,plain,
! [SV130: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV130 ) )
= $true )
| ( ( ! [SY579: $i] :
( ( in @ SY579 @ SV28 )
| ( subset @ SV28 @ ( set_difference @ SV130 @ ( singleton @ SY579 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(941,plain,
! [SV131: $i,SV181: $i,SV29: $i] :
( ( ! [SY614: $i] :
( ( SV29 = SY614 )
| ( SV29 = SV181 )
| ( ( unordered_pair @ SV29 @ SV131 )
!= ( unordered_pair @ SV181 @ SY614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(942,plain,
! [SV182: $i,SV132: $i,SV30: $i] :
( ( ! [SY615: $i] :
( ~ ( subset @ SV30 @ SV132 )
| ~ ( subset @ SV182 @ SY615 )
| ( subset @ ( cartesian_product2 @ SV30 @ SV182 ) @ ( cartesian_product2 @ SV132 @ SY615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(943,plain,
! [SV133: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV133 ) )
= $true )
| ( ( ( set_union2 @ SV31 @ SV133 )
= SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(944,plain,
! [SV183: $i,SV135: $i,SV33: $i] :
( ( ~ ( subset @ SV33 @ SV135 )
| ~ ( subset @ SV33 @ SV183 )
| ( subset @ SV33 @ ( set_intersection2 @ SV135 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(945,plain,
! [SV184: $i,SV136: $i,SV34: $i] :
( ( ~ ( subset @ SV34 @ SV136 )
| ~ ( subset @ SV136 @ SV184 )
| ( subset @ SV34 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(946,plain,
! [SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( subset @ SV35 @ ( cartesian_product2 @ ( relation_dom @ SV35 ) @ ( relation_rng @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(947,plain,
! [SV137: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV137 ) )
= $true )
| ( ( ! [SY586: $i] : ( subset @ ( set_intersection2 @ SV36 @ SY586 ) @ ( set_intersection2 @ SV137 @ SY586 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(948,plain,
! [SV138: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV138 ) )
= $true )
| ( ( ( set_intersection2 @ SV37 @ SV138 )
= SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(949,plain,
! [SV139: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV139 ) )
= $true )
| ( ( ! [SY587: $i] : ( subset @ ( set_difference @ SV38 @ SY587 ) @ ( set_difference @ SV139 @ SY587 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(950,plain,
! [SV42: $i] :
( ( ( relation @ SV42 )
= $false )
| ( ( ! [SY412: $i] :
( ~ ( relation @ SY412 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV42 @ SY412 ) ) @ ( relation_dom @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(951,plain,
! [SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( ! [SY413: $i] :
( ~ ( relation @ SY413 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV43 @ SY413 ) ) @ ( relation_rng @ SY413 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(952,plain,
! [SV143: $i,SV44: $i] :
( ( ( ~ ( subset @ SV44 @ SV143 ) )
= $true )
| ( ( SV143
= ( set_union2 @ SV44 @ ( set_difference @ SV143 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(953,plain,
! [SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( subset @ ( relation_rng @ SV45 ) @ ( relation_dom @ SY415 ) )
| ( ( relation_dom @ ( relation_composition @ SV45 @ SY415 ) )
= ( relation_dom @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(954,plain,
! [SV46: $i,SV144: $i] :
( ( ( ~ ( element @ SV144 @ ( powerset @ ( powerset @ SV46 ) ) ) )
= $true )
| ( ( ( SV144 = empty_set )
| ( ( complements_of_subsets @ SV46 @ SV144 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(955,plain,
! [SV47: $i] :
( ( ( relation @ SV47 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( relation @ SY417 )
| ~ ( subset @ ( relation_dom @ SV47 ) @ ( relation_rng @ SY417 ) )
| ( ( relation_rng @ ( relation_composition @ SY417 @ SV47 ) )
= ( relation_rng @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(956,plain,
! [SV49: $i,SV185: $i] :
( ( ( ~ ( element @ SV185 @ ( powerset @ SV49 ) )
| ! [SY616: $i] :
( ~ ( element @ SY616 @ SV49 )
| ( in @ SY616 @ SV185 )
| ( in @ SY616 @ ( subset_complement @ SV49 @ SV185 ) ) ) )
= $true )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(957,plain,
! [SV146: $i,SV50: $i,SV186: $i] :
( ( ~ ( element @ SV186 @ ( powerset @ SV50 ) )
| ~ ( in @ SV146 @ ( subset_complement @ SV50 @ SV186 ) )
| ~ ( in @ SV146 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(958,plain,
! [SV51: $i,SV147: $i] :
( ( ( ~ ( proper_subset @ SV147 @ SV51 ) )
= $true )
| ( ( ~ ( subset @ SV51 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(959,plain,
! [SV52: $i,SV187: $i,SV148: $i] :
( ( ~ ( disjoint @ SV148 @ SV187 )
| ~ ( subset @ SV52 @ SV148 )
| ( disjoint @ SV52 @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(960,plain,
! [SV149: $i,SV54: $i] :
( ( ( ~ ( subset @ ( singleton @ SV54 ) @ ( singleton @ SV149 ) ) )
= $true )
| ( ( SV54 = SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(961,plain,
! [SV188: $i,SV151: $i,SV56: $i] :
( ( ~ ( subset @ SV56 @ SV151 )
| ~ ( subset @ SV188 @ SV151 )
| ( subset @ ( set_union2 @ SV56 @ SV188 ) @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(962,plain,
! [SV152: $i,SV57: $i] :
( ( ( ! [SY591: $i] :
( ( singleton @ SV57 )
!= ( unordered_pair @ SV152 @ SY591 ) ) )
= $true )
| ( ( SV57 = SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(963,plain,
! [SV189: $i,SV153: $i,SV59: $i] :
( ( ( ( singleton @ SV59 )
!= ( unordered_pair @ SV153 @ SV189 ) )
| ( SV153 = SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(964,plain,
! [SV63: $i,SV157: $i] :
( ( ( ~ ( element @ SV157 @ ( powerset @ SV63 ) ) )
= $true )
| ( ( ( subset_complement @ SV63 @ SV157 )
= ( set_difference @ SV63 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(965,plain,
! [SV64: $i] :
( ( ( relation @ SV64 )
= $false )
| ( ( ( relation_field @ SV64 )
= ( set_union2 @ ( relation_dom @ SV64 ) @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(966,plain,
! [SV66: $i,SV158: $i] :
( ( ( ~ ( element @ SV158 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV66 @ SV158 ) @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(967,plain,
! [SV67: $i,SV159: $i] :
( ( ( ~ ( element @ SV159 @ ( powerset @ ( powerset @ SV67 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV67 @ SV159 ) @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(968,plain,
! [SV68: $i,SV160: $i] :
( ( ( ~ ( element @ SV160 @ ( powerset @ ( powerset @ SV68 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV68 @ SV160 ) @ ( powerset @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(969,plain,
! [SV190: $i,SV69: $i,SV161: $i] :
( ( ~ ( element @ SV161 @ ( powerset @ SV69 ) )
| ~ ( element @ SV190 @ ( powerset @ SV69 ) )
| ( element @ ( subset_difference @ SV69 @ SV161 @ SV190 ) @ ( powerset @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(970,plain,
! [SV70: $i,SV162: $i] :
( ( ( ~ ( element @ SV162 @ ( powerset @ ( powerset @ SV70 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV70 @ SV162 ) @ ( powerset @ ( powerset @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(971,plain,
! [SV191: $i,SV74: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV74 @ SV191 ) ) )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(972,plain,
! [SV163: $i,SV75: $i] :
( ( empty @ ( unordered_pair @ SV75 @ SV163 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(973,plain,
! [SV76: $i,SV192: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV192 @ SV76 ) ) )
= $true )
| ( ( empty @ SV76 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(974,plain,
! [SV164: $i,SV77: $i] :
( ( ( ( empty @ SV77 )
| ( empty @ SV164 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV77 @ SV164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(975,plain,
! [SV80: $i,SV165: $i] :
( ( ( ~ ( element @ SV165 @ ( powerset @ SV80 ) ) )
= $true )
| ( ( ( subset_complement @ SV80 @ ( subset_complement @ SV80 @ SV165 ) )
= SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(976,plain,
! [SV81: $i,SV166: $i] :
( ( ( ~ ( element @ SV166 @ ( powerset @ ( powerset @ SV81 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV81 @ ( complements_of_subsets @ SV81 @ SV166 ) )
= SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(977,plain,
! [SV82: $i,SV167: $i] :
( ( ( ~ ( element @ SV167 @ ( powerset @ ( powerset @ SV82 ) ) ) )
= $true )
| ( ( ( union_of_subsets @ SV82 @ SV167 )
= ( union @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(978,plain,
! [SV83: $i,SV168: $i] :
( ( ( ~ ( element @ SV168 @ ( powerset @ ( powerset @ SV83 ) ) ) )
= $true )
| ( ( ( meet_of_subsets @ SV83 @ SV168 )
= ( set_meet @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(979,plain,
! [SV193: $i,SV84: $i,SV169: $i] :
( ( ~ ( element @ SV169 @ ( powerset @ SV84 ) )
| ~ ( element @ SV193 @ ( powerset @ SV84 ) )
| ( ( subset_difference @ SV84 @ SV169 @ SV193 )
= ( set_difference @ SV169 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(980,plain,
! [SV170: $i,SV86: $i] :
( ( ( ~ ( disjoint @ SV86 @ SV170 ) )
= $true )
| ( ( disjoint @ SV170 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(981,plain,
! [SV87: $i,SV194: $i,SV171: $i] :
( ( ~ ( element @ SV171 @ ( powerset @ SV194 ) )
| ~ ( in @ SV87 @ SV171 )
| ~ ( empty @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(982,plain,
! [SV172: $i,SV88: $i] :
( ( ( ( SV88 = SV172 )
| ~ ( empty @ SV88 ) )
= $true )
| ( ( ~ ( empty @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(983,plain,
! [SV173: $i,SV89: $i] :
( ( in @ ( ordered_pair @ SV89 @ SV173 ) @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(984,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[844]) ).
thf(985,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(986,plain,
( ( empty @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(987,plain,
( ( relation @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(988,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK47_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(989,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(990,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK40_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK40_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK40_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(991,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)],[851]) ).
thf(992,plain,
! [SV90: $i] :
( ( ( relation @ SV90 )
= $false )
| ( ( ~ ( ~ ! [SY459: $i] :
( ~ ( ~ ( ! [SY460: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ SY460 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ ( sK28_SY360 @ SY459 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) ) )
| ( SY459
= ( relation_dom @ SV90 ) ) )
| ~ ! [SY461: $i] :
( ( SY461
!= ( relation_dom @ SV90 ) )
| ~ ( ~ ! [SY462: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY462 @ SY463 ) @ SV90 )
| ( in @ SY462 @ SY461 ) )
| ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SY461 )
| ( in @ ( ordered_pair @ SY464 @ ( sK26_D @ SY464 @ SY461 @ SV90 ) ) @ SV90 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(993,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY358 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK25_SY358 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(994,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 @ ( sK23_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(995,plain,
! [SV91: $i] :
( ( ~ ! [SY465: $i,SY466: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY465 ) ) )
| ~ ( ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY465 ) ) )
| ( SY466
= ( set_union2 @ SV91 @ SY465 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(996,plain,
! [SV91: $i] :
( ( ~ ! [SY467: $i,SY468: $i] :
( ( SY468
!= ( set_union2 @ SV91 @ SY467 ) )
| ~ ( ~ ! [SY469: $i] :
( ~ ( in @ SY469 @ SY468 )
| ( in @ SY469 @ SV91 )
| ( in @ SY469 @ SY467 ) )
| ~ ~ ( ~ ! [SY470: $i] :
( ~ ( in @ SY470 @ SV91 )
| ( in @ SY470 @ SY468 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY467 )
| ( in @ SX3 @ SY468 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(997,plain,
! [SV92: $i] :
( ( ~ ! [SY472: $i,SY473: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY472 )
| ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY472 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) ) ) )
| ( SY473
= ( set_difference @ SV92 @ SY472 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(998,plain,
! [SV92: $i] :
( ( ~ ! [SY474: $i,SY475: $i] :
( ( SY475
!= ( set_difference @ SV92 @ SY474 ) )
| ~ ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV92 )
| ( in @ SY476 @ SY474 )
| ( in @ SY476 @ SY475 ) )
| ~ ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY475 )
| ( in @ SY477 @ SV92 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY475 )
| ~ ( in @ SX3 @ SY474 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(999,plain,
! [SV93: $i] :
( ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( in @ SV93 @ SY480 )
| ~ ( in @ SY479 @ SY480 )
| ( subset @ ( unordered_pair @ SV93 @ SY479 ) @ SY480 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(1000,plain,
! [SV93: $i] :
( ( ~ ~ ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY481 ) @ SY482 )
| ( in @ SV93 @ SY482 ) )
| ~ ! [SY483: $i,SY484: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY483 ) @ SY484 )
| ( in @ SY483 @ SY484 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(1001,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(1002,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(1003,plain,
! [SV94: $i] :
( ( ~ ! [SY485: $i] :
( ~ ( subset @ SV94 @ SY485 )
| ! [SY486: $i] : ( subset @ ( cartesian_product2 @ SV94 @ SY486 ) @ ( cartesian_product2 @ SY485 @ SY486 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(1004,plain,
! [SV94: $i] :
( ( ~ ! [SY487: $i] :
( ~ ( subset @ SV94 @ SY487 )
| ! [SY488: $i] : ( subset @ ( cartesian_product2 @ SY488 @ SV94 ) @ ( cartesian_product2 @ SY488 @ SY487 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(1005,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(1006,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(1007,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(1008,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(1009,plain,
! [SV95: $i] :
( ( ~ ! [SY489: $i] :
( ~ ( subset @ SY489 @ ( sK7_B @ SV95 ) )
| ( are_equipotent @ SY489 @ ( sK7_B @ SV95 ) )
| ( in @ SY489 @ ( sK7_B @ SV95 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(1010,plain,
! [SV95: $i] :
( ( ~ ~ ( ~ ! [SY490: $i] :
( ~ ( in @ SY490 @ ( sK7_B @ SV95 ) )
| ( in @ ( powerset @ SY490 ) @ ( sK7_B @ SV95 ) ) )
| ~ ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) )
| ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(1011,plain,
! [SV96: $i] :
( ( ( relation @ SV96 )
= $false )
| ( ( ! [SY493: $i] :
( ~ ( relation @ SY493 )
| ~ ( ~ ! [SY494: $i] :
( ~ ( relation @ SY494 )
| ~ ( ~ ( ! [SY495: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ SY495 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY495 @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY493 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY494 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK16_SY353 @ SY494 @ SY493 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY493 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY494 @ SY493 @ SV96 ) @ ( sK15_SY349 @ SY494 @ SY493 @ SV96 ) ) @ SY494 ) ) )
| ( SY494
= ( relation_composition @ SV96 @ SY493 ) ) )
| ~ ! [SY496: $i] :
( ~ ( relation @ SY496 )
| ( SY496
!= ( relation_composition @ SV96 @ SY493 ) )
| ~ ( ~ ! [SY497: $i,SY498: $i] :
( ! [SY499: $i] :
( ~ ( in @ ( ordered_pair @ SY497 @ SY499 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY499 @ SY498 ) @ SY493 ) )
| ( in @ ( ordered_pair @ SY497 @ SY498 ) @ SY496 ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( in @ ( ordered_pair @ SY500 @ SY501 ) @ SY496 )
| ~ ( ~ ( in @ ( ordered_pair @ SY500 @ ( sK13_F @ SY501 @ SY500 @ SY496 @ SY493 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY501 @ SY500 @ SY496 @ SY493 @ SV96 ) @ SY501 ) @ SY493 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(1012,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(1013,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(1014,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(1015,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(1016,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK48_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK48_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(1017,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(1018,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK38_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK38_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(1019,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)],[874]) ).
thf(1020,plain,
! [SV174: $i,SV97: $i] :
( ( ~ ! [SY596: $i] :
( ! [SY597: $i] :
( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SY596 @ SY597 ) )
| ( SV97 = SY596 ) )
| ~ ! [SY598: $i,SY599: $i] :
( ( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SY598 @ SY599 ) )
| ( SV174 = SY599 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(1021,plain,
! [SV98: $i,SV175: $i] :
( ( ( ~ ( element @ SV175 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY600: $i] :
( ~ ( element @ SY600 @ ( powerset @ SV98 ) )
| ~ ( disjoint @ SV175 @ SY600 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SY600 ) ) )
| ~ ! [SY601: $i] :
( ~ ( element @ SY601 @ ( powerset @ SV98 ) )
| ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SY601 ) )
| ( disjoint @ SV175 @ SY601 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(1022,plain,
! [SV99: $i] :
( ( ( relation @ SV99 )
= $false )
| ( ( ~ ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV99 @ SY510 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SY510 ) ) )
| ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV99 @ SY511 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SY511 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(1023,plain,
! [SV100: $i] :
( ( ( relation @ SV100 )
= $false )
| ( ( ~ ( ~ ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) ) )
| ( SY512
= ( relation_inverse @ SV100 ) ) )
| ~ ! [SY513: $i] :
( ~ ( relation @ SY513 )
| ( SY513
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( in @ ( ordered_pair @ SY514 @ SY515 ) @ SY513 )
| ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV100 ) )
| ~ ! [SY516: $i,SY517: $i] :
( ~ ( in @ ( ordered_pair @ SY517 @ SY516 ) @ SV100 )
| ( in @ ( ordered_pair @ SY516 @ SY517 ) @ SY513 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(1024,plain,
! [SV101: $i] :
( ( ~ ! [SY518: $i,SY519: $i] :
( ~ ( ~ ( ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY518 )
| ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) )
| ~ ( ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY518 )
| ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) ) ) )
| ( SY519
= ( set_intersection2 @ SV101 @ SY518 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(1025,plain,
! [SV101: $i] :
( ( ~ ! [SY520: $i,SY521: $i] :
( ( SY521
!= ( set_intersection2 @ SV101 @ SY520 ) )
| ~ ( ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ SV101 )
| ~ ( in @ SY522 @ SY520 )
| ( in @ SY522 @ SY521 ) )
| ~ ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY521 )
| ( in @ SY523 @ SV101 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY521 )
| ( in @ SX3 @ SY520 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(1026,plain,
! [SV102: $i] :
( ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( relation @ SY526 )
| ~ ( in @ ( ordered_pair @ SV102 @ SY525 ) @ SY526 )
| ( in @ SV102 @ ( relation_field @ SY526 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[880]) ).
thf(1027,plain,
! [SV102: $i] :
( ( ~ ! [SY527: $i,SY528: $i] :
( ~ ( relation @ SY528 )
| ~ ( in @ ( ordered_pair @ SV102 @ SY527 ) @ SY528 )
| ( in @ SY527 @ ( relation_field @ SY528 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[880]) ).
thf(1028,plain,
! [SV103: $i] :
( ( ~ ! [SY529: $i] :
( ~ ( subset @ SY529 @ ( sK8_B @ SV103 ) )
| ( are_equipotent @ SY529 @ ( sK8_B @ SV103 ) )
| ( in @ SY529 @ ( sK8_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(1029,plain,
! [SV103: $i] :
( ( ~ ~ ( ~ ! [SY530: $i] :
( ~ ( ~ ! [SY531: $i] :
( ~ ( subset @ SY531 @ SY530 )
| ( in @ SY531 @ ( sK9_SY344 @ SY530 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SY530 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SY530 @ ( sK8_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(1030,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(1031,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)],[883]) ).
thf(1032,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[884]) ).
thf(1033,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(1034,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(1035,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)],[887]) ).
thf(1036,plain,
! [SV176: $i,SV104: $i] :
( ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SV104 @ SY602 )
| ~ ( in @ SV176 @ SY603 )
| ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY602 @ SY603 ) ) )
| ~ ~ ( ~ ! [SY604: $i] :
( ! [SY605: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY604 @ SY605 ) )
| ( in @ SV104 @ SY604 ) )
| ~ ! [SY606: $i,SY607: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY606 @ SY607 ) )
| ( in @ SV176 @ SY607 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(1037,plain,
! [SV105: $i] :
( ( ~ ! [SY541: $i,SY542: $i] :
( ~ ( ~ ( ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ SV105 )
| ~ ( in @ SY544 @ SY541 )
| ( ( sK33_D @ SY542 @ SY541 @ SV105 )
!= ( ordered_pair @ SY543 @ SY544 ) ) )
| ~ ( in @ ( sK33_D @ SY542 @ SY541 @ SV105 ) @ SY542 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SY542 @ SY541 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SY542 @ SY541 @ SV105 ) @ SY541 ) )
| ( ( sK33_D @ SY542 @ SY541 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SY542 @ SY541 @ SV105 ) @ ( sK35_SY366 @ SY542 @ SY541 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SY542 @ SY541 @ SV105 ) @ SY542 ) ) )
| ( SY542
= ( cartesian_product2 @ SV105 @ SY541 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(1038,plain,
! [SV105: $i] :
( ( ~ ! [SY545: $i,SY546: $i] :
( ( SY546
!= ( cartesian_product2 @ SV105 @ SY545 ) )
| ~ ( ~ ! [SY547: $i] :
( ! [SY548: $i,SY549: $i] :
( ~ ( in @ SY548 @ SV105 )
| ~ ( in @ SY549 @ SY545 )
| ( SY547
!= ( ordered_pair @ SY548 @ SY549 ) ) )
| ( in @ SY547 @ SY546 ) )
| ~ ! [SY550: $i] :
( ~ ( in @ SY550 @ SY546 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY550 @ SY546 @ SY545 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY550 @ SY546 @ SY545 @ SV105 ) @ SY545 ) )
| ( SY550
!= ( ordered_pair @ ( sK31_E @ SY550 @ SY546 @ SY545 @ SV105 ) @ ( sK32_SY361 @ SY550 @ SY546 @ SY545 @ SV105 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(1039,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(1040,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)],[891]) ).
thf(1041,plain,
! [SV106: $i] :
( ( ~ ! [SY551: $i,SY552: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
!= SY551 ) ) )
| ~ ( ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
= SV106 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
= SY551 ) ) )
| ( SY552
= ( unordered_pair @ SV106 @ SY551 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(1042,plain,
! [SV106: $i] :
( ( ~ ! [SY553: $i,SY554: $i] :
( ( SY554
!= ( unordered_pair @ SV106 @ SY553 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SY554 )
| ( SY555 = SV106 )
| ( SY555 = SY553 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ( SY556 != SV106 )
| ( in @ SY556 @ SY554 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY553 )
| ( in @ SX3 @ SY554 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(1043,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(1044,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(1045,plain,
! [SV177: $i,SV107: $i] :
( ( ~ ! [SY608: $i,SY609: $i] :
( ~ ( in @ SV107 @ SY608 )
| ~ ( in @ SV177 @ SY609 )
| ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY608 @ SY609 ) ) )
| ~ ~ ( ~ ! [SY610: $i] :
( ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY610 @ SY611 ) )
| ( in @ SV107 @ SY610 ) )
| ~ ! [SY612: $i,SY613: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY612 @ SY613 ) )
| ( in @ SV177 @ SY613 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(1046,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(1047,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(1048,plain,
! [SV108: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV108 ) @ ( powerset @ SV108 ) )
| ~ ~ ( empty @ ( sK5_B @ SV108 ) ) )
= $false )
| ( ( empty @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(1049,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK39_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(1050,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(1051,plain,
! [SV109: $i] :
( ( ( relation @ SV109 )
= $false )
| ( ( ~ ( ~ ! [SY565: $i] :
( ~ ( ~ ( ! [SY566: $i] :
~ ( in @ ( ordered_pair @ SY566 @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SY565 @ SV109 ) @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) ) )
| ( SY565
= ( relation_rng @ SV109 ) ) )
| ~ ! [SY567: $i] :
( ( SY567
!= ( relation_rng @ SV109 ) )
| ~ ( ~ ! [SY568: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY568 ) @ SV109 )
| ( in @ SY568 @ SY567 ) )
| ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ SY567 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY570 @ SY567 @ SV109 ) @ SY570 ) @ SV109 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(1052,plain,
! [SV110: $i] :
( ( ~ ! [SY571: $i,SY572: $i] :
( ~ ( relation @ SY572 )
| ~ ( in @ ( ordered_pair @ SV110 @ SY571 ) @ SY572 )
| ( in @ SV110 @ ( relation_dom @ SY572 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(1053,plain,
! [SV110: $i] :
( ( ~ ! [SY573: $i,SY574: $i] :
( ~ ( relation @ SY574 )
| ~ ( in @ ( ordered_pair @ SV110 @ SY573 ) @ SY574 )
| ( in @ SY573 @ ( relation_rng @ SY574 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(1054,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(1055,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(1056,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ ( sK43_SY367 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK41_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)],[905]) ).
thf(1057,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)],[906]) ).
thf(1058,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(1059,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)],[908]) ).
thf(1060,plain,
( ( ~ ( empty @ sK11_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[909]) ).
thf(1061,plain,
( ( relation @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(1062,plain,
! [SV111: $i,SV178: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) )
| ~ ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) ) ) )
= $true )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1063,plain,
! [SV112: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV112 )
| ~ ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV179 ) ) )
= $true )
| ( ( element @ SV112 @ ( powerset @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1064,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK46_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK46_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(1065,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY369 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(1066,plain,
! [SV113: $i] :
( ( ~ ( element @ ( sK3_B @ SV113 ) @ ( powerset @ SV113 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(1067,plain,
! [SV113: $i] :
( ( ~ ( empty @ ( sK3_B @ SV113 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(1068,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(1069,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(1070,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)],[918]) ).
thf(1071,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)],[919]) ).
thf(1072,plain,
! [SV114: $i,SV2: $i] :
( ( ( in @ SV2 @ SV114 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV114 )
= SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1073,plain,
! [SV115: $i,SV3: $i] :
( ( ( disjoint @ ( singleton @ SV3 ) @ SV115 )
= $false )
| ( ( ~ ( in @ SV3 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1074,plain,
! [SV5: $i,SV117: $i] :
( ( ( element @ SV117 @ ( powerset @ SV5 ) )
= $false )
| ( ( ! [SY577: $i] :
( ~ ( in @ SY577 @ SV117 )
| ( in @ SY577 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1075,plain,
! [SV118: $i,SV6: $i] :
( ( ( in @ SV6 @ SV118 )
= $false )
| ( ( subset @ SV6 @ ( union @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(1076,plain,
! [SV119: $i,SV9: $i] :
( ( ( in @ SV9 @ SV119 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV9 ) @ SV119 )
= SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1077,plain,
! [SV120: $i,SV10: $i] :
( ( ( in @ SV10 @ SV120 )
= $false )
| ( ( subset @ SV10 @ ( union @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1078,plain,
! [SV121: $i,SV11: $i] :
( ( ( in @ SV11 @ SV121 )
= $false )
| ( ( ~ ( in @ SV121 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1079,plain,
! [SV123: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV15 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1080,plain,
! [SV125: $i,SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( relation @ SV125 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV17 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1081,plain,
! [SV126: $i,SV20: $i] :
( ( ( in @ SV20 @ SV126 )
= $false )
| ( ( element @ SV20 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1082,plain,
! [SV127: $i,SV22: $i] :
( ( ( element @ SV22 @ SV127 )
= $false )
| ( ( ( empty @ SV127 )
| ( in @ SV22 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1083,plain,
! [SV25: $i,SV180: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ ( powerset @ SV180 ) )
| ~ ( in @ SV25 @ SV128 ) )
= $true )
| ( ( element @ SV25 @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1084,plain,
! [SV27: $i,SV129: $i] :
( ( ( empty @ SV129 )
= $false )
| ( ( ~ ( in @ SV27 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1085,plain,
! [SV130: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV130 )
= $false )
| ( ( ! [SY579: $i] :
( ( in @ SY579 @ SV28 )
| ( subset @ SV28 @ ( set_difference @ SV130 @ ( singleton @ SY579 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1086,plain,
! [SV131: $i,SV181: $i,SV195: $i,SV29: $i] :
( ( ( SV29 = SV195 )
| ( SV29 = SV181 )
| ( ( unordered_pair @ SV29 @ SV131 )
!= ( unordered_pair @ SV181 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1087,plain,
! [SV196: $i,SV182: $i,SV132: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV132 )
| ~ ( subset @ SV182 @ SV196 )
| ( subset @ ( cartesian_product2 @ SV30 @ SV182 ) @ ( cartesian_product2 @ SV132 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1088,plain,
! [SV133: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV133 )
= $false )
| ( ( ( set_union2 @ SV31 @ SV133 )
= SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1089,plain,
! [SV183: $i,SV135: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV135 )
| ~ ( subset @ SV33 @ SV183 ) )
= $true )
| ( ( subset @ SV33 @ ( set_intersection2 @ SV135 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1090,plain,
! [SV184: $i,SV136: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV136 )
| ~ ( subset @ SV136 @ SV184 ) )
= $true )
| ( ( subset @ SV34 @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1091,plain,
! [SV137: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV137 )
= $false )
| ( ( ! [SY586: $i] : ( subset @ ( set_intersection2 @ SV36 @ SY586 ) @ ( set_intersection2 @ SV137 @ SY586 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1092,plain,
! [SV138: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV138 )
= $false )
| ( ( ( set_intersection2 @ SV37 @ SV138 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1093,plain,
! [SV139: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV139 )
= $false )
| ( ( ! [SY587: $i] : ( subset @ ( set_difference @ SV38 @ SY587 ) @ ( set_difference @ SV139 @ SY587 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1094,plain,
! [SV42: $i,SV197: $i] :
( ( ( ~ ( relation @ SV197 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV42 @ SV197 ) ) @ ( relation_dom @ SV42 ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1095,plain,
! [SV43: $i,SV198: $i] :
( ( ( ~ ( relation @ SV198 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV43 @ SV198 ) ) @ ( relation_rng @ SV198 ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1096,plain,
! [SV143: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV143 )
= $false )
| ( ( SV143
= ( set_union2 @ SV44 @ ( set_difference @ SV143 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1097,plain,
! [SV45: $i,SV199: $i] :
( ( ( ~ ( relation @ SV199 )
| ~ ( subset @ ( relation_rng @ SV45 ) @ ( relation_dom @ SV199 ) )
| ( ( relation_dom @ ( relation_composition @ SV45 @ SV199 ) )
= ( relation_dom @ SV45 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1098,plain,
! [SV46: $i,SV144: $i] :
( ( ( element @ SV144 @ ( powerset @ ( powerset @ SV46 ) ) )
= $false )
| ( ( ( SV144 = empty_set )
| ( ( complements_of_subsets @ SV46 @ SV144 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1099,plain,
! [SV47: $i,SV200: $i] :
( ( ( ~ ( relation @ SV200 )
| ~ ( subset @ ( relation_dom @ SV47 ) @ ( relation_rng @ SV200 ) )
| ( ( relation_rng @ ( relation_composition @ SV200 @ SV47 ) )
= ( relation_rng @ SV47 ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1100,plain,
! [SV49: $i,SV185: $i] :
( ( ( ~ ( element @ SV185 @ ( powerset @ SV49 ) ) )
= $true )
| ( ( ! [SY616: $i] :
( ~ ( element @ SY616 @ SV49 )
| ( in @ SY616 @ SV185 )
| ( in @ SY616 @ ( subset_complement @ SV49 @ SV185 ) ) ) )
= $true )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1101,plain,
! [SV146: $i,SV50: $i,SV186: $i] :
( ( ( ~ ( element @ SV186 @ ( powerset @ SV50 ) ) )
= $true )
| ( ( ~ ( in @ SV146 @ ( subset_complement @ SV50 @ SV186 ) )
| ~ ( in @ SV146 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1102,plain,
! [SV51: $i,SV147: $i] :
( ( ( proper_subset @ SV147 @ SV51 )
= $false )
| ( ( ~ ( subset @ SV51 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1103,plain,
! [SV52: $i,SV187: $i,SV148: $i] :
( ( ( ~ ( disjoint @ SV148 @ SV187 )
| ~ ( subset @ SV52 @ SV148 ) )
= $true )
| ( ( disjoint @ SV52 @ SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1104,plain,
! [SV149: $i,SV54: $i] :
( ( ( subset @ ( singleton @ SV54 ) @ ( singleton @ SV149 ) )
= $false )
| ( ( SV54 = SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1105,plain,
! [SV188: $i,SV151: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV151 )
| ~ ( subset @ SV188 @ SV151 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV56 @ SV188 ) @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1106,plain,
! [SV201: $i,SV152: $i,SV57: $i] :
( ( ( ( ( singleton @ SV57 )
!= ( unordered_pair @ SV152 @ SV201 ) ) )
= $true )
| ( ( SV57 = SV152 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1107,plain,
! [SV189: $i,SV153: $i,SV59: $i] :
( ( ( ( ( singleton @ SV59 )
!= ( unordered_pair @ SV153 @ SV189 ) ) )
= $true )
| ( ( SV153 = SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1108,plain,
! [SV63: $i,SV157: $i] :
( ( ( element @ SV157 @ ( powerset @ SV63 ) )
= $false )
| ( ( ( subset_complement @ SV63 @ SV157 )
= ( set_difference @ SV63 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1109,plain,
! [SV66: $i,SV158: $i] :
( ( ( element @ SV158 @ ( powerset @ SV66 ) )
= $false )
| ( ( element @ ( subset_complement @ SV66 @ SV158 ) @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1110,plain,
! [SV67: $i,SV159: $i] :
( ( ( element @ SV159 @ ( powerset @ ( powerset @ SV67 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV67 @ SV159 ) @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1111,plain,
! [SV68: $i,SV160: $i] :
( ( ( element @ SV160 @ ( powerset @ ( powerset @ SV68 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV68 @ SV160 ) @ ( powerset @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1112,plain,
! [SV190: $i,SV69: $i,SV161: $i] :
( ( ( ~ ( element @ SV161 @ ( powerset @ SV69 ) )
| ~ ( element @ SV190 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV69 @ SV161 @ SV190 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1113,plain,
! [SV70: $i,SV162: $i] :
( ( ( element @ SV162 @ ( powerset @ ( powerset @ SV70 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV70 @ SV162 ) @ ( powerset @ ( powerset @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1114,plain,
! [SV191: $i,SV74: $i] :
( ( ( empty @ ( set_union2 @ SV74 @ SV191 ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1115,plain,
! [SV76: $i,SV192: $i] :
( ( ( empty @ ( set_union2 @ SV192 @ SV76 ) )
= $false )
| ( ( empty @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1116,plain,
! [SV164: $i,SV77: $i] :
( ( ( empty @ SV77 )
= $true )
| ( ( empty @ SV164 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV77 @ SV164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1117,plain,
! [SV80: $i,SV165: $i] :
( ( ( element @ SV165 @ ( powerset @ SV80 ) )
= $false )
| ( ( ( subset_complement @ SV80 @ ( subset_complement @ SV80 @ SV165 ) )
= SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1118,plain,
! [SV81: $i,SV166: $i] :
( ( ( element @ SV166 @ ( powerset @ ( powerset @ SV81 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV81 @ ( complements_of_subsets @ SV81 @ SV166 ) )
= SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1119,plain,
! [SV82: $i,SV167: $i] :
( ( ( element @ SV167 @ ( powerset @ ( powerset @ SV82 ) ) )
= $false )
| ( ( ( union_of_subsets @ SV82 @ SV167 )
= ( union @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1120,plain,
! [SV83: $i,SV168: $i] :
( ( ( element @ SV168 @ ( powerset @ ( powerset @ SV83 ) ) )
= $false )
| ( ( ( meet_of_subsets @ SV83 @ SV168 )
= ( set_meet @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1121,plain,
! [SV193: $i,SV84: $i,SV169: $i] :
( ( ( ~ ( element @ SV169 @ ( powerset @ SV84 ) )
| ~ ( element @ SV193 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ( subset_difference @ SV84 @ SV169 @ SV193 )
= ( set_difference @ SV169 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1122,plain,
! [SV170: $i,SV86: $i] :
( ( ( disjoint @ SV86 @ SV170 )
= $false )
| ( ( disjoint @ SV170 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1123,plain,
! [SV87: $i,SV194: $i,SV171: $i] :
( ( ( ~ ( element @ SV171 @ ( powerset @ SV194 ) )
| ~ ( in @ SV87 @ SV171 ) )
= $true )
| ( ( ~ ( empty @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1124,plain,
! [SV172: $i,SV88: $i] :
( ( ( SV88 = SV172 )
= $true )
| ( ( ~ ( empty @ SV88 ) )
= $true )
| ( ( ~ ( empty @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1125,plain,
! [SV202: $i] :
( ( ! [SY617: $i] :
( ~ ( ~ ( in @ ( sK30_C @ SY617 @ SV202 ) @ SV202 )
| ~ ~ ( in @ ( sK30_C @ SY617 @ SV202 ) @ SY617 ) )
| ( subset @ SV202 @ SY617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1126,plain,
! [SV203: $i] :
( ( ! [SY618: $i] :
( ~ ( subset @ SV203 @ SY618 )
| ! [SY619: $i] :
( ~ ( in @ SY619 @ SV203 )
| ( in @ SY619 @ SY618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1127,plain,
! [SV204: $i] :
( ( ! [SY620: $i] :
( ( disjoint @ SV204 @ SY620 )
| ( in @ ( sK47_C @ SY620 @ SV204 ) @ ( set_intersection2 @ SV204 @ SY620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1128,plain,
! [SV205: $i] :
( ( ! [SY621: $i] :
( ! [SY622: $i] :
~ ( in @ SY622 @ ( set_intersection2 @ SV205 @ SY621 ) )
| ~ ( disjoint @ SV205 @ SY621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1129,plain,
! [SV206: $i] :
( ( ! [SY623: $i] :
( ~ ( ~ ( ( ( sK40_C @ SY623 @ SV206 )
!= SV206 )
| ~ ( in @ ( sK40_C @ SY623 @ SV206 ) @ SY623 ) )
| ~ ( ( ( sK40_C @ SY623 @ SV206 )
= SV206 )
| ( in @ ( sK40_C @ SY623 @ SV206 ) @ SY623 ) ) )
| ( SY623
= ( singleton @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1130,plain,
! [SV207: $i] :
( ( ! [SY624: $i] :
( ( SY624
!= ( singleton @ SV207 ) )
| ~ ( ~ ! [SY625: $i] :
( ( SY625 != SV207 )
| ( in @ SY625 @ SY624 ) )
| ~ ! [SY626: $i] :
( ~ ( in @ SY626 @ SY624 )
| ( SY626 = SV207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1131,plain,
! [SV90: $i] :
( ( ( ~ ! [SY459: $i] :
( ~ ( ~ ( ! [SY460: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ SY460 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ ( sK28_SY360 @ SY459 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) ) )
| ( SY459
= ( relation_dom @ SV90 ) ) )
| ~ ! [SY461: $i] :
( ( SY461
!= ( relation_dom @ SV90 ) )
| ~ ( ~ ! [SY462: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY462 @ SY463 ) @ SV90 )
| ( in @ SY462 @ SY461 ) )
| ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SY461 )
| ( in @ ( ordered_pair @ SY464 @ ( sK26_D @ SY464 @ SY461 @ SV90 ) ) @ SV90 ) ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1132,plain,
! [SV208: $i] :
( ( ! [SY627: $i] :
( ~ ( ~ ( ! [SY628: $i] :
( ~ ( in @ ( sK24_C @ SY627 @ SV208 ) @ SY628 )
| ~ ( in @ SY628 @ SV208 ) )
| ~ ( in @ ( sK24_C @ SY627 @ SV208 ) @ SY627 ) )
| ~ ( ~ ( ~ ( in @ ( sK24_C @ SY627 @ SV208 ) @ ( sK25_SY358 @ SY627 @ SV208 ) )
| ~ ( in @ ( sK25_SY358 @ SY627 @ SV208 ) @ SV208 ) )
| ( in @ ( sK24_C @ SY627 @ SV208 ) @ SY627 ) ) )
| ( SY627
= ( union @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1133,plain,
! [SV209: $i] :
( ( ! [SY629: $i] :
( ( SY629
!= ( union @ SV209 ) )
| ~ ( ~ ! [SY630: $i] :
( ! [SY631: $i] :
( ~ ( in @ SY630 @ SY631 )
| ~ ( in @ SY631 @ SV209 ) )
| ( in @ SY630 @ SY629 ) )
| ~ ! [SY632: $i] :
( ~ ( in @ SY632 @ SY629 )
| ~ ( ~ ( in @ SY632 @ ( sK23_D @ SY632 @ SY629 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SY632 @ SY629 @ SV209 ) @ SV209 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1134,plain,
! [SV91: $i] :
( ( ! [SY465: $i,SY466: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ~ ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY465 ) ) )
| ~ ( ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY466 )
| ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SY466 @ SY465 @ SV91 ) @ SY465 ) ) )
| ( SY466
= ( set_union2 @ SV91 @ SY465 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1135,plain,
! [SV91: $i] :
( ( ! [SY467: $i,SY468: $i] :
( ( SY468
!= ( set_union2 @ SV91 @ SY467 ) )
| ~ ( ~ ! [SY469: $i] :
( ~ ( in @ SY469 @ SY468 )
| ( in @ SY469 @ SV91 )
| ( in @ SY469 @ SY467 ) )
| ~ ~ ( ~ ! [SY470: $i] :
( ~ ( in @ SY470 @ SV91 )
| ( in @ SY470 @ SY468 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY467 )
| ( in @ SX3 @ SY468 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1136,plain,
! [SV92: $i] :
( ( ! [SY472: $i,SY473: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY472 )
| ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY472 )
| ( in @ ( sK22_D @ SY473 @ SY472 @ SV92 ) @ SY473 ) ) ) )
| ( SY473
= ( set_difference @ SV92 @ SY472 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1137,plain,
! [SV92: $i] :
( ( ! [SY474: $i,SY475: $i] :
( ( SY475
!= ( set_difference @ SV92 @ SY474 ) )
| ~ ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV92 )
| ( in @ SY476 @ SY474 )
| ( in @ SY476 @ SY475 ) )
| ~ ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY475 )
| ( in @ SY477 @ SV92 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY475 )
| ~ ( in @ SX3 @ SY474 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1138,plain,
! [SV93: $i] :
( ( ! [SY479: $i,SY480: $i] :
( ~ ( in @ SV93 @ SY480 )
| ~ ( in @ SY479 @ SY480 )
| ( subset @ ( unordered_pair @ SV93 @ SY479 ) @ SY480 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1139,plain,
! [SV93: $i] :
( ( ~ ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY481 ) @ SY482 )
| ( in @ SV93 @ SY482 ) )
| ~ ! [SY483: $i,SY484: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY483 ) @ SY484 )
| ( in @ SY483 @ SY484 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1140,plain,
! [SV210: $i] :
( ( ! [SY633: $i] :
( ( ( set_difference @ SV210 @ SY633 )
!= empty_set )
| ( subset @ SV210 @ SY633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1141,plain,
! [SV211: $i] :
( ( ! [SY634: $i] :
( ~ ( subset @ SV211 @ SY634 )
| ( ( set_difference @ SV211 @ SY634 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1142,plain,
! [SV94: $i] :
( ( ! [SY485: $i] :
( ~ ( subset @ SV94 @ SY485 )
| ! [SY486: $i] : ( subset @ ( cartesian_product2 @ SV94 @ SY486 ) @ ( cartesian_product2 @ SY485 @ SY486 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1143,plain,
! [SV94: $i] :
( ( ! [SY487: $i] :
( ~ ( subset @ SV94 @ SY487 )
| ! [SY488: $i] : ( subset @ ( cartesian_product2 @ SY488 @ SV94 ) @ ( cartesian_product2 @ SY488 @ SY487 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1144,plain,
! [SV212: $i] :
( ( ! [SY635: $i] :
( ~ ( in @ SV212 @ SY635 )
| ( subset @ ( singleton @ SV212 ) @ SY635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1145,plain,
! [SV213: $i] :
( ( ! [SY636: $i] :
( ~ ( subset @ ( singleton @ SV213 ) @ SY636 )
| ( in @ SV213 @ SY636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1146,plain,
! [SV214: $i] :
( ( ! [SY637: $i] :
( ( ( set_difference @ SV214 @ SY637 )
!= empty_set )
| ( subset @ SV214 @ SY637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1147,plain,
! [SV215: $i] :
( ( ! [SY638: $i] :
( ~ ( subset @ SV215 @ SY638 )
| ( ( set_difference @ SV215 @ SY638 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1148,plain,
! [SV95: $i] :
( ( ! [SY489: $i] :
( ~ ( subset @ SY489 @ ( sK7_B @ SV95 ) )
| ( are_equipotent @ SY489 @ ( sK7_B @ SV95 ) )
| ( in @ SY489 @ ( sK7_B @ SV95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1149,plain,
! [SV95: $i] :
( ( ~ ( ~ ! [SY490: $i] :
( ~ ( in @ SY490 @ ( sK7_B @ SV95 ) )
| ( in @ ( powerset @ SY490 ) @ ( sK7_B @ SV95 ) ) )
| ~ ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) )
| ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1150,plain,
! [SV96: $i,SV216: $i] :
( ( ( ~ ( relation @ SV216 )
| ~ ( ~ ! [SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ! [SY640: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ SY640 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY640 @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) ) )
| ( SY639
= ( relation_composition @ SV96 @ SV216 ) ) )
| ~ ! [SY641: $i] :
( ~ ( relation @ SY641 )
| ( SY641
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY642 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY643 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY641 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SY641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY645 @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) @ SY646 ) @ SV216 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1151,plain,
! [SV217: $i] :
( ( ! [SY647: $i] :
( ( ( set_intersection2 @ SV217 @ SY647 )
!= empty_set )
| ( disjoint @ SV217 @ SY647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1152,plain,
! [SV218: $i] :
( ( ! [SY648: $i] :
( ~ ( disjoint @ SV218 @ SY648 )
| ( ( set_intersection2 @ SV218 @ SY648 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1153,plain,
! [SV219: $i] :
( ( ! [SY649: $i] :
( ( ( set_difference @ SV219 @ SY649 )
!= SV219 )
| ( disjoint @ SV219 @ SY649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1154,plain,
! [SV220: $i] :
( ( ! [SY650: $i] :
( ~ ( disjoint @ SV220 @ SY650 )
| ( ( set_difference @ SV220 @ SY650 )
= SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1155,plain,
! [SV221: $i] :
( ( ! [SY651: $i] :
( ( disjoint @ SV221 @ SY651 )
| ~ ( ~ ( in @ ( sK48_C @ SY651 @ SV221 ) @ SV221 )
| ~ ( in @ ( sK48_C @ SY651 @ SV221 ) @ SY651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1156,plain,
! [SV222: $i] :
( ( ! [SY652: $i] :
( ! [SY653: $i] :
( ~ ( in @ SY653 @ SV222 )
| ~ ( in @ SY653 @ SY652 ) )
| ~ ( disjoint @ SV222 @ SY652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1157,plain,
! [SV223: $i] :
( ( ! [SY654: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_C @ SY654 @ SV223 ) @ SY654 )
| ~ ( subset @ ( sK38_C @ SY654 @ SV223 ) @ SV223 ) )
| ~ ( ( in @ ( sK38_C @ SY654 @ SV223 ) @ SY654 )
| ( subset @ ( sK38_C @ SY654 @ SV223 ) @ SV223 ) ) )
| ( SY654
= ( powerset @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1158,plain,
! [SV224: $i] :
( ( ! [SY655: $i] :
( ( SY655
!= ( powerset @ SV224 ) )
| ~ ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SY655 )
| ( subset @ SY656 @ SV224 ) )
| ~ ! [SY657: $i] :
( ~ ( subset @ SY657 @ SV224 )
| ( in @ SY657 @ SY655 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1159,plain,
! [SV174: $i,SV97: $i] :
( ( ~ ! [SY596: $i] :
( ! [SY597: $i] :
( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SY596 @ SY597 ) )
| ( SV97 = SY596 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1160,plain,
! [SV174: $i,SV97: $i] :
( ( ~ ! [SY598: $i,SY599: $i] :
( ( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SY598 @ SY599 ) )
| ( SV174 = SY599 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1161,plain,
! [SV98: $i,SV175: $i] :
( ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false )
| ( ( ~ ( ~ ! [SY600: $i] :
( ~ ( element @ SY600 @ ( powerset @ SV98 ) )
| ~ ( disjoint @ SV175 @ SY600 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SY600 ) ) )
| ~ ! [SY601: $i] :
( ~ ( element @ SY601 @ ( powerset @ SV98 ) )
| ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SY601 ) )
| ( disjoint @ SV175 @ SY601 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1162,plain,
! [SV99: $i] :
( ( ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV99 @ SY510 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SY510 ) ) )
| ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV99 @ SY511 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SY511 ) ) ) )
= $false )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1163,plain,
! [SV100: $i] :
( ( ( ~ ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) ) )
| ( SY512
= ( relation_inverse @ SV100 ) ) )
| ~ ! [SY513: $i] :
( ~ ( relation @ SY513 )
| ( SY513
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( in @ ( ordered_pair @ SY514 @ SY515 ) @ SY513 )
| ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV100 ) )
| ~ ! [SY516: $i,SY517: $i] :
( ~ ( in @ ( ordered_pair @ SY517 @ SY516 ) @ SV100 )
| ( in @ ( ordered_pair @ SY516 @ SY517 ) @ SY513 ) ) ) ) )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1164,plain,
! [SV101: $i] :
( ( ! [SY518: $i,SY519: $i] :
( ~ ( ~ ( ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY518 )
| ~ ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) )
| ~ ( ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY518 )
| ( in @ ( sK29_D @ SY519 @ SY518 @ SV101 ) @ SY519 ) ) ) )
| ( SY519
= ( set_intersection2 @ SV101 @ SY518 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1165,plain,
! [SV101: $i] :
( ( ! [SY520: $i,SY521: $i] :
( ( SY521
!= ( set_intersection2 @ SV101 @ SY520 ) )
| ~ ( ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ SV101 )
| ~ ( in @ SY522 @ SY520 )
| ( in @ SY522 @ SY521 ) )
| ~ ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY521 )
| ( in @ SY523 @ SV101 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY521 )
| ( in @ SX3 @ SY520 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1166,plain,
! [SV102: $i] :
( ( ! [SY525: $i,SY526: $i] :
( ~ ( relation @ SY526 )
| ~ ( in @ ( ordered_pair @ SV102 @ SY525 ) @ SY526 )
| ( in @ SV102 @ ( relation_field @ SY526 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1167,plain,
! [SV102: $i] :
( ( ! [SY527: $i,SY528: $i] :
( ~ ( relation @ SY528 )
| ~ ( in @ ( ordered_pair @ SV102 @ SY527 ) @ SY528 )
| ( in @ SY527 @ ( relation_field @ SY528 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1168,plain,
! [SV103: $i] :
( ( ! [SY529: $i] :
( ~ ( subset @ SY529 @ ( sK8_B @ SV103 ) )
| ( are_equipotent @ SY529 @ ( sK8_B @ SV103 ) )
| ( in @ SY529 @ ( sK8_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1028]) ).
thf(1169,plain,
! [SV103: $i] :
( ( ~ ( ~ ! [SY530: $i] :
( ~ ( ~ ! [SY531: $i] :
( ~ ( subset @ SY531 @ SY530 )
| ( in @ SY531 @ ( sK9_SY344 @ SY530 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SY530 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SY530 @ ( sK8_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1170,plain,
! [SV225: $i] :
( ( ! [SY658: $i] :
( ~ ( subset @ SV225 @ SY658 )
| ~ ( subset @ SY658 @ SV225 )
| ( SV225 = SY658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1171,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)],[1031]) ).
thf(1172,plain,
! [SV226: $i] :
( ( ! [SY659: $i] :
( ~ ( in @ SV226 @ SY659 )
| ( subset @ ( singleton @ SV226 ) @ SY659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1173,plain,
! [SV227: $i] :
( ( ! [SY660: $i] :
( ~ ( subset @ ( singleton @ SV227 ) @ SY660 )
| ( in @ SV227 @ SY660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1174,plain,
! [SV228: $i] :
( ( ! [SY661: $i] :
( ~ ( subset @ SV228 @ ( singleton @ SY661 ) )
| ( SV228 = empty_set )
| ( SV228
= ( singleton @ SY661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1175,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)],[1035]) ).
thf(1176,plain,
! [SV176: $i,SV104: $i] :
( ( ~ ! [SY602: $i,SY603: $i] :
( ~ ( in @ SV104 @ SY602 )
| ~ ( in @ SV176 @ SY603 )
| ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY602 @ SY603 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1177,plain,
! [SV176: $i,SV104: $i] :
( ( ~ ~ ( ~ ! [SY604: $i] :
( ! [SY605: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY604 @ SY605 ) )
| ( in @ SV104 @ SY604 ) )
| ~ ! [SY606: $i,SY607: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY606 @ SY607 ) )
| ( in @ SV176 @ SY607 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1178,plain,
! [SV105: $i] :
( ( ! [SY541: $i,SY542: $i] :
( ~ ( ~ ( ! [SY543: $i,SY544: $i] :
( ~ ( in @ SY543 @ SV105 )
| ~ ( in @ SY544 @ SY541 )
| ( ( sK33_D @ SY542 @ SY541 @ SV105 )
!= ( ordered_pair @ SY543 @ SY544 ) ) )
| ~ ( in @ ( sK33_D @ SY542 @ SY541 @ SV105 ) @ SY542 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SY542 @ SY541 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SY542 @ SY541 @ SV105 ) @ SY541 ) )
| ( ( sK33_D @ SY542 @ SY541 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SY542 @ SY541 @ SV105 ) @ ( sK35_SY366 @ SY542 @ SY541 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SY542 @ SY541 @ SV105 ) @ SY542 ) ) )
| ( SY542
= ( cartesian_product2 @ SV105 @ SY541 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1179,plain,
! [SV105: $i] :
( ( ! [SY545: $i,SY546: $i] :
( ( SY546
!= ( cartesian_product2 @ SV105 @ SY545 ) )
| ~ ( ~ ! [SY547: $i] :
( ! [SY548: $i,SY549: $i] :
( ~ ( in @ SY548 @ SV105 )
| ~ ( in @ SY549 @ SY545 )
| ( SY547
!= ( ordered_pair @ SY548 @ SY549 ) ) )
| ( in @ SY547 @ SY546 ) )
| ~ ! [SY550: $i] :
( ~ ( in @ SY550 @ SY546 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY550 @ SY546 @ SY545 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY550 @ SY546 @ SY545 @ SV105 ) @ SY545 ) )
| ( SY550
!= ( ordered_pair @ ( sK31_E @ SY550 @ SY546 @ SY545 @ SV105 ) @ ( sK32_SY361 @ SY550 @ SY546 @ SY545 @ SV105 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1038]) ).
thf(1180,plain,
! [SV229: $i] :
( ( ! [SY662: $i] :
( ~ ( subset @ SV229 @ ( singleton @ SY662 ) )
| ( SV229 = empty_set )
| ( SV229
= ( singleton @ SY662 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1181,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)],[1040]) ).
thf(1182,plain,
! [SV106: $i] :
( ( ! [SY551: $i,SY552: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
!= SY551 ) ) )
| ~ ( ( in @ ( sK37_D @ SY552 @ SY551 @ SV106 ) @ SY552 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
= SV106 )
| ( ( sK37_D @ SY552 @ SY551 @ SV106 )
= SY551 ) ) )
| ( SY552
= ( unordered_pair @ SV106 @ SY551 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1183,plain,
! [SV106: $i] :
( ( ! [SY553: $i,SY554: $i] :
( ( SY554
!= ( unordered_pair @ SV106 @ SY553 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SY554 )
| ( SY555 = SV106 )
| ( SY555 = SY553 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ( SY556 != SV106 )
| ( in @ SY556 @ SY554 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY553 )
| ( in @ SX3 @ SY554 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1184,plain,
! [SV230: $i] :
( ( ! [SY663: $i] :
( ( ( set_difference @ SV230 @ ( singleton @ SY663 ) )
!= SV230 )
| ~ ( in @ SY663 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1185,plain,
! [SV231: $i] :
( ( ! [SY664: $i] :
( ( in @ SY664 @ SV231 )
| ( ( set_difference @ SV231 @ ( singleton @ SY664 ) )
= SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1186,plain,
! [SV177: $i,SV107: $i] :
( ( ~ ! [SY608: $i,SY609: $i] :
( ~ ( in @ SV107 @ SY608 )
| ~ ( in @ SV177 @ SY609 )
| ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY608 @ SY609 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1187,plain,
! [SV177: $i,SV107: $i] :
( ( ~ ~ ( ~ ! [SY610: $i] :
( ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY610 @ SY611 ) )
| ( in @ SV107 @ SY610 ) )
| ~ ! [SY612: $i,SY613: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY612 @ SY613 ) )
| ( in @ SV177 @ SY613 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1188,plain,
! [SV232: $i] :
( ( ~ ( relation @ SV232 )
| ( ( relation_rng @ SV232 )
= ( relation_dom @ ( relation_inverse @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1189,plain,
! [SV233: $i] :
( ( ~ ( relation @ SV233 )
| ( ( relation_dom @ SV233 )
= ( relation_rng @ ( relation_inverse @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1190,plain,
! [SV108: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV108 ) @ ( powerset @ SV108 ) ) )
= $false )
| ( ( empty @ SV108 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1191,plain,
! [SV108: $i] :
( ( ( ~ ~ ( empty @ ( sK5_B @ SV108 ) ) )
= $false )
| ( ( empty @ SV108 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1192,plain,
! [SV234: $i] :
( ( ( in @ ( sK39_B @ SV234 ) @ SV234 )
| ( SV234 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1193,plain,
! [SV235: $i] :
( ( ( SV235 != empty_set )
| ! [SY665: $i] :
~ ( in @ SY665 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1194,plain,
! [SV109: $i] :
( ( ( ~ ! [SY565: $i] :
( ~ ( ~ ( ! [SY566: $i] :
~ ( in @ ( ordered_pair @ SY566 @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SY565 @ SV109 ) @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) ) )
| ( SY565
= ( relation_rng @ SV109 ) ) )
| ~ ! [SY567: $i] :
( ( SY567
!= ( relation_rng @ SV109 ) )
| ~ ( ~ ! [SY568: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY568 ) @ SV109 )
| ( in @ SY568 @ SY567 ) )
| ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ SY567 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY570 @ SY567 @ SV109 ) @ SY570 ) @ SV109 ) ) ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1195,plain,
! [SV110: $i] :
( ( ! [SY571: $i,SY572: $i] :
( ~ ( relation @ SY572 )
| ~ ( in @ ( ordered_pair @ SV110 @ SY571 ) @ SY572 )
| ( in @ SV110 @ ( relation_dom @ SY572 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1196,plain,
! [SV110: $i] :
( ( ! [SY573: $i,SY574: $i] :
( ~ ( relation @ SY574 )
| ~ ( in @ ( ordered_pair @ SV110 @ SY573 ) @ SY574 )
| ( in @ SY573 @ ( relation_rng @ SY574 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1197,plain,
! [SV236: $i] :
( ( ! [SY666: $i] :
( ~ ( element @ SV236 @ ( powerset @ SY666 ) )
| ( subset @ SV236 @ SY666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1198,plain,
! [SV237: $i] :
( ( ! [SY667: $i] :
( ~ ( subset @ SV237 @ SY667 )
| ( element @ SV237 @ ( powerset @ SY667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1199,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ ( sK43_SY367 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK41_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)],[1056]) ).
thf(1200,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)],[1057]) ).
thf(1201,plain,
! [SV238: $i] :
( ( ! [SY668: $i] :
( ( SV238 = SY668 )
| ~ ( subset @ SV238 @ SY668 )
| ( proper_subset @ SV238 @ SY668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1202,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)],[1059]) ).
thf(1203,plain,
( ( empty @ sK11_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1204,plain,
! [SV111: $i,SV178: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) )
| ~ ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) ) )
= $false )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1205,plain,
! [SV112: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV112 )
| ~ ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV179 ) )
= $false )
| ( ( element @ SV112 @ ( powerset @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1206,plain,
! [SV239: $i] :
( ( ~ ( ~ ! [SY669: $i,SY670: $i] :
( ( sK46_B @ SV239 )
!= ( ordered_pair @ SY669 @ SY670 ) )
| ~ ( in @ ( sK46_B @ SV239 ) @ SV239 ) )
| ( relation @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1207,plain,
! [SV240: $i] :
( ( ~ ( relation @ SV240 )
| ! [SY671: $i] :
( ( SY671
= ( ordered_pair @ ( sK44_C @ SY671 @ SV240 ) @ ( sK45_SY369 @ SY671 @ SV240 ) ) )
| ~ ( in @ SY671 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1208,plain,
! [SV113: $i] :
( ( element @ ( sK3_B @ SV113 ) @ ( powerset @ SV113 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1209,plain,
! [SV113: $i] :
( ( empty @ ( sK3_B @ SV113 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1210,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)],[1070]) ).
thf(1211,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)],[1071]) ).
thf(1212,plain,
! [SV115: $i,SV3: $i] :
( ( ( in @ SV3 @ SV115 )
= $false )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1213,plain,
! [SV5: $i,SV117: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV117 )
| ( in @ SV241 @ SV5 ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1214,plain,
! [SV11: $i,SV121: $i] :
( ( ( in @ SV121 @ SV11 )
= $false )
| ( ( in @ SV11 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1215,plain,
! [SV123: $i,SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV15 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1216,plain,
! [SV125: $i,SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ~ ( relation @ SV125 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV17 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1217,plain,
! [SV22: $i,SV127: $i] :
( ( ( empty @ SV127 )
= $true )
| ( ( in @ SV22 @ SV127 )
= $true )
| ( ( element @ SV22 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1218,plain,
! [SV25: $i,SV180: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ ( powerset @ SV180 ) ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV128 ) )
= $true )
| ( ( element @ SV25 @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1219,plain,
! [SV129: $i,SV27: $i] :
( ( ( in @ SV27 @ SV129 )
= $false )
| ( ( empty @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1220,plain,
! [SV130: $i,SV28: $i,SV242: $i] :
( ( ( ( in @ SV242 @ SV28 )
| ( subset @ SV28 @ ( set_difference @ SV130 @ ( singleton @ SV242 ) ) ) )
= $true )
| ( ( subset @ SV28 @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1221,plain,
! [SV131: $i,SV181: $i,SV195: $i,SV29: $i] :
( ( ( SV29 = SV195 )
= $true )
| ( ( ( SV29 = SV181 )
| ( ( unordered_pair @ SV29 @ SV131 )
!= ( unordered_pair @ SV181 @ SV195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1222,plain,
! [SV196: $i,SV182: $i,SV132: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV132 )
| ~ ( subset @ SV182 @ SV196 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV30 @ SV182 ) @ ( cartesian_product2 @ SV132 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1223,plain,
! [SV183: $i,SV135: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV135 ) )
= $true )
| ( ( ~ ( subset @ SV33 @ SV183 ) )
= $true )
| ( ( subset @ SV33 @ ( set_intersection2 @ SV135 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1224,plain,
! [SV184: $i,SV136: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV136 ) )
= $true )
| ( ( ~ ( subset @ SV136 @ SV184 ) )
= $true )
| ( ( subset @ SV34 @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1225,plain,
! [SV137: $i,SV243: $i,SV36: $i] :
( ( ( subset @ ( set_intersection2 @ SV36 @ SV243 ) @ ( set_intersection2 @ SV137 @ SV243 ) )
= $true )
| ( ( subset @ SV36 @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1226,plain,
! [SV139: $i,SV244: $i,SV38: $i] :
( ( ( subset @ ( set_difference @ SV38 @ SV244 ) @ ( set_difference @ SV139 @ SV244 ) )
= $true )
| ( ( subset @ SV38 @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1227,plain,
! [SV42: $i,SV197: $i] :
( ( ( ~ ( relation @ SV197 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV42 @ SV197 ) ) @ ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1228,plain,
! [SV43: $i,SV198: $i] :
( ( ( ~ ( relation @ SV198 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV43 @ SV198 ) ) @ ( relation_rng @ SV198 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1229,plain,
! [SV45: $i,SV199: $i] :
( ( ( ~ ( relation @ SV199 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV45 ) @ ( relation_dom @ SV199 ) )
| ( ( relation_dom @ ( relation_composition @ SV45 @ SV199 ) )
= ( relation_dom @ SV45 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1230,plain,
! [SV46: $i,SV144: $i] :
( ( ( SV144 = empty_set )
= $true )
| ( ( ( ( complements_of_subsets @ SV46 @ SV144 )
!= empty_set ) )
= $true )
| ( ( element @ SV144 @ ( powerset @ ( powerset @ SV46 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1231,plain,
! [SV47: $i,SV200: $i] :
( ( ( ~ ( relation @ SV200 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV47 ) @ ( relation_rng @ SV200 ) )
| ( ( relation_rng @ ( relation_composition @ SV200 @ SV47 ) )
= ( relation_rng @ SV47 ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1232,plain,
! [SV49: $i,SV185: $i] :
( ( ( element @ SV185 @ ( powerset @ SV49 ) )
= $false )
| ( ( ! [SY616: $i] :
( ~ ( element @ SY616 @ SV49 )
| ( in @ SY616 @ SV185 )
| ( in @ SY616 @ ( subset_complement @ SV49 @ SV185 ) ) ) )
= $true )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1233,plain,
! [SV146: $i,SV50: $i,SV186: $i] :
( ( ( element @ SV186 @ ( powerset @ SV50 ) )
= $false )
| ( ( ~ ( in @ SV146 @ ( subset_complement @ SV50 @ SV186 ) )
| ~ ( in @ SV146 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1234,plain,
! [SV147: $i,SV51: $i] :
( ( ( subset @ SV51 @ SV147 )
= $false )
| ( ( proper_subset @ SV147 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1235,plain,
! [SV52: $i,SV187: $i,SV148: $i] :
( ( ( ~ ( disjoint @ SV148 @ SV187 ) )
= $true )
| ( ( ~ ( subset @ SV52 @ SV148 ) )
= $true )
| ( ( disjoint @ SV52 @ SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1236,plain,
! [SV188: $i,SV151: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV151 ) )
= $true )
| ( ( ~ ( subset @ SV188 @ SV151 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV56 @ SV188 ) @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1237,plain,
! [SV201: $i,SV152: $i,SV57: $i] :
( ( ( ( singleton @ SV57 )
= ( unordered_pair @ SV152 @ SV201 ) )
= $false )
| ( ( SV57 = SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1238,plain,
! [SV189: $i,SV153: $i,SV59: $i] :
( ( ( ( singleton @ SV59 )
= ( unordered_pair @ SV153 @ SV189 ) )
= $false )
| ( ( SV153 = SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1239,plain,
! [SV190: $i,SV69: $i,SV161: $i] :
( ( ( ~ ( element @ SV161 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ~ ( element @ SV190 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV69 @ SV161 @ SV190 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1240,plain,
! [SV164: $i,SV77: $i] :
( ( ( empty @ ( cartesian_product2 @ SV77 @ SV164 ) )
= $false )
| ( ( empty @ SV164 )
= $true )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1241,plain,
! [SV193: $i,SV84: $i,SV169: $i] :
( ( ( ~ ( element @ SV169 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ~ ( element @ SV193 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ( subset_difference @ SV84 @ SV169 @ SV193 )
= ( set_difference @ SV169 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1242,plain,
! [SV87: $i,SV194: $i,SV171: $i] :
( ( ( ~ ( element @ SV171 @ ( powerset @ SV194 ) ) )
= $true )
| ( ( ~ ( in @ SV87 @ SV171 ) )
= $true )
| ( ( ~ ( empty @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1243,plain,
! [SV172: $i,SV88: $i] :
( ( ( empty @ SV88 )
= $false )
| ( ( SV88 = SV172 )
= $true )
| ( ( ~ ( empty @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1244,plain,
! [SV202: $i,SV245: $i] :
( ( ~ ( ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV202 )
| ~ ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV245 ) )
| ( subset @ SV202 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1245,plain,
! [SV246: $i,SV203: $i] :
( ( ~ ( subset @ SV203 @ SV246 )
| ! [SY672: $i] :
( ~ ( in @ SY672 @ SV203 )
| ( in @ SY672 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1246,plain,
! [SV247: $i,SV204: $i] :
( ( ( disjoint @ SV204 @ SV247 )
| ( in @ ( sK47_C @ SV247 @ SV204 ) @ ( set_intersection2 @ SV204 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1247,plain,
! [SV248: $i,SV205: $i] :
( ( ! [SY673: $i] :
~ ( in @ SY673 @ ( set_intersection2 @ SV205 @ SV248 ) )
| ~ ( disjoint @ SV205 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1248,plain,
! [SV206: $i,SV249: $i] :
( ( ~ ( ~ ( ( ( sK40_C @ SV249 @ SV206 )
!= SV206 )
| ~ ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) )
| ~ ( ( ( sK40_C @ SV249 @ SV206 )
= SV206 )
| ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) ) )
| ( SV249
= ( singleton @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1249,plain,
! [SV207: $i,SV250: $i] :
( ( ( SV250
!= ( singleton @ SV207 ) )
| ~ ( ~ ! [SY674: $i] :
( ( SY674 != SV207 )
| ( in @ SY674 @ SV250 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV250 )
| ( SY675 = SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1250,plain,
! [SV90: $i] :
( ( ( ~ ! [SY459: $i] :
( ~ ( ~ ( ! [SY460: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ SY460 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ ( sK28_SY360 @ SY459 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) ) )
| ( SY459
= ( relation_dom @ SV90 ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1251,plain,
! [SV90: $i] :
( ( ( ~ ! [SY461: $i] :
( ( SY461
!= ( relation_dom @ SV90 ) )
| ~ ( ~ ! [SY462: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY462 @ SY463 ) @ SV90 )
| ( in @ SY462 @ SY461 ) )
| ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SY461 )
| ( in @ ( ordered_pair @ SY464 @ ( sK26_D @ SY464 @ SY461 @ SV90 ) ) @ SV90 ) ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1252,plain,
! [SV208: $i,SV251: $i] :
( ( ~ ( ~ ( ! [SY676: $i] :
( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SY676 )
| ~ ( in @ SY676 @ SV208 ) )
| ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
| ~ ( ~ ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) )
| ~ ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 ) )
| ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) ) )
| ( SV251
= ( union @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1253,plain,
! [SV209: $i,SV252: $i] :
( ( ( SV252
!= ( union @ SV209 ) )
| ~ ( ~ ! [SY677: $i] :
( ! [SY631: $i] :
( ~ ( in @ SY677 @ SY631 )
| ~ ( in @ SY631 @ SV209 ) )
| ( in @ SY677 @ SV252 ) )
| ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV252 )
| ~ ( ~ ( in @ SY679 @ ( sK23_D @ SY679 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SY679 @ SV252 @ SV209 ) @ SV209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1254,plain,
! [SV91: $i,SV253: $i] :
( ( ! [SY680: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SY680 @ SV253 @ SV91 ) @ SY680 )
| ~ ( in @ ( sK36_D @ SY680 @ SV253 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SY680 @ SV253 @ SV91 ) @ SY680 )
| ~ ( in @ ( sK36_D @ SY680 @ SV253 @ SV91 ) @ SV253 ) ) )
| ~ ( ( in @ ( sK36_D @ SY680 @ SV253 @ SV91 ) @ SY680 )
| ( in @ ( sK36_D @ SY680 @ SV253 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SY680 @ SV253 @ SV91 ) @ SV253 ) ) )
| ( SY680
= ( set_union2 @ SV91 @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1255,plain,
! [SV254: $i,SV91: $i] :
( ( ! [SY681: $i] :
( ( SY681
!= ( set_union2 @ SV91 @ SV254 ) )
| ~ ( ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SY681 )
| ( in @ SY682 @ SV91 )
| ( in @ SY682 @ SV254 ) )
| ~ ~ ( ~ ! [SY470: $i] :
( ~ ( in @ SY470 @ SV91 )
| ( in @ SY470 @ SY681 ) )
| ~ ! [SY684: $i] :
( ~ ( in @ SY684 @ SV254 )
| ( in @ SY684 @ SY681 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1256,plain,
! [SV92: $i,SV255: $i] :
( ( ! [SY685: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY685 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY685 @ SV255 @ SV92 ) @ SV255 )
| ~ ( in @ ( sK22_D @ SY685 @ SV255 @ SV92 ) @ SY685 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY685 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SY685 @ SV255 @ SV92 ) @ SY685 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY685 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SY685 @ SV255 @ SV92 ) @ SY685 ) ) ) )
| ( SY685
= ( set_difference @ SV92 @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1257,plain,
! [SV256: $i,SV92: $i] :
( ( ! [SY686: $i] :
( ( SY686
!= ( set_difference @ SV92 @ SV256 ) )
| ~ ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV92 )
| ( in @ SY687 @ SV256 )
| ( in @ SY687 @ SY686 ) )
| ~ ~ ( ~ ! [SY477: $i] :
( ~ ( in @ SY477 @ SY686 )
| ( in @ SY477 @ SV92 ) )
| ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SY686 )
| ~ ( in @ SY689 @ SV256 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1258,plain,
! [SV257: $i,SV93: $i] :
( ( ! [SY690: $i] :
( ~ ( in @ SV93 @ SY690 )
| ~ ( in @ SV257 @ SY690 )
| ( subset @ ( unordered_pair @ SV93 @ SV257 ) @ SY690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1259,plain,
! [SV93: $i] :
( ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY481 ) @ SY482 )
| ( in @ SV93 @ SY482 ) )
| ~ ! [SY483: $i,SY484: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY483 ) @ SY484 )
| ( in @ SY483 @ SY484 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1260,plain,
! [SV258: $i,SV210: $i] :
( ( ( ( set_difference @ SV210 @ SV258 )
!= empty_set )
| ( subset @ SV210 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1261,plain,
! [SV259: $i,SV211: $i] :
( ( ~ ( subset @ SV211 @ SV259 )
| ( ( set_difference @ SV211 @ SV259 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1262,plain,
! [SV260: $i,SV94: $i] :
( ( ~ ( subset @ SV94 @ SV260 )
| ! [SY691: $i] : ( subset @ ( cartesian_product2 @ SV94 @ SY691 ) @ ( cartesian_product2 @ SV260 @ SY691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1263,plain,
! [SV261: $i,SV94: $i] :
( ( ~ ( subset @ SV94 @ SV261 )
| ! [SY692: $i] : ( subset @ ( cartesian_product2 @ SY692 @ SV94 ) @ ( cartesian_product2 @ SY692 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1264,plain,
! [SV262: $i,SV212: $i] :
( ( ~ ( in @ SV212 @ SV262 )
| ( subset @ ( singleton @ SV212 ) @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1265,plain,
! [SV263: $i,SV213: $i] :
( ( ~ ( subset @ ( singleton @ SV213 ) @ SV263 )
| ( in @ SV213 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1266,plain,
! [SV264: $i,SV214: $i] :
( ( ( ( set_difference @ SV214 @ SV264 )
!= empty_set )
| ( subset @ SV214 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1267,plain,
! [SV265: $i,SV215: $i] :
( ( ~ ( subset @ SV215 @ SV265 )
| ( ( set_difference @ SV215 @ SV265 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1268,plain,
! [SV95: $i,SV266: $i] :
( ( ~ ( subset @ SV266 @ ( sK7_B @ SV95 ) )
| ( are_equipotent @ SV266 @ ( sK7_B @ SV95 ) )
| ( in @ SV266 @ ( sK7_B @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1269,plain,
! [SV95: $i] :
( ( ~ ! [SY490: $i] :
( ~ ( in @ SY490 @ ( sK7_B @ SV95 ) )
| ( in @ ( powerset @ SY490 ) @ ( sK7_B @ SV95 ) ) )
| ~ ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) )
| ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1270,plain,
! [SV96: $i,SV216: $i] :
( ( ( ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( ~ ! [SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ! [SY640: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ SY640 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY640 @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) ) )
| ( SY639
= ( relation_composition @ SV96 @ SV216 ) ) )
| ~ ! [SY641: $i] :
( ~ ( relation @ SY641 )
| ( SY641
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY642 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY643 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY641 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SY641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY645 @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) @ SY646 ) @ SV216 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1271,plain,
! [SV267: $i,SV217: $i] :
( ( ( ( set_intersection2 @ SV217 @ SV267 )
!= empty_set )
| ( disjoint @ SV217 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1272,plain,
! [SV268: $i,SV218: $i] :
( ( ~ ( disjoint @ SV218 @ SV268 )
| ( ( set_intersection2 @ SV218 @ SV268 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1273,plain,
! [SV269: $i,SV219: $i] :
( ( ( ( set_difference @ SV219 @ SV269 )
!= SV219 )
| ( disjoint @ SV219 @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1274,plain,
! [SV270: $i,SV220: $i] :
( ( ~ ( disjoint @ SV220 @ SV270 )
| ( ( set_difference @ SV220 @ SV270 )
= SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1275,plain,
! [SV271: $i,SV221: $i] :
( ( ( disjoint @ SV221 @ SV271 )
| ~ ( ~ ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV221 )
| ~ ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1276,plain,
! [SV272: $i,SV222: $i] :
( ( ! [SY693: $i] :
( ~ ( in @ SY693 @ SV222 )
| ~ ( in @ SY693 @ SV272 ) )
| ~ ( disjoint @ SV222 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1277,plain,
! [SV223: $i,SV273: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ~ ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) )
| ~ ( ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) ) )
| ( SV273
= ( powerset @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1278,plain,
! [SV224: $i,SV274: $i] :
( ( ( SV274
!= ( powerset @ SV224 ) )
| ~ ( ~ ! [SY694: $i] :
( ~ ( in @ SY694 @ SV274 )
| ( subset @ SY694 @ SV224 ) )
| ~ ! [SY695: $i] :
( ~ ( subset @ SY695 @ SV224 )
| ( in @ SY695 @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1279,plain,
! [SV174: $i,SV97: $i] :
( ( ! [SY596: $i] :
( ! [SY597: $i] :
( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SY596 @ SY597 ) )
| ( SV97 = SY596 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1280,plain,
! [SV174: $i,SV97: $i] :
( ( ! [SY598: $i,SY599: $i] :
( ( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SY598 @ SY599 ) )
| ( SV174 = SY599 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1281,plain,
! [SV175: $i,SV98: $i] :
( ( ( ~ ! [SY600: $i] :
( ~ ( element @ SY600 @ ( powerset @ SV98 ) )
| ~ ( disjoint @ SV175 @ SY600 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SY600 ) ) )
| ~ ! [SY601: $i] :
( ~ ( element @ SY601 @ ( powerset @ SV98 ) )
| ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SY601 ) )
| ( disjoint @ SV175 @ SY601 ) ) )
= $false )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1282,plain,
! [SV99: $i] :
( ( ( ~ ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV99 @ SY510 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SY510 ) ) ) )
= $false )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1283,plain,
! [SV99: $i] :
( ( ( ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV99 @ SY511 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SY511 ) ) ) )
= $false )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1284,plain,
! [SV100: $i] :
( ( ( ~ ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) ) )
| ( SY512
= ( relation_inverse @ SV100 ) ) ) )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1285,plain,
! [SV100: $i] :
( ( ( ~ ! [SY513: $i] :
( ~ ( relation @ SY513 )
| ( SY513
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( in @ ( ordered_pair @ SY514 @ SY515 ) @ SY513 )
| ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV100 ) )
| ~ ! [SY516: $i,SY517: $i] :
( ~ ( in @ ( ordered_pair @ SY517 @ SY516 ) @ SV100 )
| ( in @ ( ordered_pair @ SY516 @ SY517 ) @ SY513 ) ) ) ) )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1286,plain,
! [SV101: $i,SV275: $i] :
( ( ! [SY696: $i] :
( ~ ( ~ ( ~ ( in @ ( sK29_D @ SY696 @ SV275 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SY696 @ SV275 @ SV101 ) @ SV275 )
| ~ ( in @ ( sK29_D @ SY696 @ SV275 @ SV101 ) @ SY696 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SY696 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SY696 @ SV275 @ SV101 ) @ SY696 ) )
| ~ ( ( in @ ( sK29_D @ SY696 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SY696 @ SV275 @ SV101 ) @ SY696 ) ) ) )
| ( SY696
= ( set_intersection2 @ SV101 @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1287,plain,
! [SV276: $i,SV101: $i] :
( ( ! [SY697: $i] :
( ( SY697
!= ( set_intersection2 @ SV101 @ SV276 ) )
| ~ ( ~ ! [SY698: $i] :
( ~ ( in @ SY698 @ SV101 )
| ~ ( in @ SY698 @ SV276 )
| ( in @ SY698 @ SY697 ) )
| ~ ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY697 )
| ( in @ SY523 @ SV101 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY697 )
| ( in @ SY700 @ SV276 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1288,plain,
! [SV277: $i,SV102: $i] :
( ( ! [SY701: $i] :
( ~ ( relation @ SY701 )
| ~ ( in @ ( ordered_pair @ SV102 @ SV277 ) @ SY701 )
| ( in @ SV102 @ ( relation_field @ SY701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1289,plain,
! [SV278: $i,SV102: $i] :
( ( ! [SY702: $i] :
( ~ ( relation @ SY702 )
| ~ ( in @ ( ordered_pair @ SV102 @ SV278 ) @ SY702 )
| ( in @ SV278 @ ( relation_field @ SY702 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1290,plain,
! [SV103: $i,SV279: $i] :
( ( ~ ( subset @ SV279 @ ( sK8_B @ SV103 ) )
| ( are_equipotent @ SV279 @ ( sK8_B @ SV103 ) )
| ( in @ SV279 @ ( sK8_B @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1291,plain,
! [SV103: $i] :
( ( ~ ! [SY530: $i] :
( ~ ( ~ ! [SY531: $i] :
( ~ ( subset @ SY531 @ SY530 )
| ( in @ SY531 @ ( sK9_SY344 @ SY530 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SY530 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SY530 @ ( sK8_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1292,plain,
! [SV280: $i,SV225: $i] :
( ( ~ ( subset @ SV225 @ SV280 )
| ~ ( subset @ SV280 @ SV225 )
| ( SV225 = SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1293,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1294,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1295,plain,
! [SV281: $i,SV226: $i] :
( ( ~ ( in @ SV226 @ SV281 )
| ( subset @ ( singleton @ SV226 ) @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1296,plain,
! [SV282: $i,SV227: $i] :
( ( ~ ( subset @ ( singleton @ SV227 ) @ SV282 )
| ( in @ SV227 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1297,plain,
! [SV283: $i,SV228: $i] :
( ( ~ ( subset @ SV228 @ ( singleton @ SV283 ) )
| ( SV228 = empty_set )
| ( SV228
= ( singleton @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1298,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1299,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1300,plain,
! [SV176: $i,SV104: $i] :
( ( ! [SY602: $i,SY603: $i] :
( ~ ( in @ SV104 @ SY602 )
| ~ ( in @ SV176 @ SY603 )
| ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY602 @ SY603 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1301,plain,
! [SV176: $i,SV104: $i] :
( ( ~ ( ~ ! [SY604: $i] :
( ! [SY605: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY604 @ SY605 ) )
| ( in @ SV104 @ SY604 ) )
| ~ ! [SY606: $i,SY607: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY606 @ SY607 ) )
| ( in @ SV176 @ SY607 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1302,plain,
! [SV284: $i,SV105: $i] :
( ( ! [SY703: $i] :
( ~ ( ~ ( ! [SY704: $i,SY705: $i] :
( ~ ( in @ SY704 @ SV105 )
| ~ ( in @ SY705 @ SV284 )
| ( ( sK33_D @ SY703 @ SV284 @ SV105 )
!= ( ordered_pair @ SY704 @ SY705 ) ) )
| ~ ( in @ ( sK33_D @ SY703 @ SV284 @ SV105 ) @ SY703 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SY703 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SY703 @ SV284 @ SV105 ) @ SV284 ) )
| ( ( sK33_D @ SY703 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SY703 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SY703 @ SV284 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SY703 @ SV284 @ SV105 ) @ SY703 ) ) )
| ( SY703
= ( cartesian_product2 @ SV105 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1303,plain,
! [SV285: $i,SV105: $i] :
( ( ! [SY706: $i] :
( ( SY706
!= ( cartesian_product2 @ SV105 @ SV285 ) )
| ~ ( ~ ! [SY707: $i] :
( ! [SY708: $i,SY709: $i] :
( ~ ( in @ SY708 @ SV105 )
| ~ ( in @ SY709 @ SV285 )
| ( SY707
!= ( ordered_pair @ SY708 @ SY709 ) ) )
| ( in @ SY707 @ SY706 ) )
| ~ ! [SY710: $i] :
( ~ ( in @ SY710 @ SY706 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY710 @ SY706 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY710 @ SY706 @ SV285 @ SV105 ) @ SV285 ) )
| ( SY710
!= ( ordered_pair @ ( sK31_E @ SY710 @ SY706 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SY710 @ SY706 @ SV285 @ SV105 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1304,plain,
! [SV286: $i,SV229: $i] :
( ( ~ ( subset @ SV229 @ ( singleton @ SV286 ) )
| ( SV229 = empty_set )
| ( SV229
= ( singleton @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1305,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1306,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1307,plain,
! [SV106: $i,SV287: $i] :
( ( ! [SY711: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY711 @ SV287 @ SV106 ) @ SY711 )
| ( ( sK37_D @ SY711 @ SV287 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY711 @ SV287 @ SV106 ) @ SY711 )
| ( ( sK37_D @ SY711 @ SV287 @ SV106 )
!= SV287 ) ) )
| ~ ( ( in @ ( sK37_D @ SY711 @ SV287 @ SV106 ) @ SY711 )
| ( ( sK37_D @ SY711 @ SV287 @ SV106 )
= SV106 )
| ( ( sK37_D @ SY711 @ SV287 @ SV106 )
= SV287 ) ) )
| ( SY711
= ( unordered_pair @ SV106 @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1308,plain,
! [SV288: $i,SV106: $i] :
( ( ! [SY712: $i] :
( ( SY712
!= ( unordered_pair @ SV106 @ SV288 ) )
| ~ ( ~ ! [SY713: $i] :
( ~ ( in @ SY713 @ SY712 )
| ( SY713 = SV106 )
| ( SY713 = SV288 ) )
| ~ ~ ( ~ ! [SY556: $i] :
( ( SY556 != SV106 )
| ( in @ SY556 @ SY712 ) )
| ~ ! [SY715: $i] :
( ( SY715 != SV288 )
| ( in @ SY715 @ SY712 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1309,plain,
! [SV289: $i,SV230: $i] :
( ( ( ( set_difference @ SV230 @ ( singleton @ SV289 ) )
!= SV230 )
| ~ ( in @ SV289 @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1310,plain,
! [SV231: $i,SV290: $i] :
( ( ( in @ SV290 @ SV231 )
| ( ( set_difference @ SV231 @ ( singleton @ SV290 ) )
= SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1311,plain,
! [SV177: $i,SV107: $i] :
( ( ! [SY608: $i,SY609: $i] :
( ~ ( in @ SV107 @ SY608 )
| ~ ( in @ SV177 @ SY609 )
| ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY608 @ SY609 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1312,plain,
! [SV177: $i,SV107: $i] :
( ( ~ ( ~ ! [SY610: $i] :
( ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY610 @ SY611 ) )
| ( in @ SV107 @ SY610 ) )
| ~ ! [SY612: $i,SY613: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY612 @ SY613 ) )
| ( in @ SV177 @ SY613 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1313,plain,
! [SV232: $i] :
( ( ( ~ ( relation @ SV232 ) )
= $true )
| ( ( ( relation_rng @ SV232 )
= ( relation_dom @ ( relation_inverse @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1314,plain,
! [SV233: $i] :
( ( ( ~ ( relation @ SV233 ) )
= $true )
| ( ( ( relation_dom @ SV233 )
= ( relation_rng @ ( relation_inverse @ SV233 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1315,plain,
! [SV108: $i] :
( ( ( element @ ( sK5_B @ SV108 ) @ ( powerset @ SV108 ) )
= $true )
| ( ( empty @ SV108 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1316,plain,
! [SV108: $i] :
( ( ( ~ ( empty @ ( sK5_B @ SV108 ) ) )
= $true )
| ( ( empty @ SV108 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1317,plain,
! [SV234: $i] :
( ( ( in @ ( sK39_B @ SV234 ) @ SV234 )
= $true )
| ( ( SV234 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1318,plain,
! [SV235: $i] :
( ( ( ( SV235 != empty_set ) )
= $true )
| ( ( ! [SY665: $i] :
~ ( in @ SY665 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1319,plain,
! [SV109: $i] :
( ( ( ~ ! [SY565: $i] :
( ~ ( ~ ( ! [SY566: $i] :
~ ( in @ ( ordered_pair @ SY566 @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SY565 @ SV109 ) @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) ) )
| ( SY565
= ( relation_rng @ SV109 ) ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1320,plain,
! [SV109: $i] :
( ( ( ~ ! [SY567: $i] :
( ( SY567
!= ( relation_rng @ SV109 ) )
| ~ ( ~ ! [SY568: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY568 ) @ SV109 )
| ( in @ SY568 @ SY567 ) )
| ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ SY567 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY570 @ SY567 @ SV109 ) @ SY570 ) @ SV109 ) ) ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1321,plain,
! [SV291: $i,SV110: $i] :
( ( ! [SY716: $i] :
( ~ ( relation @ SY716 )
| ~ ( in @ ( ordered_pair @ SV110 @ SV291 ) @ SY716 )
| ( in @ SV110 @ ( relation_dom @ SY716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1322,plain,
! [SV292: $i,SV110: $i] :
( ( ! [SY717: $i] :
( ~ ( relation @ SY717 )
| ~ ( in @ ( ordered_pair @ SV110 @ SV292 ) @ SY717 )
| ( in @ SV292 @ ( relation_rng @ SY717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1323,plain,
! [SV293: $i,SV236: $i] :
( ( ~ ( element @ SV236 @ ( powerset @ SV293 ) )
| ( subset @ SV236 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1324,plain,
! [SV294: $i,SV237: $i] :
( ( ~ ( subset @ SV237 @ SV294 )
| ( element @ SV237 @ ( powerset @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1325,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ ( sK43_SY367 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1326,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK41_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)],[1199]) ).
thf(1327,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1200]) ).
thf(1328,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1200]) ).
thf(1329,plain,
! [SV295: $i,SV238: $i] :
( ( ( SV238 = SV295 )
| ~ ( subset @ SV238 @ SV295 )
| ( proper_subset @ SV238 @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1330,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1331,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1332,plain,
! [SV111: $i,SV178: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) ) )
= $false )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1333,plain,
! [SV111: $i,SV178: $i] :
( ( ( ~ ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) ) )
= $false )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1334,plain,
! [SV112: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV112 ) )
= $false )
| ( ( element @ SV112 @ ( powerset @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1335,plain,
! [SV112: $i,SV179: $i] :
( ( ( ~ ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV179 ) )
= $false )
| ( ( element @ SV112 @ ( powerset @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1336,plain,
! [SV239: $i] :
( ( ( ~ ( ~ ! [SY669: $i,SY670: $i] :
( ( sK46_B @ SV239 )
!= ( ordered_pair @ SY669 @ SY670 ) )
| ~ ( in @ ( sK46_B @ SV239 ) @ SV239 ) ) )
= $true )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1337,plain,
! [SV240: $i] :
( ( ( ~ ( relation @ SV240 ) )
= $true )
| ( ( ! [SY671: $i] :
( ( SY671
= ( ordered_pair @ ( sK44_C @ SY671 @ SV240 ) @ ( sK45_SY369 @ SY671 @ SV240 ) ) )
| ~ ( in @ SY671 @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1338,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1210]) ).
thf(1339,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1210]) ).
thf(1340,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1341,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1342,plain,
! [SV5: $i,SV117: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV117 ) )
= $true )
| ( ( in @ SV241 @ SV5 )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1343,plain,
! [SV15: $i,SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV15 )
= $false )
| ( ( relation @ ( relation_composition @ SV15 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1344,plain,
! [SV17: $i,SV125: $i] :
( ( ( relation @ SV125 )
= $false )
| ( ( relation @ SV17 )
= $false )
| ( ( relation @ ( set_union2 @ SV17 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1345,plain,
! [SV25: $i,SV180: $i,SV128: $i] :
( ( ( element @ SV128 @ ( powerset @ SV180 ) )
= $false )
| ( ( ~ ( in @ SV25 @ SV128 ) )
= $true )
| ( ( element @ SV25 @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1346,plain,
! [SV130: $i,SV28: $i,SV242: $i] :
( ( ( in @ SV242 @ SV28 )
= $true )
| ( ( subset @ SV28 @ ( set_difference @ SV130 @ ( singleton @ SV242 ) ) )
= $true )
| ( ( subset @ SV28 @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1347,plain,
! [SV195: $i,SV131: $i,SV181: $i,SV29: $i] :
( ( ( SV29 = SV181 )
= $true )
| ( ( ( ( unordered_pair @ SV29 @ SV131 )
!= ( unordered_pair @ SV181 @ SV195 ) ) )
= $true )
| ( ( SV29 = SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1348,plain,
! [SV196: $i,SV182: $i,SV132: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV132 ) )
= $true )
| ( ( ~ ( subset @ SV182 @ SV196 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV30 @ SV182 ) @ ( cartesian_product2 @ SV132 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1349,plain,
! [SV183: $i,SV135: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV135 )
= $false )
| ( ( ~ ( subset @ SV33 @ SV183 ) )
= $true )
| ( ( subset @ SV33 @ ( set_intersection2 @ SV135 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1350,plain,
! [SV184: $i,SV136: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV136 )
= $false )
| ( ( ~ ( subset @ SV136 @ SV184 ) )
= $true )
| ( ( subset @ SV34 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1351,plain,
! [SV42: $i,SV197: $i] :
( ( ( relation @ SV197 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV42 @ SV197 ) ) @ ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1352,plain,
! [SV43: $i,SV198: $i] :
( ( ( relation @ SV198 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV43 @ SV198 ) ) @ ( relation_rng @ SV198 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1353,plain,
! [SV45: $i,SV199: $i] :
( ( ( relation @ SV199 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV45 ) @ ( relation_dom @ SV199 ) )
| ( ( relation_dom @ ( relation_composition @ SV45 @ SV199 ) )
= ( relation_dom @ SV45 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1354,plain,
! [SV144: $i,SV46: $i] :
( ( ( ( complements_of_subsets @ SV46 @ SV144 )
= empty_set )
= $false )
| ( ( SV144 = empty_set )
= $true )
| ( ( element @ SV144 @ ( powerset @ ( powerset @ SV46 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1355,plain,
! [SV47: $i,SV200: $i] :
( ( ( relation @ SV200 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV47 ) @ ( relation_rng @ SV200 ) )
| ( ( relation_rng @ ( relation_composition @ SV200 @ SV47 ) )
= ( relation_rng @ SV47 ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1356,plain,
! [SV185: $i,SV49: $i,SV296: $i] :
( ( ( ~ ( element @ SV296 @ SV49 )
| ( in @ SV296 @ SV185 )
| ( in @ SV296 @ ( subset_complement @ SV49 @ SV185 ) ) )
= $true )
| ( ( element @ SV185 @ ( powerset @ SV49 ) )
= $false )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1357,plain,
! [SV186: $i,SV50: $i,SV146: $i] :
( ( ( ~ ( in @ SV146 @ ( subset_complement @ SV50 @ SV186 ) ) )
= $true )
| ( ( ~ ( in @ SV146 @ SV186 ) )
= $true )
| ( ( element @ SV186 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1358,plain,
! [SV52: $i,SV187: $i,SV148: $i] :
( ( ( disjoint @ SV148 @ SV187 )
= $false )
| ( ( ~ ( subset @ SV52 @ SV148 ) )
= $true )
| ( ( disjoint @ SV52 @ SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1359,plain,
! [SV188: $i,SV151: $i,SV56: $i] :
( ( ( subset @ SV56 @ SV151 )
= $false )
| ( ( ~ ( subset @ SV188 @ SV151 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV56 @ SV188 ) @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1360,plain,
! [SV190: $i,SV69: $i,SV161: $i] :
( ( ( element @ SV161 @ ( powerset @ SV69 ) )
= $false )
| ( ( ~ ( element @ SV190 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV69 @ SV161 @ SV190 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1361,plain,
! [SV193: $i,SV84: $i,SV169: $i] :
( ( ( element @ SV169 @ ( powerset @ SV84 ) )
= $false )
| ( ( ~ ( element @ SV193 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ( subset_difference @ SV84 @ SV169 @ SV193 )
= ( set_difference @ SV169 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1362,plain,
! [SV87: $i,SV194: $i,SV171: $i] :
( ( ( element @ SV171 @ ( powerset @ SV194 ) )
= $false )
| ( ( ~ ( in @ SV87 @ SV171 ) )
= $true )
| ( ( ~ ( empty @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1363,plain,
! [SV88: $i,SV172: $i] :
( ( ( empty @ SV172 )
= $false )
| ( ( SV88 = SV172 )
= $true )
| ( ( empty @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1364,plain,
! [SV202: $i,SV245: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV202 )
| ~ ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV245 ) ) )
= $true )
| ( ( subset @ SV202 @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1365,plain,
! [SV246: $i,SV203: $i] :
( ( ( ~ ( subset @ SV203 @ SV246 ) )
= $true )
| ( ( ! [SY672: $i] :
( ~ ( in @ SY672 @ SV203 )
| ( in @ SY672 @ SV246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1366,plain,
! [SV247: $i,SV204: $i] :
( ( ( disjoint @ SV204 @ SV247 )
= $true )
| ( ( in @ ( sK47_C @ SV247 @ SV204 ) @ ( set_intersection2 @ SV204 @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1367,plain,
! [SV248: $i,SV205: $i] :
( ( ( ! [SY673: $i] :
~ ( in @ SY673 @ ( set_intersection2 @ SV205 @ SV248 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV205 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1368,plain,
! [SV206: $i,SV249: $i] :
( ( ( ~ ( ~ ( ( ( sK40_C @ SV249 @ SV206 )
!= SV206 )
| ~ ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) )
| ~ ( ( ( sK40_C @ SV249 @ SV206 )
= SV206 )
| ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) ) ) )
= $true )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1369,plain,
! [SV207: $i,SV250: $i] :
( ( ( ( SV250
!= ( singleton @ SV207 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY674: $i] :
( ( SY674 != SV207 )
| ( in @ SY674 @ SV250 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV250 )
| ( SY675 = SV207 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1370,plain,
! [SV90: $i] :
( ( ( ! [SY459: $i] :
( ~ ( ~ ( ! [SY460: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ SY460 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SY459 @ SV90 ) @ ( sK28_SY360 @ SY459 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SY459 @ SV90 ) @ SY459 ) ) )
| ( SY459
= ( relation_dom @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1371,plain,
! [SV90: $i] :
( ( ( ! [SY461: $i] :
( ( SY461
!= ( relation_dom @ SV90 ) )
| ~ ( ~ ! [SY462: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY462 @ SY463 ) @ SV90 )
| ( in @ SY462 @ SY461 ) )
| ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SY461 )
| ( in @ ( ordered_pair @ SY464 @ ( sK26_D @ SY464 @ SY461 @ SV90 ) ) @ SV90 ) ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1372,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( ~ ( ! [SY676: $i] :
( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SY676 )
| ~ ( in @ SY676 @ SV208 ) )
| ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
| ~ ( ~ ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) )
| ~ ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 ) )
| ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) ) ) )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1373,plain,
! [SV209: $i,SV252: $i] :
( ( ( ( SV252
!= ( union @ SV209 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY677: $i] :
( ! [SY631: $i] :
( ~ ( in @ SY677 @ SY631 )
| ~ ( in @ SY631 @ SV209 ) )
| ( in @ SY677 @ SV252 ) )
| ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV252 )
| ~ ( ~ ( in @ SY679 @ ( sK23_D @ SY679 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SY679 @ SV252 @ SV209 ) @ SV209 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1374,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) )
| ~ ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) )
| ( SV297
= ( set_union2 @ SV91 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1375,plain,
! [SV254: $i,SV91: $i,SV298: $i] :
( ( ( SV298
!= ( set_union2 @ SV91 @ SV254 ) )
| ~ ( ~ ! [SY718: $i] :
( ~ ( in @ SY718 @ SV298 )
| ( in @ SY718 @ SV91 )
| ( in @ SY718 @ SV254 ) )
| ~ ~ ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) )
| ~ ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1376,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) ) )
| ( SV299
= ( set_difference @ SV92 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1377,plain,
! [SV256: $i,SV92: $i,SV300: $i] :
( ( ( SV300
!= ( set_difference @ SV92 @ SV256 ) )
| ~ ( ~ ! [SY721: $i] :
( ~ ( in @ SY721 @ SV92 )
| ( in @ SY721 @ SV256 )
| ( in @ SY721 @ SV300 ) )
| ~ ~ ( ~ ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1378,plain,
! [SV257: $i,SV301: $i,SV93: $i] :
( ( ~ ( in @ SV93 @ SV301 )
| ~ ( in @ SV257 @ SV301 )
| ( subset @ ( unordered_pair @ SV93 @ SV257 ) @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1379,plain,
! [SV93: $i] :
( ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY481 ) @ SY482 )
| ( in @ SV93 @ SY482 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1380,plain,
! [SV93: $i] :
( ( ~ ! [SY483: $i,SY484: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY483 ) @ SY484 )
| ( in @ SY483 @ SY484 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1381,plain,
! [SV258: $i,SV210: $i] :
( ( ( ( ( set_difference @ SV210 @ SV258 )
!= empty_set ) )
= $true )
| ( ( subset @ SV210 @ SV258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1382,plain,
! [SV259: $i,SV211: $i] :
( ( ( ~ ( subset @ SV211 @ SV259 ) )
= $true )
| ( ( ( set_difference @ SV211 @ SV259 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1383,plain,
! [SV260: $i,SV94: $i] :
( ( ( ~ ( subset @ SV94 @ SV260 ) )
= $true )
| ( ( ! [SY691: $i] : ( subset @ ( cartesian_product2 @ SV94 @ SY691 ) @ ( cartesian_product2 @ SV260 @ SY691 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1384,plain,
! [SV261: $i,SV94: $i] :
( ( ( ~ ( subset @ SV94 @ SV261 ) )
= $true )
| ( ( ! [SY692: $i] : ( subset @ ( cartesian_product2 @ SY692 @ SV94 ) @ ( cartesian_product2 @ SY692 @ SV261 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1385,plain,
! [SV262: $i,SV212: $i] :
( ( ( ~ ( in @ SV212 @ SV262 ) )
= $true )
| ( ( subset @ ( singleton @ SV212 ) @ SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1386,plain,
! [SV263: $i,SV213: $i] :
( ( ( ~ ( subset @ ( singleton @ SV213 ) @ SV263 ) )
= $true )
| ( ( in @ SV213 @ SV263 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1387,plain,
! [SV264: $i,SV214: $i] :
( ( ( ( ( set_difference @ SV214 @ SV264 )
!= empty_set ) )
= $true )
| ( ( subset @ SV214 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1388,plain,
! [SV265: $i,SV215: $i] :
( ( ( ~ ( subset @ SV215 @ SV265 ) )
= $true )
| ( ( ( set_difference @ SV215 @ SV265 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1389,plain,
! [SV95: $i,SV266: $i] :
( ( ( ~ ( subset @ SV266 @ ( sK7_B @ SV95 ) )
| ( are_equipotent @ SV266 @ ( sK7_B @ SV95 ) ) )
= $true )
| ( ( in @ SV266 @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1390,plain,
! [SV95: $i] :
( ( ~ ! [SY490: $i] :
( ~ ( in @ SY490 @ ( sK7_B @ SV95 ) )
| ( in @ ( powerset @ SY490 ) @ ( sK7_B @ SV95 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1391,plain,
! [SV95: $i] :
( ( ~ ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) )
| ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1392,plain,
! [SV96: $i,SV216: $i] :
( ( ( relation @ SV216 )
= $false )
| ( ( ~ ( ~ ! [SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ! [SY640: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ SY640 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY640 @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) ) )
| ( SY639
= ( relation_composition @ SV96 @ SV216 ) ) )
| ~ ! [SY641: $i] :
( ~ ( relation @ SY641 )
| ( SY641
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY642 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY643 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY641 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SY641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY645 @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) @ SY646 ) @ SV216 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1393,plain,
! [SV267: $i,SV217: $i] :
( ( ( ( ( set_intersection2 @ SV217 @ SV267 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV217 @ SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1394,plain,
! [SV268: $i,SV218: $i] :
( ( ( ~ ( disjoint @ SV218 @ SV268 ) )
= $true )
| ( ( ( set_intersection2 @ SV218 @ SV268 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1395,plain,
! [SV269: $i,SV219: $i] :
( ( ( ( ( set_difference @ SV219 @ SV269 )
!= SV219 ) )
= $true )
| ( ( disjoint @ SV219 @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1396,plain,
! [SV270: $i,SV220: $i] :
( ( ( ~ ( disjoint @ SV220 @ SV270 ) )
= $true )
| ( ( ( set_difference @ SV220 @ SV270 )
= SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1397,plain,
! [SV271: $i,SV221: $i] :
( ( ( disjoint @ SV221 @ SV271 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV221 )
| ~ ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV271 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1398,plain,
! [SV272: $i,SV222: $i] :
( ( ( ! [SY693: $i] :
( ~ ( in @ SY693 @ SV222 )
| ~ ( in @ SY693 @ SV272 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV222 @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1399,plain,
! [SV223: $i,SV273: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ~ ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) )
| ~ ( ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) ) ) )
= $true )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1277]) ).
thf(1400,plain,
! [SV224: $i,SV274: $i] :
( ( ( ( SV274
!= ( powerset @ SV224 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY694: $i] :
( ~ ( in @ SY694 @ SV274 )
| ( subset @ SY694 @ SV224 ) )
| ~ ! [SY695: $i] :
( ~ ( subset @ SY695 @ SV224 )
| ( in @ SY695 @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1401,plain,
! [SV302: $i,SV174: $i,SV97: $i] :
( ( ! [SY724: $i] :
( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SV302 @ SY724 ) )
| ( SV97 = SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1402,plain,
! [SV303: $i,SV174: $i,SV97: $i] :
( ( ! [SY725: $i] :
( ( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SV303 @ SY725 ) )
| ( SV174 = SY725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1403,plain,
! [SV175: $i,SV98: $i] :
( ( ( ~ ! [SY600: $i] :
( ~ ( element @ SY600 @ ( powerset @ SV98 ) )
| ~ ( disjoint @ SV175 @ SY600 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SY600 ) ) ) )
= $false )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1404,plain,
! [SV175: $i,SV98: $i] :
( ( ( ~ ! [SY601: $i] :
( ~ ( element @ SY601 @ ( powerset @ SV98 ) )
| ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SY601 ) )
| ( disjoint @ SV175 @ SY601 ) ) )
= $false )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1405,plain,
! [SV99: $i] :
( ( ( ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( subset @ SV99 @ SY510 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SY510 ) ) ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1282]) ).
thf(1406,plain,
! [SV99: $i] :
( ( ( ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( subset @ SV99 @ SY511 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SY511 ) ) ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1283]) ).
thf(1407,plain,
! [SV100: $i] :
( ( ( ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SY512 @ SV100 ) @ ( sK18_SY354 @ SY512 @ SV100 ) ) @ SY512 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SY512 @ SV100 ) @ ( sK17_C @ SY512 @ SV100 ) ) @ SV100 ) ) )
| ( SY512
= ( relation_inverse @ SV100 ) ) ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1284]) ).
thf(1408,plain,
! [SV100: $i] :
( ( ( ! [SY513: $i] :
( ~ ( relation @ SY513 )
| ( SY513
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( in @ ( ordered_pair @ SY514 @ SY515 ) @ SY513 )
| ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV100 ) )
| ~ ! [SY516: $i,SY517: $i] :
( ~ ( in @ ( ordered_pair @ SY517 @ SY516 ) @ SV100 )
| ( in @ ( ordered_pair @ SY516 @ SY517 ) @ SY513 ) ) ) ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1409,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) ) )
| ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1410,plain,
! [SV276: $i,SV101: $i,SV305: $i] :
( ( ( SV305
!= ( set_intersection2 @ SV101 @ SV276 ) )
| ~ ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV101 )
| ~ ( in @ SY726 @ SV276 )
| ( in @ SY726 @ SV305 ) )
| ~ ~ ( ~ ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1411,plain,
! [SV277: $i,SV102: $i,SV306: $i] :
( ( ~ ( relation @ SV306 )
| ~ ( in @ ( ordered_pair @ SV102 @ SV277 ) @ SV306 )
| ( in @ SV102 @ ( relation_field @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1412,plain,
! [SV278: $i,SV102: $i,SV307: $i] :
( ( ~ ( relation @ SV307 )
| ~ ( in @ ( ordered_pair @ SV102 @ SV278 ) @ SV307 )
| ( in @ SV278 @ ( relation_field @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1413,plain,
! [SV103: $i,SV279: $i] :
( ( ( ~ ( subset @ SV279 @ ( sK8_B @ SV103 ) )
| ( are_equipotent @ SV279 @ ( sK8_B @ SV103 ) ) )
= $true )
| ( ( in @ SV279 @ ( sK8_B @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1414,plain,
! [SV103: $i] :
( ( ~ ! [SY530: $i] :
( ~ ( ~ ! [SY531: $i] :
( ~ ( subset @ SY531 @ SY530 )
| ( in @ SY531 @ ( sK9_SY344 @ SY530 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SY530 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SY530 @ ( sK8_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1415,plain,
! [SV103: $i] :
( ( ~ ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1416,plain,
! [SV280: $i,SV225: $i] :
( ( ( ~ ( subset @ SV225 @ SV280 )
| ~ ( subset @ SV280 @ SV225 ) )
= $true )
| ( ( SV225 = SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1417,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1293]) ).
thf(1418,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1419,plain,
! [SV281: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ SV281 ) )
= $true )
| ( ( subset @ ( singleton @ SV226 ) @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1420,plain,
! [SV282: $i,SV227: $i] :
( ( ( ~ ( subset @ ( singleton @ SV227 ) @ SV282 ) )
= $true )
| ( ( in @ SV227 @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1421,plain,
! [SV283: $i,SV228: $i] :
( ( ( ~ ( subset @ SV228 @ ( singleton @ SV283 ) ) )
= $true )
| ( ( ( SV228 = empty_set )
| ( SV228
= ( singleton @ SV283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1422,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1423,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1424,plain,
! [SV176: $i,SV308: $i,SV104: $i] :
( ( ! [SY729: $i] :
( ~ ( in @ SV104 @ SV308 )
| ~ ( in @ SV176 @ SY729 )
| ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV308 @ SY729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1425,plain,
! [SV176: $i,SV104: $i] :
( ( ~ ! [SY604: $i] :
( ! [SY605: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY604 @ SY605 ) )
| ( in @ SV104 @ SY604 ) )
| ~ ! [SY606: $i,SY607: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY606 @ SY607 ) )
| ( in @ SV176 @ SY607 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1426,plain,
! [SV309: $i,SV284: $i,SV105: $i] :
( ( ~ ( ~ ( ! [SY730: $i,SY731: $i] :
( ~ ( in @ SY730 @ SV105 )
| ~ ( in @ SY731 @ SV284 )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SY730 @ SY731 ) ) )
| ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) ) )
| ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1427,plain,
! [SV285: $i,SV105: $i,SV310: $i] :
( ( ( SV310
!= ( cartesian_product2 @ SV105 @ SV285 ) )
| ~ ( ~ ! [SY732: $i] :
( ! [SY708: $i,SY709: $i] :
( ~ ( in @ SY708 @ SV105 )
| ~ ( in @ SY709 @ SV285 )
| ( SY732
!= ( ordered_pair @ SY708 @ SY709 ) ) )
| ( in @ SY732 @ SV310 ) )
| ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV310 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SY735
!= ( ordered_pair @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1428,plain,
! [SV286: $i,SV229: $i] :
( ( ( ~ ( subset @ SV229 @ ( singleton @ SV286 ) ) )
= $true )
| ( ( ( SV229 = empty_set )
| ( SV229
= ( singleton @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1429,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1305]) ).
thf(1430,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1306]) ).
thf(1431,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) ) )
| ~ ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV106 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV287 ) ) )
| ( SV311
= ( unordered_pair @ SV106 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1432,plain,
! [SV288: $i,SV106: $i,SV312: $i] :
( ( ( SV312
!= ( unordered_pair @ SV106 @ SV288 ) )
| ~ ( ~ ! [SY736: $i] :
( ~ ( in @ SY736 @ SV312 )
| ( SY736 = SV106 )
| ( SY736 = SV288 ) )
| ~ ~ ( ~ ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) )
| ~ ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1433,plain,
! [SV289: $i,SV230: $i] :
( ( ( ( ( set_difference @ SV230 @ ( singleton @ SV289 ) )
!= SV230 ) )
= $true )
| ( ( ~ ( in @ SV289 @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1434,plain,
! [SV231: $i,SV290: $i] :
( ( ( in @ SV290 @ SV231 )
= $true )
| ( ( ( set_difference @ SV231 @ ( singleton @ SV290 ) )
= SV231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1435,plain,
! [SV177: $i,SV313: $i,SV107: $i] :
( ( ! [SY739: $i] :
( ~ ( in @ SV107 @ SV313 )
| ~ ( in @ SV177 @ SY739 )
| ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV313 @ SY739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1436,plain,
! [SV177: $i,SV107: $i] :
( ( ~ ! [SY610: $i] :
( ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY610 @ SY611 ) )
| ( in @ SV107 @ SY610 ) )
| ~ ! [SY612: $i,SY613: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY612 @ SY613 ) )
| ( in @ SV177 @ SY613 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1437,plain,
! [SV232: $i] :
( ( ( relation @ SV232 )
= $false )
| ( ( ( relation_rng @ SV232 )
= ( relation_dom @ ( relation_inverse @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1438,plain,
! [SV233: $i] :
( ( ( relation @ SV233 )
= $false )
| ( ( ( relation_dom @ SV233 )
= ( relation_rng @ ( relation_inverse @ SV233 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1439,plain,
! [SV108: $i] :
( ( ( empty @ ( sK5_B @ SV108 ) )
= $false )
| ( ( empty @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1440,plain,
! [SV235: $i] :
( ( ( SV235 = empty_set )
= $false )
| ( ( ! [SY665: $i] :
~ ( in @ SY665 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1441,plain,
! [SV109: $i] :
( ( ( ! [SY565: $i] :
( ~ ( ~ ( ! [SY566: $i] :
~ ( in @ ( ordered_pair @ SY566 @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SY565 @ SV109 ) @ ( sK20_C @ SY565 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SY565 @ SV109 ) @ SY565 ) ) )
| ( SY565
= ( relation_rng @ SV109 ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1319]) ).
thf(1442,plain,
! [SV109: $i] :
( ( ( ! [SY567: $i] :
( ( SY567
!= ( relation_rng @ SV109 ) )
| ~ ( ~ ! [SY568: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY568 ) @ SV109 )
| ( in @ SY568 @ SY567 ) )
| ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ SY567 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY570 @ SY567 @ SV109 ) @ SY570 ) @ SV109 ) ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1320]) ).
thf(1443,plain,
! [SV291: $i,SV110: $i,SV314: $i] :
( ( ~ ( relation @ SV314 )
| ~ ( in @ ( ordered_pair @ SV110 @ SV291 ) @ SV314 )
| ( in @ SV110 @ ( relation_dom @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1444,plain,
! [SV292: $i,SV110: $i,SV315: $i] :
( ( ~ ( relation @ SV315 )
| ~ ( in @ ( ordered_pair @ SV110 @ SV292 ) @ SV315 )
| ( in @ SV292 @ ( relation_rng @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1445,plain,
! [SV293: $i,SV236: $i] :
( ( ( ~ ( element @ SV236 @ ( powerset @ SV293 ) ) )
= $true )
| ( ( subset @ SV236 @ SV293 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1446,plain,
! [SV294: $i,SV237: $i] :
( ( ( ~ ( subset @ SV237 @ SV294 ) )
= $true )
| ( ( element @ SV237 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1447,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ ( sK43_SY367 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1448,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK41_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)],[1326]) ).
thf(1449,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1327]) ).
thf(1450,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1451,plain,
! [SV295: $i,SV238: $i] :
( ( ( ( SV238 = SV295 )
| ~ ( subset @ SV238 @ SV295 ) )
= $true )
| ( ( proper_subset @ SV238 @ SV295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1452,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1453,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1331]) ).
thf(1454,plain,
! [SV111: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) )
= $true )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1455,plain,
! [SV111: $i,SV178: $i] :
( ( ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
| ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) )
= $true )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1456,plain,
! [SV112: $i,SV179: $i] :
( ( ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV112 )
= $true )
| ( ( element @ SV112 @ ( powerset @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1457,plain,
! [SV112: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV179 ) )
= $true )
| ( ( element @ SV112 @ ( powerset @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1458,plain,
! [SV239: $i] :
( ( ( ~ ! [SY669: $i,SY670: $i] :
( ( sK46_B @ SV239 )
!= ( ordered_pair @ SY669 @ SY670 ) )
| ~ ( in @ ( sK46_B @ SV239 ) @ SV239 ) )
= $false )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1459,plain,
! [SV240: $i] :
( ( ( relation @ SV240 )
= $false )
| ( ( ! [SY671: $i] :
( ( SY671
= ( ordered_pair @ ( sK44_C @ SY671 @ SV240 ) @ ( sK45_SY369 @ SY671 @ SV240 ) ) )
| ~ ( in @ SY671 @ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1460,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1461,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1339]) ).
thf(1462,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1463,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1341]) ).
thf(1464,plain,
! [SV5: $i,SV117: $i,SV241: $i] :
( ( ( in @ SV241 @ SV117 )
= $false )
| ( ( in @ SV241 @ SV5 )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1465,plain,
! [SV180: $i,SV128: $i,SV25: $i] :
( ( ( in @ SV25 @ SV128 )
= $false )
| ( ( element @ SV128 @ ( powerset @ SV180 ) )
= $false )
| ( ( element @ SV25 @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1466,plain,
! [SV195: $i,SV181: $i,SV131: $i,SV29: $i] :
( ( ( ( unordered_pair @ SV29 @ SV131 )
= ( unordered_pair @ SV181 @ SV195 ) )
= $false )
| ( ( SV29 = SV181 )
= $true )
| ( ( SV29 = SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1467,plain,
! [SV196: $i,SV182: $i,SV132: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV132 )
= $false )
| ( ( ~ ( subset @ SV182 @ SV196 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV30 @ SV182 ) @ ( cartesian_product2 @ SV132 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1468,plain,
! [SV135: $i,SV183: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV183 )
= $false )
| ( ( subset @ SV33 @ SV135 )
= $false )
| ( ( subset @ SV33 @ ( set_intersection2 @ SV135 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1469,plain,
! [SV34: $i,SV184: $i,SV136: $i] :
( ( ( subset @ SV136 @ SV184 )
= $false )
| ( ( subset @ SV34 @ SV136 )
= $false )
| ( ( subset @ SV34 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1470,plain,
! [SV199: $i,SV45: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV45 ) @ ( relation_dom @ SV199 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV45 @ SV199 ) )
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1471,plain,
! [SV200: $i,SV47: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV47 ) @ ( relation_rng @ SV200 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV200 @ SV47 ) )
= ( relation_rng @ SV47 ) )
= $true )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1472,plain,
! [SV185: $i,SV49: $i,SV296: $i] :
( ( ( ~ ( element @ SV296 @ SV49 ) )
= $true )
| ( ( ( in @ SV296 @ SV185 )
| ( in @ SV296 @ ( subset_complement @ SV49 @ SV185 ) ) )
= $true )
| ( ( element @ SV185 @ ( powerset @ SV49 ) )
= $false )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1473,plain,
! [SV186: $i,SV50: $i,SV146: $i] :
( ( ( in @ SV146 @ ( subset_complement @ SV50 @ SV186 ) )
= $false )
| ( ( ~ ( in @ SV146 @ SV186 ) )
= $true )
| ( ( element @ SV186 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1474,plain,
! [SV187: $i,SV148: $i,SV52: $i] :
( ( ( subset @ SV52 @ SV148 )
= $false )
| ( ( disjoint @ SV148 @ SV187 )
= $false )
| ( ( disjoint @ SV52 @ SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1475,plain,
! [SV56: $i,SV151: $i,SV188: $i] :
( ( ( subset @ SV188 @ SV151 )
= $false )
| ( ( subset @ SV56 @ SV151 )
= $false )
| ( ( subset @ ( set_union2 @ SV56 @ SV188 ) @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1476,plain,
! [SV161: $i,SV69: $i,SV190: $i] :
( ( ( element @ SV190 @ ( powerset @ SV69 ) )
= $false )
| ( ( element @ SV161 @ ( powerset @ SV69 ) )
= $false )
| ( ( element @ ( subset_difference @ SV69 @ SV161 @ SV190 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1477,plain,
! [SV169: $i,SV84: $i,SV193: $i] :
( ( ( element @ SV193 @ ( powerset @ SV84 ) )
= $false )
| ( ( element @ SV169 @ ( powerset @ SV84 ) )
= $false )
| ( ( ( subset_difference @ SV84 @ SV169 @ SV193 )
= ( set_difference @ SV169 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1478,plain,
! [SV194: $i,SV171: $i,SV87: $i] :
( ( ( in @ SV87 @ SV171 )
= $false )
| ( ( element @ SV171 @ ( powerset @ SV194 ) )
= $false )
| ( ( ~ ( empty @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1479,plain,
! [SV202: $i,SV245: $i] :
( ( ( ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV202 )
| ~ ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV245 ) )
= $false )
| ( ( subset @ SV202 @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1480,plain,
! [SV246: $i,SV203: $i] :
( ( ( subset @ SV203 @ SV246 )
= $false )
| ( ( ! [SY672: $i] :
( ~ ( in @ SY672 @ SV203 )
| ( in @ SY672 @ SV246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1481,plain,
! [SV248: $i,SV205: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ ( set_intersection2 @ SV205 @ SV248 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV205 @ SV248 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1482,plain,
! [SV206: $i,SV249: $i] :
( ( ( ~ ( ( ( sK40_C @ SV249 @ SV206 )
!= SV206 )
| ~ ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) )
| ~ ( ( ( sK40_C @ SV249 @ SV206 )
= SV206 )
| ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) ) )
= $false )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1483,plain,
! [SV207: $i,SV250: $i] :
( ( ( SV250
= ( singleton @ SV207 ) )
= $false )
| ( ( ~ ( ~ ! [SY674: $i] :
( ( SY674 != SV207 )
| ( in @ SY674 @ SV250 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV250 )
| ( SY675 = SV207 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1484,plain,
! [SV90: $i,SV317: $i] :
( ( ( ~ ( ~ ( ! [SY740: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SY740 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ ( sK28_SY360 @ SV317 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) ) )
| ( SV317
= ( relation_dom @ SV90 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1485,plain,
! [SV90: $i,SV318: $i] :
( ( ( ( SV318
!= ( relation_dom @ SV90 ) )
| ~ ( ~ ! [SY741: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY741 @ SY463 ) @ SV90 )
| ( in @ SY741 @ SV318 ) )
| ~ ! [SY743: $i] :
( ~ ( in @ SY743 @ SV318 )
| ( in @ ( ordered_pair @ SY743 @ ( sK26_D @ SY743 @ SV318 @ SV90 ) ) @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1486,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( ! [SY676: $i] :
( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SY676 )
| ~ ( in @ SY676 @ SV208 ) )
| ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
| ~ ( ~ ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) )
| ~ ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 ) )
| ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) ) )
= $false )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1487,plain,
! [SV209: $i,SV252: $i] :
( ( ( SV252
= ( union @ SV209 ) )
= $false )
| ( ( ~ ( ~ ! [SY677: $i] :
( ! [SY631: $i] :
( ~ ( in @ SY677 @ SY631 )
| ~ ( in @ SY631 @ SV209 ) )
| ( in @ SY677 @ SV252 ) )
| ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV252 )
| ~ ( ~ ( in @ SY679 @ ( sK23_D @ SY679 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SY679 @ SV252 @ SV209 ) @ SV209 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1488,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) )
| ~ ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1489,plain,
! [SV254: $i,SV91: $i,SV298: $i] :
( ( ( ( SV298
!= ( set_union2 @ SV91 @ SV254 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY718: $i] :
( ~ ( in @ SY718 @ SV298 )
| ( in @ SY718 @ SV91 )
| ( in @ SY718 @ SV254 ) )
| ~ ~ ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) )
| ~ ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1490,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) ) ) )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1491,plain,
! [SV256: $i,SV92: $i,SV300: $i] :
( ( ( ( SV300
!= ( set_difference @ SV92 @ SV256 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY721: $i] :
( ~ ( in @ SY721 @ SV92 )
| ( in @ SY721 @ SV256 )
| ( in @ SY721 @ SV300 ) )
| ~ ~ ( ~ ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1492,plain,
! [SV257: $i,SV301: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ SV301 )
| ~ ( in @ SV257 @ SV301 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV93 @ SV257 ) @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1493,plain,
! [SV93: $i] :
( ( ! [SY481: $i,SY482: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY481 ) @ SY482 )
| ( in @ SV93 @ SY482 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1494,plain,
! [SV93: $i] :
( ( ! [SY483: $i,SY484: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SY483 ) @ SY484 )
| ( in @ SY483 @ SY484 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1495,plain,
! [SV258: $i,SV210: $i] :
( ( ( ( set_difference @ SV210 @ SV258 )
= empty_set )
= $false )
| ( ( subset @ SV210 @ SV258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1496,plain,
! [SV259: $i,SV211: $i] :
( ( ( subset @ SV211 @ SV259 )
= $false )
| ( ( ( set_difference @ SV211 @ SV259 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1497,plain,
! [SV260: $i,SV94: $i] :
( ( ( subset @ SV94 @ SV260 )
= $false )
| ( ( ! [SY691: $i] : ( subset @ ( cartesian_product2 @ SV94 @ SY691 ) @ ( cartesian_product2 @ SV260 @ SY691 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1498,plain,
! [SV261: $i,SV94: $i] :
( ( ( subset @ SV94 @ SV261 )
= $false )
| ( ( ! [SY692: $i] : ( subset @ ( cartesian_product2 @ SY692 @ SV94 ) @ ( cartesian_product2 @ SY692 @ SV261 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1499,plain,
! [SV262: $i,SV212: $i] :
( ( ( in @ SV212 @ SV262 )
= $false )
| ( ( subset @ ( singleton @ SV212 ) @ SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1500,plain,
! [SV263: $i,SV213: $i] :
( ( ( subset @ ( singleton @ SV213 ) @ SV263 )
= $false )
| ( ( in @ SV213 @ SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1501,plain,
! [SV264: $i,SV214: $i] :
( ( ( ( set_difference @ SV214 @ SV264 )
= empty_set )
= $false )
| ( ( subset @ SV214 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1502,plain,
! [SV265: $i,SV215: $i] :
( ( ( subset @ SV215 @ SV265 )
= $false )
| ( ( ( set_difference @ SV215 @ SV265 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1503,plain,
! [SV95: $i,SV266: $i] :
( ( ( ~ ( subset @ SV266 @ ( sK7_B @ SV95 ) ) )
= $true )
| ( ( are_equipotent @ SV266 @ ( sK7_B @ SV95 ) )
= $true )
| ( ( in @ SV266 @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1504,plain,
! [SV95: $i] :
( ( ! [SY490: $i] :
( ~ ( in @ SY490 @ ( sK7_B @ SV95 ) )
| ( in @ ( powerset @ SY490 ) @ ( sK7_B @ SV95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1390]) ).
thf(1505,plain,
! [SV95: $i] :
( ( ~ ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) )
| ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1391]) ).
thf(1506,plain,
! [SV96: $i,SV216: $i] :
( ( ( ~ ! [SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ! [SY640: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ SY640 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY640 @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) ) )
| ( SY639
= ( relation_composition @ SV96 @ SV216 ) ) )
| ~ ! [SY641: $i] :
( ~ ( relation @ SY641 )
| ( SY641
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY642 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY643 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY641 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SY641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY645 @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) @ SY646 ) @ SV216 ) ) ) ) ) )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1507,plain,
! [SV267: $i,SV217: $i] :
( ( ( ( set_intersection2 @ SV217 @ SV267 )
= empty_set )
= $false )
| ( ( disjoint @ SV217 @ SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1508,plain,
! [SV268: $i,SV218: $i] :
( ( ( disjoint @ SV218 @ SV268 )
= $false )
| ( ( ( set_intersection2 @ SV218 @ SV268 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1509,plain,
! [SV269: $i,SV219: $i] :
( ( ( ( set_difference @ SV219 @ SV269 )
= SV219 )
= $false )
| ( ( disjoint @ SV219 @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1510,plain,
! [SV270: $i,SV220: $i] :
( ( ( disjoint @ SV220 @ SV270 )
= $false )
| ( ( ( set_difference @ SV220 @ SV270 )
= SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1511,plain,
! [SV221: $i,SV271: $i] :
( ( ( ~ ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV221 )
| ~ ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV271 ) )
= $false )
| ( ( disjoint @ SV221 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1512,plain,
! [SV272: $i,SV222: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ SV222 )
| ~ ( in @ SV319 @ SV272 ) )
= $true )
| ( ( ~ ( disjoint @ SV222 @ SV272 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1513,plain,
! [SV223: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ~ ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) )
| ~ ( ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) ) )
= $false )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1514,plain,
! [SV224: $i,SV274: $i] :
( ( ( SV274
= ( powerset @ SV224 ) )
= $false )
| ( ( ~ ( ~ ! [SY694: $i] :
( ~ ( in @ SY694 @ SV274 )
| ( subset @ SY694 @ SV224 ) )
| ~ ! [SY695: $i] :
( ~ ( subset @ SY695 @ SV224 )
| ( in @ SY695 @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1515,plain,
! [SV302: $i,SV174: $i,SV97: $i] :
( ( ( ! [SY724: $i] :
( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SV302 @ SY724 ) ) )
= $true )
| ( ( SV97 = SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1516,plain,
! [SV320: $i,SV303: $i,SV174: $i,SV97: $i] :
( ( ( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SV303 @ SV320 ) )
| ( SV174 = SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1517,plain,
! [SV175: $i,SV98: $i] :
( ( ( ! [SY600: $i] :
( ~ ( element @ SY600 @ ( powerset @ SV98 ) )
| ~ ( disjoint @ SV175 @ SY600 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SY600 ) ) ) )
= $true )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1518,plain,
! [SV175: $i,SV98: $i] :
( ( ( ! [SY601: $i] :
( ~ ( element @ SY601 @ ( powerset @ SV98 ) )
| ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SY601 ) )
| ( disjoint @ SV175 @ SY601 ) ) )
= $true )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1519,plain,
! [SV99: $i,SV321: $i] :
( ( ( ~ ( relation @ SV321 )
| ~ ( subset @ SV99 @ SV321 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SV321 ) ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1520,plain,
! [SV99: $i,SV322: $i] :
( ( ( ~ ( relation @ SV322 )
| ~ ( subset @ SV99 @ SV322 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SV322 ) ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1521,plain,
! [SV100: $i,SV323: $i] :
( ( ( ~ ( relation @ SV323 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) ) )
| ( SV323
= ( relation_inverse @ SV100 ) ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1522,plain,
! [SV100: $i,SV324: $i] :
( ( ( ~ ( relation @ SV324 )
| ( SV324
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY744: $i,SY745: $i] :
( ~ ( in @ ( ordered_pair @ SY744 @ SY745 ) @ SV324 )
| ( in @ ( ordered_pair @ SY745 @ SY744 ) @ SV100 ) )
| ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ ( ordered_pair @ SY747 @ SY746 ) @ SV100 )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV324 ) ) ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1523,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) ) ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1524,plain,
! [SV276: $i,SV101: $i,SV305: $i] :
( ( ( ( SV305
!= ( set_intersection2 @ SV101 @ SV276 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV101 )
| ~ ( in @ SY726 @ SV276 )
| ( in @ SY726 @ SV305 ) )
| ~ ~ ( ~ ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1525,plain,
! [SV277: $i,SV102: $i,SV306: $i] :
( ( ( ~ ( relation @ SV306 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV277 ) @ SV306 )
| ( in @ SV102 @ ( relation_field @ SV306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1526,plain,
! [SV278: $i,SV102: $i,SV307: $i] :
( ( ( ~ ( relation @ SV307 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV278 ) @ SV307 )
| ( in @ SV278 @ ( relation_field @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1527,plain,
! [SV103: $i,SV279: $i] :
( ( ( ~ ( subset @ SV279 @ ( sK8_B @ SV103 ) ) )
= $true )
| ( ( are_equipotent @ SV279 @ ( sK8_B @ SV103 ) )
= $true )
| ( ( in @ SV279 @ ( sK8_B @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1528,plain,
! [SV103: $i] :
( ( ! [SY530: $i] :
( ~ ( ~ ! [SY531: $i] :
( ~ ( subset @ SY531 @ SY530 )
| ( in @ SY531 @ ( sK9_SY344 @ SY530 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SY530 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SY530 @ ( sK8_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1529,plain,
! [SV103: $i] :
( ( ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1415]) ).
thf(1530,plain,
! [SV280: $i,SV225: $i] :
( ( ( ~ ( subset @ SV225 @ SV280 ) )
= $true )
| ( ( ~ ( subset @ SV280 @ SV225 ) )
= $true )
| ( ( SV225 = SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1531,plain,
! [SV325: $i] :
( ( ! [SY748: $i] :
( ( SV325 != SY748 )
| ( subset @ SV325 @ SY748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1532,plain,
! [SV326: $i] :
( ( ! [SY749: $i] :
( ( SV326 != SY749 )
| ( subset @ SY749 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1533,plain,
! [SV281: $i,SV226: $i] :
( ( ( in @ SV226 @ SV281 )
= $false )
| ( ( subset @ ( singleton @ SV226 ) @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1534,plain,
! [SV282: $i,SV227: $i] :
( ( ( subset @ ( singleton @ SV227 ) @ SV282 )
= $false )
| ( ( in @ SV227 @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1535,plain,
! [SV283: $i,SV228: $i] :
( ( ( subset @ SV228 @ ( singleton @ SV283 ) )
= $false )
| ( ( ( SV228 = empty_set )
| ( SV228
= ( singleton @ SV283 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1536,plain,
! [SV327: $i] :
( ( ( SV327 != empty_set )
| ! [SY750: $i] : ( subset @ SV327 @ ( singleton @ SY750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1537,plain,
! [SV328: $i] :
( ( ! [SY751: $i] :
( ( SV328
!= ( singleton @ SY751 ) )
| ( subset @ SV328 @ ( singleton @ SY751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1538,plain,
! [SV329: $i,SV176: $i,SV308: $i,SV104: $i] :
( ( ~ ( in @ SV104 @ SV308 )
| ~ ( in @ SV176 @ SV329 )
| ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV308 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1539,plain,
! [SV176: $i,SV104: $i] :
( ( ~ ! [SY604: $i] :
( ! [SY605: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY604 @ SY605 ) )
| ( in @ SV104 @ SY604 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1540,plain,
! [SV176: $i,SV104: $i] :
( ( ~ ! [SY606: $i,SY607: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY606 @ SY607 ) )
| ( in @ SV176 @ SY607 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1541,plain,
! [SV309: $i,SV284: $i,SV105: $i] :
( ( ( ~ ( ~ ( ! [SY730: $i,SY731: $i] :
( ~ ( in @ SY730 @ SV105 )
| ~ ( in @ SY731 @ SV284 )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SY730 @ SY731 ) ) )
| ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) ) ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1542,plain,
! [SV285: $i,SV105: $i,SV310: $i] :
( ( ( ( SV310
!= ( cartesian_product2 @ SV105 @ SV285 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY732: $i] :
( ! [SY708: $i,SY709: $i] :
( ~ ( in @ SY708 @ SV105 )
| ~ ( in @ SY709 @ SV285 )
| ( SY732
!= ( ordered_pair @ SY708 @ SY709 ) ) )
| ( in @ SY732 @ SV310 ) )
| ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV310 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SY735
!= ( ordered_pair @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1543,plain,
! [SV286: $i,SV229: $i] :
( ( ( subset @ SV229 @ ( singleton @ SV286 ) )
= $false )
| ( ( ( SV229 = empty_set )
| ( SV229
= ( singleton @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1544,plain,
! [SV330: $i] :
( ( ( SV330 != empty_set )
| ! [SY752: $i] : ( subset @ SV330 @ ( singleton @ SY752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1545,plain,
! [SV331: $i] :
( ( ! [SY753: $i] :
( ( SV331
!= ( singleton @ SY753 ) )
| ( subset @ SV331 @ ( singleton @ SY753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1546,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) ) )
| ~ ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV106 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV287 ) ) ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1547,plain,
! [SV288: $i,SV106: $i,SV312: $i] :
( ( ( ( SV312
!= ( unordered_pair @ SV106 @ SV288 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY736: $i] :
( ~ ( in @ SY736 @ SV312 )
| ( SY736 = SV106 )
| ( SY736 = SV288 ) )
| ~ ~ ( ~ ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) )
| ~ ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1548,plain,
! [SV289: $i,SV230: $i] :
( ( ( ( set_difference @ SV230 @ ( singleton @ SV289 ) )
= SV230 )
= $false )
| ( ( ~ ( in @ SV289 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1549,plain,
! [SV332: $i,SV177: $i,SV313: $i,SV107: $i] :
( ( ~ ( in @ SV107 @ SV313 )
| ~ ( in @ SV177 @ SV332 )
| ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV313 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1550,plain,
! [SV177: $i,SV107: $i] :
( ( ~ ! [SY610: $i] :
( ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY610 @ SY611 ) )
| ( in @ SV107 @ SY610 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1551,plain,
! [SV177: $i,SV107: $i] :
( ( ~ ! [SY612: $i,SY613: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY612 @ SY613 ) )
| ( in @ SV177 @ SY613 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1552,plain,
! [SV235: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV235 ) )
= $true )
| ( ( SV235 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1553,plain,
! [SV109: $i,SV334: $i] :
( ( ( ~ ( ~ ( ! [SY754: $i] :
~ ( in @ ( ordered_pair @ SY754 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SV334 @ SV109 ) @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) ) )
| ( SV334
= ( relation_rng @ SV109 ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1554,plain,
! [SV109: $i,SV335: $i] :
( ( ( ( SV335
!= ( relation_rng @ SV109 ) )
| ~ ( ~ ! [SY755: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY755 ) @ SV109 )
| ( in @ SY755 @ SV335 ) )
| ~ ! [SY757: $i] :
( ~ ( in @ SY757 @ SV335 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY757 @ SV335 @ SV109 ) @ SY757 ) @ SV109 ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1555,plain,
! [SV291: $i,SV110: $i,SV314: $i] :
( ( ( ~ ( relation @ SV314 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV110 @ SV291 ) @ SV314 )
| ( in @ SV110 @ ( relation_dom @ SV314 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1556,plain,
! [SV292: $i,SV110: $i,SV315: $i] :
( ( ( ~ ( relation @ SV315 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV110 @ SV292 ) @ SV315 )
| ( in @ SV292 @ ( relation_rng @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1557,plain,
! [SV293: $i,SV236: $i] :
( ( ( element @ SV236 @ ( powerset @ SV293 ) )
= $false )
| ( ( subset @ SV236 @ SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1558,plain,
! [SV294: $i,SV237: $i] :
( ( ( subset @ SV237 @ SV294 )
= $false )
| ( ( element @ SV237 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1559,plain,
! [SV336: $i] :
( ( ( SV336 = empty_set )
| ! [SY758: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SY758 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SY758 @ SV336 ) @ ( sK43_SY367 @ SY758 @ SV336 ) ) )
| ~ ( in @ ( sK42_C @ SY758 @ SV336 ) @ SY758 ) )
| ~ ( ! [SY759: $i] :
( ~ ( in @ SY759 @ SV336 )
| ( in @ ( sK42_C @ SY758 @ SV336 ) @ SY759 ) )
| ( in @ ( sK42_C @ SY758 @ SV336 ) @ SY758 ) ) )
| ( SY758
= ( set_meet @ SV336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1560,plain,
! [SV337: $i] :
( ( ( SV337 = empty_set )
| ! [SY760: $i] :
( ( SY760
!= ( set_meet @ SV337 ) )
| ~ ( ~ ! [SY761: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SY761 @ SY760 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SY761 @ ( sK41_D @ SY761 @ SY760 @ SV337 ) ) )
| ( in @ SY761 @ SY760 ) )
| ~ ! [SY762: $i] :
( ~ ( in @ SY762 @ SY760 )
| ! [SY763: $i] :
( ~ ( in @ SY763 @ SV337 )
| ( in @ SY762 @ SY763 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1561,plain,
! [SV338: $i] :
( ( ( SV338 != empty_set )
| ! [SY764: $i] :
( ( SY764
!= ( set_meet @ SV338 ) )
| ( SY764 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1562,plain,
! [SV339: $i] :
( ( ( SV339 != empty_set )
| ! [SY765: $i] :
( ( SY765 != empty_set )
| ( SY765
= ( set_meet @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1563,plain,
! [SV295: $i,SV238: $i] :
( ( ( SV238 = SV295 )
= $true )
| ( ( ~ ( subset @ SV238 @ SV295 ) )
= $true )
| ( ( proper_subset @ SV238 @ SV295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1564,plain,
! [SV340: $i] :
( ( ! [SY766: $i] :
( ~ ( proper_subset @ SV340 @ SY766 )
| ( SV340 != SY766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1565,plain,
! [SV341: $i] :
( ( ! [SY767: $i] :
( ~ ( proper_subset @ SV341 @ SY767 )
| ( subset @ SV341 @ SY767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1566,plain,
! [SV111: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) )
= $true )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1567,plain,
! [SV111: $i,SV178: $i] :
( ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 )
= $true )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1568,plain,
! [SV112: $i,SV179: $i] :
( ( ( in @ ( sK49_C @ SV179 @ SV112 ) @ SV179 )
= $false )
| ( ( element @ SV112 @ ( powerset @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1569,plain,
! [SV239: $i] :
( ( ( ~ ! [SY669: $i,SY670: $i] :
( ( sK46_B @ SV239 )
!= ( ordered_pair @ SY669 @ SY670 ) ) )
= $false )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1570,plain,
! [SV239: $i] :
( ( ( ~ ( in @ ( sK46_B @ SV239 ) @ SV239 ) )
= $false )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1571,plain,
! [SV240: $i,SV342: $i] :
( ( ( ( SV342
= ( ordered_pair @ ( sK44_C @ SV342 @ SV240 ) @ ( sK45_SY369 @ SV342 @ SV240 ) ) )
| ~ ( in @ SV342 @ SV240 ) )
= $true )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1572,plain,
! [SV343: $i] :
( ( ( empty @ SV343 )
| ! [SY768: $i] :
( ~ ( element @ SY768 @ SV343 )
| ( in @ SY768 @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1573,plain,
! [SV344: $i] :
( ( ( empty @ SV344 )
| ! [SY769: $i] :
( ~ ( in @ SY769 @ SV344 )
| ( element @ SY769 @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1574,plain,
! [SV345: $i] :
( ( ~ ( empty @ SV345 )
| ! [SY770: $i] :
( ~ ( element @ SY770 @ SV345 )
| ( empty @ SY770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1575,plain,
! [SV346: $i] :
( ( ~ ( empty @ SV346 )
| ! [SY771: $i] :
( ~ ( empty @ SY771 )
| ( element @ SY771 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1576,plain,
! [SV132: $i,SV30: $i,SV196: $i,SV182: $i] :
( ( ( subset @ SV182 @ SV196 )
= $false )
| ( ( subset @ SV30 @ SV132 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV30 @ SV182 ) @ ( cartesian_product2 @ SV132 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1577,plain,
! [SV199: $i,SV45: $i] :
( ( ( subset @ ( relation_rng @ SV45 ) @ ( relation_dom @ SV199 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV45 @ SV199 ) )
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1578,plain,
! [SV200: $i,SV47: $i] :
( ( ( subset @ ( relation_dom @ SV47 ) @ ( relation_rng @ SV200 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV200 @ SV47 ) )
= ( relation_rng @ SV47 ) )
= $true )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1579,plain,
! [SV185: $i,SV49: $i,SV296: $i] :
( ( ( element @ SV296 @ SV49 )
= $false )
| ( ( ( in @ SV296 @ SV185 )
| ( in @ SV296 @ ( subset_complement @ SV49 @ SV185 ) ) )
= $true )
| ( ( element @ SV185 @ ( powerset @ SV49 ) )
= $false )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1580,plain,
! [SV50: $i,SV186: $i,SV146: $i] :
( ( ( in @ SV146 @ SV186 )
= $false )
| ( ( in @ SV146 @ ( subset_complement @ SV50 @ SV186 ) )
= $false )
| ( ( element @ SV186 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1581,plain,
! [SV87: $i,SV171: $i,SV194: $i] :
( ( ( empty @ SV194 )
= $false )
| ( ( element @ SV171 @ ( powerset @ SV194 ) )
= $false )
| ( ( in @ SV87 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1582,plain,
! [SV202: $i,SV245: $i] :
( ( ( ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV202 ) )
= $false )
| ( ( subset @ SV202 @ SV245 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1583,plain,
! [SV202: $i,SV245: $i] :
( ( ( ~ ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV245 ) )
= $false )
| ( ( subset @ SV202 @ SV245 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1584,plain,
! [SV246: $i,SV203: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ SV203 )
| ( in @ SV347 @ SV246 ) )
= $true )
| ( ( subset @ SV203 @ SV246 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1585,plain,
! [SV248: $i,SV205: $i,SV316: $i] :
( ( ( in @ SV316 @ ( set_intersection2 @ SV205 @ SV248 ) )
= $false )
| ( ( ~ ( disjoint @ SV205 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1586,plain,
! [SV206: $i,SV249: $i] :
( ( ( ~ ( ( ( sK40_C @ SV249 @ SV206 )
!= SV206 )
| ~ ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) ) )
= $false )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1587,plain,
! [SV206: $i,SV249: $i] :
( ( ( ~ ( ( ( sK40_C @ SV249 @ SV206 )
= SV206 )
| ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) ) )
= $false )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1588,plain,
! [SV250: $i,SV207: $i] :
( ( ( ~ ! [SY674: $i] :
( ( SY674 != SV207 )
| ( in @ SY674 @ SV250 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV250 )
| ( SY675 = SV207 ) ) )
= $false )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1589,plain,
! [SV90: $i,SV317: $i] :
( ( ( ~ ( ~ ( ! [SY740: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SY740 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ ( sK28_SY360 @ SV317 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) ) ) )
= $true )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1590,plain,
! [SV90: $i,SV318: $i] :
( ( ( ( SV318
!= ( relation_dom @ SV90 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY741: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY741 @ SY463 ) @ SV90 )
| ( in @ SY741 @ SV318 ) )
| ~ ! [SY743: $i] :
( ~ ( in @ SY743 @ SV318 )
| ( in @ ( ordered_pair @ SY743 @ ( sK26_D @ SY743 @ SV318 @ SV90 ) ) @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1591,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( ! [SY676: $i] :
( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SY676 )
| ~ ( in @ SY676 @ SV208 ) )
| ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) ) )
= $false )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1592,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) )
| ~ ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 ) )
| ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) ) )
= $false )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1593,plain,
! [SV252: $i,SV209: $i] :
( ( ( ~ ! [SY677: $i] :
( ! [SY631: $i] :
( ~ ( in @ SY677 @ SY631 )
| ~ ( in @ SY631 @ SV209 ) )
| ( in @ SY677 @ SV252 ) )
| ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV252 )
| ~ ( ~ ( in @ SY679 @ ( sK23_D @ SY679 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SY679 @ SV252 @ SV209 ) @ SV209 ) ) ) )
= $false )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1594,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) )
| ~ ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) )
= $false )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1595,plain,
! [SV254: $i,SV91: $i,SV298: $i] :
( ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false )
| ( ( ~ ( ~ ! [SY718: $i] :
( ~ ( in @ SY718 @ SV298 )
| ( in @ SY718 @ SV91 )
| ( in @ SY718 @ SV254 ) )
| ~ ~ ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) )
| ~ ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1596,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) ) )
= $false )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1597,plain,
! [SV256: $i,SV92: $i,SV300: $i] :
( ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false )
| ( ( ~ ( ~ ! [SY721: $i] :
( ~ ( in @ SY721 @ SV92 )
| ( in @ SY721 @ SV256 )
| ( in @ SY721 @ SV300 ) )
| ~ ~ ( ~ ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1598,plain,
! [SV257: $i,SV301: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ SV301 ) )
= $true )
| ( ( ~ ( in @ SV257 @ SV301 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV93 @ SV257 ) @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1599,plain,
! [SV348: $i,SV93: $i] :
( ( ! [SY772: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SV348 ) @ SY772 )
| ( in @ SV93 @ SY772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1600,plain,
! [SV349: $i,SV93: $i] :
( ( ! [SY773: $i] :
( ~ ( subset @ ( unordered_pair @ SV93 @ SV349 ) @ SY773 )
| ( in @ SV349 @ SY773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1601,plain,
! [SV260: $i,SV350: $i,SV94: $i] :
( ( ( subset @ ( cartesian_product2 @ SV94 @ SV350 ) @ ( cartesian_product2 @ SV260 @ SV350 ) )
= $true )
| ( ( subset @ SV94 @ SV260 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1602,plain,
! [SV261: $i,SV94: $i,SV351: $i] :
( ( ( subset @ ( cartesian_product2 @ SV351 @ SV94 ) @ ( cartesian_product2 @ SV351 @ SV261 ) )
= $true )
| ( ( subset @ SV94 @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1603,plain,
! [SV95: $i,SV266: $i] :
( ( ( subset @ SV266 @ ( sK7_B @ SV95 ) )
= $false )
| ( ( are_equipotent @ SV266 @ ( sK7_B @ SV95 ) )
= $true )
| ( ( in @ SV266 @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1604,plain,
! [SV95: $i,SV352: $i] :
( ( ~ ( in @ SV352 @ ( sK7_B @ SV95 ) )
| ( in @ ( powerset @ SV352 ) @ ( sK7_B @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1605,plain,
! [SV95: $i] :
( ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) )
| ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1606,plain,
! [SV96: $i,SV216: $i] :
( ( ( ~ ! [SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ! [SY640: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ SY640 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY640 @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) ) )
| ( SY639
= ( relation_composition @ SV96 @ SV216 ) ) ) )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1607,plain,
! [SV216: $i,SV96: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( relation @ SY641 )
| ( SY641
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY642 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY643 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY641 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SY641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY645 @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) @ SY646 ) @ SV216 ) ) ) ) ) )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1608,plain,
! [SV221: $i,SV271: $i] :
( ( ( ~ ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV221 ) )
= $false )
| ( ( disjoint @ SV221 @ SV271 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1609,plain,
! [SV221: $i,SV271: $i] :
( ( ( ~ ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV271 ) )
= $false )
| ( ( disjoint @ SV221 @ SV271 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1610,plain,
! [SV272: $i,SV222: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ SV222 ) )
= $true )
| ( ( ~ ( in @ SV319 @ SV272 ) )
= $true )
| ( ( ~ ( disjoint @ SV222 @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1611,plain,
! [SV223: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ~ ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) ) )
= $false )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1612,plain,
! [SV223: $i,SV273: $i] :
( ( ( ~ ( ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) ) )
= $false )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1613,plain,
! [SV224: $i,SV274: $i] :
( ( ( ~ ! [SY694: $i] :
( ~ ( in @ SY694 @ SV274 )
| ( subset @ SY694 @ SV224 ) )
| ~ ! [SY695: $i] :
( ~ ( subset @ SY695 @ SV224 )
| ( in @ SY695 @ SV274 ) ) )
= $false )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1614,plain,
! [SV353: $i,SV302: $i,SV174: $i,SV97: $i] :
( ( ( ( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SV302 @ SV353 ) ) )
= $true )
| ( ( SV97 = SV302 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1615,plain,
! [SV320: $i,SV303: $i,SV174: $i,SV97: $i] :
( ( ( ( ( ordered_pair @ SV97 @ SV174 )
!= ( ordered_pair @ SV303 @ SV320 ) ) )
= $true )
| ( ( SV174 = SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1616,plain,
! [SV175: $i,SV98: $i,SV354: $i] :
( ( ( ~ ( element @ SV354 @ ( powerset @ SV98 ) )
| ~ ( disjoint @ SV175 @ SV354 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SV354 ) ) )
= $true )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1617,plain,
! [SV175: $i,SV98: $i,SV355: $i] :
( ( ( ~ ( element @ SV355 @ ( powerset @ SV98 ) )
| ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SV355 ) )
| ( disjoint @ SV175 @ SV355 ) )
= $true )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1618,plain,
! [SV99: $i,SV321: $i] :
( ( ( ~ ( relation @ SV321 ) )
= $true )
| ( ( ~ ( subset @ SV99 @ SV321 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SV321 ) ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1619,plain,
! [SV99: $i,SV322: $i] :
( ( ( ~ ( relation @ SV322 ) )
= $true )
| ( ( ~ ( subset @ SV99 @ SV322 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SV322 ) ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1620,plain,
! [SV100: $i,SV323: $i] :
( ( ( ~ ( relation @ SV323 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) ) )
| ( SV323
= ( relation_inverse @ SV100 ) ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1621,plain,
! [SV100: $i,SV324: $i] :
( ( ( ~ ( relation @ SV324 ) )
= $true )
| ( ( ( SV324
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY744: $i,SY745: $i] :
( ~ ( in @ ( ordered_pair @ SY744 @ SY745 ) @ SV324 )
| ( in @ ( ordered_pair @ SY745 @ SY744 ) @ SV100 ) )
| ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ ( ordered_pair @ SY747 @ SY746 ) @ SV100 )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV324 ) ) ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1622,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ~ ( ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) ) )
= $false )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1623,plain,
! [SV276: $i,SV101: $i,SV305: $i] :
( ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false )
| ( ( ~ ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV101 )
| ~ ( in @ SY726 @ SV276 )
| ( in @ SY726 @ SV305 ) )
| ~ ~ ( ~ ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1624,plain,
! [SV277: $i,SV102: $i,SV306: $i] :
( ( ( relation @ SV306 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV277 ) @ SV306 )
| ( in @ SV102 @ ( relation_field @ SV306 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1625,plain,
! [SV278: $i,SV102: $i,SV307: $i] :
( ( ( relation @ SV307 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV278 ) @ SV307 )
| ( in @ SV278 @ ( relation_field @ SV307 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1626,plain,
! [SV103: $i,SV279: $i] :
( ( ( subset @ SV279 @ ( sK8_B @ SV103 ) )
= $false )
| ( ( are_equipotent @ SV279 @ ( sK8_B @ SV103 ) )
= $true )
| ( ( in @ SV279 @ ( sK8_B @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1627,plain,
! [SV103: $i,SV356: $i] :
( ( ~ ( ~ ! [SY774: $i] :
( ~ ( subset @ SY774 @ SV356 )
| ( in @ SY774 @ ( sK9_SY344 @ SV356 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SV356 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1628,plain,
! [SV103: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1629,plain,
! [SV280: $i,SV225: $i] :
( ( ( subset @ SV225 @ SV280 )
= $false )
| ( ( ~ ( subset @ SV280 @ SV225 ) )
= $true )
| ( ( SV225 = SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1630,plain,
! [SV357: $i,SV325: $i] :
( ( ( SV325 != SV357 )
| ( subset @ SV325 @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1631,plain,
! [SV358: $i,SV326: $i] :
( ( ( SV326 != SV358 )
| ( subset @ SV358 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1632,plain,
! [SV283: $i,SV228: $i] :
( ( ( SV228 = empty_set )
= $true )
| ( ( SV228
= ( singleton @ SV283 ) )
= $true )
| ( ( subset @ SV228 @ ( singleton @ SV283 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1633,plain,
! [SV327: $i] :
( ( ( ( SV327 != empty_set ) )
= $true )
| ( ( ! [SY750: $i] : ( subset @ SV327 @ ( singleton @ SY750 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1634,plain,
! [SV359: $i,SV328: $i] :
( ( ( SV328
!= ( singleton @ SV359 ) )
| ( subset @ SV328 @ ( singleton @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1635,plain,
! [SV329: $i,SV176: $i,SV308: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV308 )
| ~ ( in @ SV176 @ SV329 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV308 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1636,plain,
! [SV176: $i,SV104: $i] :
( ( ! [SY604: $i] :
( ! [SY605: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY604 @ SY605 ) )
| ( in @ SV104 @ SY604 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1637,plain,
! [SV176: $i,SV104: $i] :
( ( ! [SY606: $i,SY607: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SY606 @ SY607 ) )
| ( in @ SV176 @ SY607 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1638,plain,
! [SV309: $i,SV284: $i,SV105: $i] :
( ( ( ~ ( ! [SY730: $i,SY731: $i] :
( ~ ( in @ SY730 @ SV105 )
| ~ ( in @ SY731 @ SV284 )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SY730 @ SY731 ) ) )
| ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) ) )
= $false )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1639,plain,
! [SV285: $i,SV105: $i,SV310: $i] :
( ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false )
| ( ( ~ ( ~ ! [SY732: $i] :
( ! [SY708: $i,SY709: $i] :
( ~ ( in @ SY708 @ SV105 )
| ~ ( in @ SY709 @ SV285 )
| ( SY732
!= ( ordered_pair @ SY708 @ SY709 ) ) )
| ( in @ SY732 @ SV310 ) )
| ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV310 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SY735
!= ( ordered_pair @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1640,plain,
! [SV286: $i,SV229: $i] :
( ( ( SV229 = empty_set )
= $true )
| ( ( SV229
= ( singleton @ SV286 ) )
= $true )
| ( ( subset @ SV229 @ ( singleton @ SV286 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1641,plain,
! [SV330: $i] :
( ( ( ( SV330 != empty_set ) )
= $true )
| ( ( ! [SY752: $i] : ( subset @ SV330 @ ( singleton @ SY752 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1642,plain,
! [SV360: $i,SV331: $i] :
( ( ( SV331
!= ( singleton @ SV360 ) )
| ( subset @ SV331 @ ( singleton @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1643,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) ) )
| ~ ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV106 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV287 ) ) )
= $false )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1644,plain,
! [SV288: $i,SV106: $i,SV312: $i] :
( ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false )
| ( ( ~ ( ~ ! [SY736: $i] :
( ~ ( in @ SY736 @ SV312 )
| ( SY736 = SV106 )
| ( SY736 = SV288 ) )
| ~ ~ ( ~ ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) )
| ~ ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1645,plain,
! [SV230: $i,SV289: $i] :
( ( ( in @ SV289 @ SV230 )
= $false )
| ( ( ( set_difference @ SV230 @ ( singleton @ SV289 ) )
= SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1646,plain,
! [SV332: $i,SV177: $i,SV313: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV313 )
| ~ ( in @ SV177 @ SV332 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV313 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1647,plain,
! [SV177: $i,SV107: $i] :
( ( ! [SY610: $i] :
( ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY610 @ SY611 ) )
| ( in @ SV107 @ SY610 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1648,plain,
! [SV177: $i,SV107: $i] :
( ( ! [SY612: $i,SY613: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SY612 @ SY613 ) )
| ( in @ SV177 @ SY613 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1649,plain,
! [SV235: $i,SV333: $i] :
( ( ( in @ SV333 @ SV235 )
= $false )
| ( ( SV235 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1650,plain,
! [SV109: $i,SV334: $i] :
( ( ( ~ ( ~ ( ! [SY754: $i] :
~ ( in @ ( ordered_pair @ SY754 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SV334 @ SV109 ) @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) ) ) )
= $true )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1651,plain,
! [SV109: $i,SV335: $i] :
( ( ( ( SV335
!= ( relation_rng @ SV109 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY755: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY755 ) @ SV109 )
| ( in @ SY755 @ SV335 ) )
| ~ ! [SY757: $i] :
( ~ ( in @ SY757 @ SV335 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY757 @ SV335 @ SV109 ) @ SY757 ) @ SV109 ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1652,plain,
! [SV291: $i,SV110: $i,SV314: $i] :
( ( ( relation @ SV314 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV110 @ SV291 ) @ SV314 )
| ( in @ SV110 @ ( relation_dom @ SV314 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1653,plain,
! [SV292: $i,SV110: $i,SV315: $i] :
( ( ( relation @ SV315 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV110 @ SV292 ) @ SV315 )
| ( in @ SV292 @ ( relation_rng @ SV315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1654,plain,
! [SV336: $i] :
( ( ( SV336 = empty_set )
= $true )
| ( ( ! [SY758: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SY758 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SY758 @ SV336 ) @ ( sK43_SY367 @ SY758 @ SV336 ) ) )
| ~ ( in @ ( sK42_C @ SY758 @ SV336 ) @ SY758 ) )
| ~ ( ! [SY759: $i] :
( ~ ( in @ SY759 @ SV336 )
| ( in @ ( sK42_C @ SY758 @ SV336 ) @ SY759 ) )
| ( in @ ( sK42_C @ SY758 @ SV336 ) @ SY758 ) ) )
| ( SY758
= ( set_meet @ SV336 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1655,plain,
! [SV337: $i] :
( ( ( SV337 = empty_set )
= $true )
| ( ( ! [SY760: $i] :
( ( SY760
!= ( set_meet @ SV337 ) )
| ~ ( ~ ! [SY761: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SY761 @ SY760 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SY761 @ ( sK41_D @ SY761 @ SY760 @ SV337 ) ) )
| ( in @ SY761 @ SY760 ) )
| ~ ! [SY762: $i] :
( ~ ( in @ SY762 @ SY760 )
| ! [SY763: $i] :
( ~ ( in @ SY763 @ SV337 )
| ( in @ SY762 @ SY763 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1656,plain,
! [SV338: $i] :
( ( ( ( SV338 != empty_set ) )
= $true )
| ( ( ! [SY764: $i] :
( ( SY764
!= ( set_meet @ SV338 ) )
| ( SY764 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1657,plain,
! [SV339: $i] :
( ( ( ( SV339 != empty_set ) )
= $true )
| ( ( ! [SY765: $i] :
( ( SY765 != empty_set )
| ( SY765
= ( set_meet @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1658,plain,
! [SV295: $i,SV238: $i] :
( ( ( subset @ SV238 @ SV295 )
= $false )
| ( ( SV238 = SV295 )
= $true )
| ( ( proper_subset @ SV238 @ SV295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1659,plain,
! [SV361: $i,SV340: $i] :
( ( ~ ( proper_subset @ SV340 @ SV361 )
| ( SV340 != SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1660,plain,
! [SV362: $i,SV341: $i] :
( ( ~ ( proper_subset @ SV341 @ SV362 )
| ( subset @ SV341 @ SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1661,plain,
! [SV111: $i,SV178: $i] :
( ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
= $false )
| ( ( ~ ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 ) )
= $true )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1662,plain,
! [SV239: $i] :
( ( ( ! [SY669: $i,SY670: $i] :
( ( sK46_B @ SV239 )
!= ( ordered_pair @ SY669 @ SY670 ) ) )
= $true )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1663,plain,
! [SV239: $i] :
( ( ( in @ ( sK46_B @ SV239 ) @ SV239 )
= $true )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1664,plain,
! [SV240: $i,SV342: $i] :
( ( ( SV342
= ( ordered_pair @ ( sK44_C @ SV342 @ SV240 ) @ ( sK45_SY369 @ SV342 @ SV240 ) ) )
= $true )
| ( ( ~ ( in @ SV342 @ SV240 ) )
= $true )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1665,plain,
! [SV343: $i] :
( ( ( empty @ SV343 )
= $true )
| ( ( ! [SY768: $i] :
( ~ ( element @ SY768 @ SV343 )
| ( in @ SY768 @ SV343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1666,plain,
! [SV344: $i] :
( ( ( empty @ SV344 )
= $true )
| ( ( ! [SY769: $i] :
( ~ ( in @ SY769 @ SV344 )
| ( element @ SY769 @ SV344 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1667,plain,
! [SV345: $i] :
( ( ( ~ ( empty @ SV345 ) )
= $true )
| ( ( ! [SY770: $i] :
( ~ ( element @ SY770 @ SV345 )
| ( empty @ SY770 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1574]) ).
thf(1668,plain,
! [SV346: $i] :
( ( ( ~ ( empty @ SV346 ) )
= $true )
| ( ( ! [SY771: $i] :
( ~ ( empty @ SY771 )
| ( element @ SY771 @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1669,plain,
! [SV49: $i,SV185: $i,SV296: $i] :
( ( ( in @ SV296 @ SV185 )
= $true )
| ( ( in @ SV296 @ ( subset_complement @ SV49 @ SV185 ) )
= $true )
| ( ( element @ SV296 @ SV49 )
= $false )
| ( ( element @ SV185 @ ( powerset @ SV49 ) )
= $false )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1670,plain,
! [SV202: $i,SV245: $i] :
( ( ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV202 )
= $true )
| ( ( subset @ SV202 @ SV245 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1671,plain,
! [SV202: $i,SV245: $i] :
( ( ( ~ ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV245 ) )
= $true )
| ( ( subset @ SV202 @ SV245 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1672,plain,
! [SV246: $i,SV203: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ SV203 ) )
= $true )
| ( ( in @ SV347 @ SV246 )
= $true )
| ( ( subset @ SV203 @ SV246 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1673,plain,
! [SV316: $i,SV248: $i,SV205: $i] :
( ( ( disjoint @ SV205 @ SV248 )
= $false )
| ( ( in @ SV316 @ ( set_intersection2 @ SV205 @ SV248 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1674,plain,
! [SV206: $i,SV249: $i] :
( ( ( ( ( sK40_C @ SV249 @ SV206 )
!= SV206 )
| ~ ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) )
= $true )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1675,plain,
! [SV206: $i,SV249: $i] :
( ( ( ( ( sK40_C @ SV249 @ SV206 )
= SV206 )
| ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) )
= $true )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1676,plain,
! [SV250: $i,SV207: $i] :
( ( ( ~ ! [SY674: $i] :
( ( SY674 != SV207 )
| ( in @ SY674 @ SV250 ) ) )
= $false )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1677,plain,
! [SV207: $i,SV250: $i] :
( ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV250 )
| ( SY675 = SV207 ) ) )
= $false )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1678,plain,
! [SV90: $i,SV317: $i] :
( ( ( ~ ( ! [SY740: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SY740 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ ( sK28_SY360 @ SV317 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) ) )
= $false )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1679,plain,
! [SV90: $i,SV318: $i] :
( ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( ~ ( ~ ! [SY741: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY741 @ SY463 ) @ SV90 )
| ( in @ SY741 @ SV318 ) )
| ~ ! [SY743: $i] :
( ~ ( in @ SY743 @ SV318 )
| ( in @ ( ordered_pair @ SY743 @ ( sK26_D @ SY743 @ SV318 @ SV90 ) ) @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1680,plain,
! [SV208: $i,SV251: $i] :
( ( ( ! [SY676: $i] :
( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SY676 )
| ~ ( in @ SY676 @ SV208 ) )
| ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1681,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) )
| ~ ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 ) )
| ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1682,plain,
! [SV252: $i,SV209: $i] :
( ( ( ~ ! [SY677: $i] :
( ! [SY631: $i] :
( ~ ( in @ SY677 @ SY631 )
| ~ ( in @ SY631 @ SV209 ) )
| ( in @ SY677 @ SV252 ) ) )
= $false )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1683,plain,
! [SV209: $i,SV252: $i] :
( ( ( ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV252 )
| ~ ( ~ ( in @ SY679 @ ( sK23_D @ SY679 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SY679 @ SV252 @ SV209 ) @ SV209 ) ) ) )
= $false )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1684,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) ) )
= $false )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1685,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) )
= $false )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1686,plain,
! [SV254: $i,SV91: $i,SV298: $i] :
( ( ( ~ ! [SY718: $i] :
( ~ ( in @ SY718 @ SV298 )
| ( in @ SY718 @ SV91 )
| ( in @ SY718 @ SV254 ) )
| ~ ~ ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) )
| ~ ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) ) )
= $false )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1687,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) )
= $false )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1688,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) ) )
= $false )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1689,plain,
! [SV300: $i,SV256: $i,SV92: $i] :
( ( ( ~ ! [SY721: $i] :
( ~ ( in @ SY721 @ SV92 )
| ( in @ SY721 @ SV256 )
| ( in @ SY721 @ SV300 ) )
| ~ ~ ( ~ ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) ) )
= $false )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1690,plain,
! [SV257: $i,SV301: $i,SV93: $i] :
( ( ( in @ SV93 @ SV301 )
= $false )
| ( ( ~ ( in @ SV257 @ SV301 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV93 @ SV257 ) @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1691,plain,
! [SV363: $i,SV348: $i,SV93: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV93 @ SV348 ) @ SV363 )
| ( in @ SV93 @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1692,plain,
! [SV364: $i,SV349: $i,SV93: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV93 @ SV349 ) @ SV364 )
| ( in @ SV349 @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1693,plain,
! [SV95: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ ( sK7_B @ SV95 ) ) )
= $true )
| ( ( in @ ( powerset @ SV352 ) @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1694,plain,
! [SV95: $i] :
( ( ~ ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1695,plain,
! [SV95: $i] :
( ( ~ ( in @ SV95 @ ( sK7_B @ SV95 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1696,plain,
! [SV96: $i,SV216: $i] :
( ( ( ! [SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ! [SY640: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ SY640 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY640 @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY639 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SY639 @ SV216 @ SV96 ) ) @ SY639 ) ) )
| ( SY639
= ( relation_composition @ SV96 @ SV216 ) ) ) )
= $true )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1697,plain,
! [SV216: $i,SV96: $i] :
( ( ( ! [SY641: $i] :
( ~ ( relation @ SY641 )
| ( SY641
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY642 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY643 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY641 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ( in @ ( ordered_pair @ SY645 @ SY646 ) @ SY641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY645 @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY646 @ SY645 @ SY641 @ SV216 @ SV96 ) @ SY646 ) @ SV216 ) ) ) ) ) )
= $true )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1698,plain,
! [SV221: $i,SV271: $i] :
( ( ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV221 )
= $true )
| ( ( disjoint @ SV221 @ SV271 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1699,plain,
! [SV221: $i,SV271: $i] :
( ( ( in @ ( sK48_C @ SV271 @ SV221 ) @ SV271 )
= $true )
| ( ( disjoint @ SV221 @ SV271 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1700,plain,
! [SV272: $i,SV222: $i,SV319: $i] :
( ( ( in @ SV319 @ SV222 )
= $false )
| ( ( ~ ( in @ SV319 @ SV272 ) )
= $true )
| ( ( ~ ( disjoint @ SV222 @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1701,plain,
! [SV223: $i,SV273: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ~ ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) )
= $true )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1702,plain,
! [SV223: $i,SV273: $i] :
( ( ( ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
| ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) )
= $true )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1703,plain,
! [SV224: $i,SV274: $i] :
( ( ( ~ ! [SY694: $i] :
( ~ ( in @ SY694 @ SV274 )
| ( subset @ SY694 @ SV224 ) ) )
= $false )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1704,plain,
! [SV274: $i,SV224: $i] :
( ( ( ~ ! [SY695: $i] :
( ~ ( subset @ SY695 @ SV224 )
| ( in @ SY695 @ SV274 ) ) )
= $false )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1705,plain,
! [SV353: $i,SV302: $i,SV174: $i,SV97: $i] :
( ( ( ( ordered_pair @ SV97 @ SV174 )
= ( ordered_pair @ SV302 @ SV353 ) )
= $false )
| ( ( SV97 = SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1706,plain,
! [SV320: $i,SV303: $i,SV174: $i,SV97: $i] :
( ( ( ( ordered_pair @ SV97 @ SV174 )
= ( ordered_pair @ SV303 @ SV320 ) )
= $false )
| ( ( SV174 = SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1707,plain,
! [SV175: $i,SV98: $i,SV354: $i] :
( ( ( ~ ( element @ SV354 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV175 @ SV354 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SV354 ) ) )
= $true )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1708,plain,
! [SV175: $i,SV98: $i,SV355: $i] :
( ( ( ~ ( element @ SV355 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SV355 ) )
| ( disjoint @ SV175 @ SV355 ) )
= $true )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1709,plain,
! [SV99: $i,SV321: $i] :
( ( ( relation @ SV321 )
= $false )
| ( ( ~ ( subset @ SV99 @ SV321 )
| ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SV321 ) ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1710,plain,
! [SV99: $i,SV322: $i] :
( ( ( relation @ SV322 )
= $false )
| ( ( ~ ( subset @ SV99 @ SV322 )
| ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SV322 ) ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1711,plain,
! [SV100: $i,SV323: $i] :
( ( ( relation @ SV323 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) ) )
| ( SV323
= ( relation_inverse @ SV100 ) ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1712,plain,
! [SV100: $i,SV324: $i] :
( ( ( relation @ SV324 )
= $false )
| ( ( ( SV324
!= ( relation_inverse @ SV100 ) )
| ~ ( ~ ! [SY744: $i,SY745: $i] :
( ~ ( in @ ( ordered_pair @ SY744 @ SY745 ) @ SV324 )
| ( in @ ( ordered_pair @ SY745 @ SY744 ) @ SV100 ) )
| ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ ( ordered_pair @ SY747 @ SY746 ) @ SV100 )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV324 ) ) ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1713,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) )
= $false )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1714,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) ) )
= $false )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1715,plain,
! [SV305: $i,SV276: $i,SV101: $i] :
( ( ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV101 )
| ~ ( in @ SY726 @ SV276 )
| ( in @ SY726 @ SV305 ) )
| ~ ~ ( ~ ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) ) )
= $false )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1716,plain,
! [SV306: $i,SV277: $i,SV102: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV277 ) @ SV306 ) )
= $true )
| ( ( in @ SV102 @ ( relation_field @ SV306 ) )
= $true )
| ( ( relation @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1717,plain,
! [SV307: $i,SV278: $i,SV102: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV278 ) @ SV307 ) )
= $true )
| ( ( in @ SV278 @ ( relation_field @ SV307 ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1718,plain,
! [SV103: $i,SV356: $i] :
( ( ( ~ ( ~ ! [SY774: $i] :
( ~ ( subset @ SY774 @ SV356 )
| ( in @ SY774 @ ( sK9_SY344 @ SV356 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SV356 @ SV103 ) @ ( sK8_B @ SV103 ) ) ) )
= $true )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1719,plain,
! [SV103: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1720,plain,
! [SV103: $i] :
( ( ~ ( in @ SV103 @ ( sK8_B @ SV103 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1721,plain,
! [SV225: $i,SV280: $i] :
( ( ( subset @ SV280 @ SV225 )
= $false )
| ( ( subset @ SV225 @ SV280 )
= $false )
| ( ( SV225 = SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1722,plain,
! [SV357: $i,SV325: $i] :
( ( ( ( SV325 != SV357 ) )
= $true )
| ( ( subset @ SV325 @ SV357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1723,plain,
! [SV358: $i,SV326: $i] :
( ( ( ( SV326 != SV358 ) )
= $true )
| ( ( subset @ SV358 @ SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1724,plain,
! [SV327: $i] :
( ( ( SV327 = empty_set )
= $false )
| ( ( ! [SY750: $i] : ( subset @ SV327 @ ( singleton @ SY750 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1725,plain,
! [SV359: $i,SV328: $i] :
( ( ( ( SV328
!= ( singleton @ SV359 ) ) )
= $true )
| ( ( subset @ SV328 @ ( singleton @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1726,plain,
! [SV329: $i,SV176: $i,SV308: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV308 ) )
= $true )
| ( ( ~ ( in @ SV176 @ SV329 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV308 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1727,plain,
! [SV365: $i,SV176: $i,SV104: $i] :
( ( ! [SY775: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV365 @ SY775 ) )
| ( in @ SV104 @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1728,plain,
! [SV366: $i,SV176: $i,SV104: $i] :
( ( ! [SY776: $i] :
( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV366 @ SY776 ) )
| ( in @ SV176 @ SY776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1729,plain,
! [SV309: $i,SV284: $i,SV105: $i] :
( ( ( ~ ( ! [SY730: $i,SY731: $i] :
( ~ ( in @ SY730 @ SV105 )
| ~ ( in @ SY731 @ SV284 )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SY730 @ SY731 ) ) )
| ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) ) )
= $false )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1730,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) ) )
= $false )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1731,plain,
! [SV310: $i,SV285: $i,SV105: $i] :
( ( ( ~ ! [SY732: $i] :
( ! [SY708: $i,SY709: $i] :
( ~ ( in @ SY708 @ SV105 )
| ~ ( in @ SY709 @ SV285 )
| ( SY732
!= ( ordered_pair @ SY708 @ SY709 ) ) )
| ( in @ SY732 @ SV310 ) )
| ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV310 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SY735
!= ( ordered_pair @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) ) ) ) ) )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1732,plain,
! [SV330: $i] :
( ( ( SV330 = empty_set )
= $false )
| ( ( ! [SY752: $i] : ( subset @ SV330 @ ( singleton @ SY752 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1733,plain,
! [SV360: $i,SV331: $i] :
( ( ( ( SV331
!= ( singleton @ SV360 ) ) )
= $true )
| ( ( subset @ SV331 @ ( singleton @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1734,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) ) ) )
= $false )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1643]) ).
thf(1735,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV106 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV287 ) ) )
= $false )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1643]) ).
thf(1736,plain,
! [SV288: $i,SV106: $i,SV312: $i] :
( ( ( ~ ! [SY736: $i] :
( ~ ( in @ SY736 @ SV312 )
| ( SY736 = SV106 )
| ( SY736 = SV288 ) )
| ~ ~ ( ~ ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) )
| ~ ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) ) )
= $false )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1737,plain,
! [SV332: $i,SV177: $i,SV313: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV313 ) )
= $true )
| ( ( ~ ( in @ SV177 @ SV332 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV313 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1738,plain,
! [SV367: $i,SV177: $i,SV107: $i] :
( ( ! [SY777: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV367 @ SY777 ) )
| ( in @ SV107 @ SV367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1739,plain,
! [SV368: $i,SV177: $i,SV107: $i] :
( ( ! [SY778: $i] :
( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV368 @ SY778 ) )
| ( in @ SV177 @ SY778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1740,plain,
! [SV109: $i,SV334: $i] :
( ( ( ~ ( ! [SY754: $i] :
~ ( in @ ( ordered_pair @ SY754 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SV334 @ SV109 ) @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) ) )
= $false )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1650]) ).
thf(1741,plain,
! [SV109: $i,SV335: $i] :
( ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( ~ ( ~ ! [SY755: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY755 ) @ SV109 )
| ( in @ SY755 @ SV335 ) )
| ~ ! [SY757: $i] :
( ~ ( in @ SY757 @ SV335 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY757 @ SV335 @ SV109 ) @ SY757 ) @ SV109 ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1742,plain,
! [SV314: $i,SV291: $i,SV110: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV110 @ SV291 ) @ SV314 ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV314 ) )
= $true )
| ( ( relation @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1743,plain,
! [SV315: $i,SV292: $i,SV110: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV110 @ SV292 ) @ SV315 ) )
= $true )
| ( ( in @ SV292 @ ( relation_rng @ SV315 ) )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1744,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) )
| ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
| ~ ( ! [SY779: $i] :
( ~ ( in @ SY779 @ SV336 )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SY779 ) )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) ) )
| ( SV369
= ( set_meet @ SV336 ) ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1745,plain,
! [SV337: $i,SV370: $i] :
( ( ( ( SV370
!= ( set_meet @ SV337 ) )
| ~ ( ~ ! [SY780: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SY780 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SY780 @ ( sK41_D @ SY780 @ SV370 @ SV337 ) ) )
| ( in @ SY780 @ SV370 ) )
| ~ ! [SY781: $i] :
( ~ ( in @ SY781 @ SV370 )
| ! [SY763: $i] :
( ~ ( in @ SY763 @ SV337 )
| ( in @ SY781 @ SY763 ) ) ) ) )
= $true )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1746,plain,
! [SV338: $i] :
( ( ( SV338 = empty_set )
= $false )
| ( ( ! [SY764: $i] :
( ( SY764
!= ( set_meet @ SV338 ) )
| ( SY764 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1747,plain,
! [SV339: $i] :
( ( ( SV339 = empty_set )
= $false )
| ( ( ! [SY765: $i] :
( ( SY765 != empty_set )
| ( SY765
= ( set_meet @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1748,plain,
! [SV361: $i,SV340: $i] :
( ( ( ~ ( proper_subset @ SV340 @ SV361 ) )
= $true )
| ( ( ( SV340 != SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1749,plain,
! [SV362: $i,SV341: $i] :
( ( ( ~ ( proper_subset @ SV341 @ SV362 ) )
= $true )
| ( ( subset @ SV341 @ SV362 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1750,plain,
! [SV111: $i,SV178: $i] :
( ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV178 )
= $false )
| ( ( in @ ( sK10_C @ SV178 @ SV111 ) @ SV111 )
= $false )
| ( ( SV111 = SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1751,plain,
! [SV371: $i,SV239: $i] :
( ( ( ! [SY783: $i] :
( ( sK46_B @ SV239 )
!= ( ordered_pair @ SV371 @ SY783 ) ) )
= $true )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1752,plain,
! [SV240: $i,SV342: $i] :
( ( ( in @ SV342 @ SV240 )
= $false )
| ( ( SV342
= ( ordered_pair @ ( sK44_C @ SV342 @ SV240 ) @ ( sK45_SY369 @ SV342 @ SV240 ) ) )
= $true )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1753,plain,
! [SV343: $i,SV372: $i] :
( ( ( ~ ( element @ SV372 @ SV343 )
| ( in @ SV372 @ SV343 ) )
= $true )
| ( ( empty @ SV343 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1754,plain,
! [SV344: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV344 )
| ( element @ SV373 @ SV344 ) )
= $true )
| ( ( empty @ SV344 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1755,plain,
! [SV345: $i] :
( ( ( empty @ SV345 )
= $false )
| ( ( ! [SY770: $i] :
( ~ ( element @ SY770 @ SV345 )
| ( empty @ SY770 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1756,plain,
! [SV346: $i] :
( ( ( empty @ SV346 )
= $false )
| ( ( ! [SY771: $i] :
( ~ ( empty @ SY771 )
| ( element @ SY771 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1757,plain,
! [SV202: $i,SV245: $i] :
( ( ( in @ ( sK30_C @ SV245 @ SV202 ) @ SV245 )
= $false )
| ( ( subset @ SV202 @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1758,plain,
! [SV246: $i,SV203: $i,SV347: $i] :
( ( ( in @ SV347 @ SV203 )
= $false )
| ( ( in @ SV347 @ SV246 )
= $true )
| ( ( subset @ SV203 @ SV246 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1759,plain,
! [SV206: $i,SV249: $i] :
( ( ( ( ( sK40_C @ SV249 @ SV206 )
!= SV206 ) )
= $true )
| ( ( ~ ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) )
= $true )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1760,plain,
! [SV206: $i,SV249: $i] :
( ( ( ( sK40_C @ SV249 @ SV206 )
= SV206 )
= $true )
| ( ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 )
= $true )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1761,plain,
! [SV250: $i,SV207: $i] :
( ( ( ! [SY674: $i] :
( ( SY674 != SV207 )
| ( in @ SY674 @ SV250 ) ) )
= $true )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1762,plain,
! [SV207: $i,SV250: $i] :
( ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV250 )
| ( SY675 = SV207 ) ) )
= $true )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1763,plain,
! [SV90: $i,SV317: $i] :
( ( ( ~ ( ! [SY740: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SY740 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) ) )
= $false )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1678]) ).
thf(1764,plain,
! [SV90: $i,SV317: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ ( sK28_SY360 @ SV317 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) ) )
= $false )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1678]) ).
thf(1765,plain,
! [SV318: $i,SV90: $i] :
( ( ( ~ ! [SY741: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY741 @ SY463 ) @ SV90 )
| ( in @ SY741 @ SV318 ) )
| ~ ! [SY743: $i] :
( ~ ( in @ SY743 @ SV318 )
| ( in @ ( ordered_pair @ SY743 @ ( sK26_D @ SY743 @ SV318 @ SV90 ) ) @ SV90 ) ) )
= $false )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1766,plain,
! [SV208: $i,SV251: $i] :
( ( ( ! [SY676: $i] :
( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SY676 )
| ~ ( in @ SY676 @ SV208 ) ) )
= $true )
| ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1767,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) )
| ~ ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 ) ) )
= $true )
| ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1768,plain,
! [SV252: $i,SV209: $i] :
( ( ( ! [SY677: $i] :
( ! [SY631: $i] :
( ~ ( in @ SY677 @ SY631 )
| ~ ( in @ SY631 @ SV209 ) )
| ( in @ SY677 @ SV252 ) ) )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1769,plain,
! [SV209: $i,SV252: $i] :
( ( ( ! [SY679: $i] :
( ~ ( in @ SY679 @ SV252 )
| ~ ( ~ ( in @ SY679 @ ( sK23_D @ SY679 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SY679 @ SV252 @ SV209 ) @ SV209 ) ) ) )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1683]) ).
thf(1770,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1771,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1685]) ).
thf(1772,plain,
! [SV254: $i,SV91: $i,SV298: $i] :
( ( ( ~ ! [SY718: $i] :
( ~ ( in @ SY718 @ SV298 )
| ( in @ SY718 @ SV91 )
| ( in @ SY718 @ SV254 ) ) )
= $false )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1773,plain,
! [SV254: $i,SV298: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) )
| ~ ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) ) )
= $false )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1774,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1775,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) ) )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1776,plain,
! [SV300: $i,SV256: $i,SV92: $i] :
( ( ( ~ ! [SY721: $i] :
( ~ ( in @ SY721 @ SV92 )
| ( in @ SY721 @ SV256 )
| ( in @ SY721 @ SV300 ) ) )
= $false )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1777,plain,
! [SV256: $i,SV92: $i,SV300: $i] :
( ( ( ~ ~ ( ~ ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) ) )
= $false )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1778,plain,
! [SV93: $i,SV301: $i,SV257: $i] :
( ( ( in @ SV257 @ SV301 )
= $false )
| ( ( in @ SV93 @ SV301 )
= $false )
| ( ( subset @ ( unordered_pair @ SV93 @ SV257 ) @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1779,plain,
! [SV363: $i,SV348: $i,SV93: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV93 @ SV348 ) @ SV363 ) )
= $true )
| ( ( in @ SV93 @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1780,plain,
! [SV364: $i,SV349: $i,SV93: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV93 @ SV349 ) @ SV364 ) )
= $true )
| ( ( in @ SV349 @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1781,plain,
! [SV95: $i,SV352: $i] :
( ( ( in @ SV352 @ ( sK7_B @ SV95 ) )
= $false )
| ( ( in @ ( powerset @ SV352 ) @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1782,plain,
! [SV95: $i] :
( ( ! [SY491: $i,SY492: $i] :
( ~ ( in @ SY491 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY492 @ SY491 )
| ( in @ SY492 @ ( sK7_B @ SV95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1783,plain,
! [SV95: $i] :
( ( in @ SV95 @ ( sK7_B @ SV95 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1784,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( relation @ SV374 )
| ~ ( ~ ( ! [SY784: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SY784 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY784 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) ) )
| ( SV374
= ( relation_composition @ SV96 @ SV216 ) ) )
= $true )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(1785,plain,
! [SV216: $i,SV96: $i,SV375: $i] :
( ( ( ~ ( relation @ SV375 )
| ( SV375
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY785: $i,SY786: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY785 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY786 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY785 @ SY786 ) @ SV375 ) )
| ~ ! [SY788: $i,SY789: $i] :
( ~ ( in @ ( ordered_pair @ SY788 @ SY789 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SY788 @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) @ SY789 ) @ SV216 ) ) ) ) )
= $true )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1786,plain,
! [SV222: $i,SV272: $i,SV319: $i] :
( ( ( in @ SV319 @ SV272 )
= $false )
| ( ( in @ SV319 @ SV222 )
= $false )
| ( ( ~ ( disjoint @ SV222 @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1787,plain,
! [SV223: $i,SV273: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 ) )
= $true )
| ( ( ~ ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) )
= $true )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1788,plain,
! [SV223: $i,SV273: $i] :
( ( ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
= $true )
| ( ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 )
= $true )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1789,plain,
! [SV224: $i,SV274: $i] :
( ( ( ! [SY694: $i] :
( ~ ( in @ SY694 @ SV274 )
| ( subset @ SY694 @ SV224 ) ) )
= $true )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1790,plain,
! [SV274: $i,SV224: $i] :
( ( ( ! [SY695: $i] :
( ~ ( subset @ SY695 @ SV224 )
| ( in @ SY695 @ SV274 ) ) )
= $true )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1791,plain,
! [SV175: $i,SV98: $i,SV354: $i] :
( ( ( element @ SV354 @ ( powerset @ SV98 ) )
= $false )
| ( ( ~ ( disjoint @ SV175 @ SV354 )
| ( subset @ SV175 @ ( subset_complement @ SV98 @ SV354 ) ) )
= $true )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1792,plain,
! [SV175: $i,SV98: $i,SV355: $i] :
( ( ( element @ SV355 @ ( powerset @ SV98 ) )
= $false )
| ( ( ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SV355 ) )
| ( disjoint @ SV175 @ SV355 ) )
= $true )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1793,plain,
! [SV321: $i,SV99: $i] :
( ( ( ~ ( subset @ SV99 @ SV321 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SV321 ) )
= $true )
| ( ( relation @ SV321 )
= $false )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1794,plain,
! [SV322: $i,SV99: $i] :
( ( ( ~ ( subset @ SV99 @ SV322 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SV322 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1795,plain,
! [SV100: $i,SV323: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) ) ) )
= $true )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1796,plain,
! [SV100: $i,SV324: $i] :
( ( ( ( SV324
!= ( relation_inverse @ SV100 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY744: $i,SY745: $i] :
( ~ ( in @ ( ordered_pair @ SY744 @ SY745 ) @ SV324 )
| ( in @ ( ordered_pair @ SY745 @ SY744 ) @ SV100 ) )
| ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ ( ordered_pair @ SY747 @ SY746 ) @ SV100 )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV324 ) ) ) )
= $true )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(1797,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1798,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1799,plain,
! [SV305: $i,SV276: $i,SV101: $i] :
( ( ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV101 )
| ~ ( in @ SY726 @ SV276 )
| ( in @ SY726 @ SV305 ) ) )
= $false )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1800,plain,
! [SV276: $i,SV101: $i,SV305: $i] :
( ( ( ~ ~ ( ~ ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) ) )
= $false )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1801,plain,
! [SV306: $i,SV277: $i,SV102: $i] :
( ( ( in @ ( ordered_pair @ SV102 @ SV277 ) @ SV306 )
= $false )
| ( ( in @ SV102 @ ( relation_field @ SV306 ) )
= $true )
| ( ( relation @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1802,plain,
! [SV307: $i,SV278: $i,SV102: $i] :
( ( ( in @ ( ordered_pair @ SV102 @ SV278 ) @ SV307 )
= $false )
| ( ( in @ SV278 @ ( relation_field @ SV307 ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1803,plain,
! [SV103: $i,SV356: $i] :
( ( ( ~ ! [SY774: $i] :
( ~ ( subset @ SY774 @ SV356 )
| ( in @ SY774 @ ( sK9_SY344 @ SV356 @ SV103 ) ) )
| ~ ( in @ ( sK9_SY344 @ SV356 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
= $false )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1804,plain,
! [SV103: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY533 @ SY532 )
| ( in @ SY533 @ ( sK8_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1805,plain,
! [SV103: $i] :
( ( in @ SV103 @ ( sK8_B @ SV103 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1806,plain,
! [SV357: $i,SV325: $i] :
( ( ( SV325 = SV357 )
= $false )
| ( ( subset @ SV325 @ SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1807,plain,
! [SV358: $i,SV326: $i] :
( ( ( SV326 = SV358 )
= $false )
| ( ( subset @ SV358 @ SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1808,plain,
! [SV376: $i,SV327: $i] :
( ( ( subset @ SV327 @ ( singleton @ SV376 ) )
= $true )
| ( ( SV327 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(1809,plain,
! [SV359: $i,SV328: $i] :
( ( ( SV328
= ( singleton @ SV359 ) )
= $false )
| ( ( subset @ SV328 @ ( singleton @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1810,plain,
! [SV329: $i,SV176: $i,SV308: $i,SV104: $i] :
( ( ( in @ SV104 @ SV308 )
= $false )
| ( ( ~ ( in @ SV176 @ SV329 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV308 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1811,plain,
! [SV365: $i,SV176: $i,SV104: $i] :
( ( ( ! [SY775: $i] :
~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV365 @ SY775 ) ) )
= $true )
| ( ( in @ SV104 @ SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1812,plain,
! [SV377: $i,SV366: $i,SV176: $i,SV104: $i] :
( ( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV366 @ SV377 ) )
| ( in @ SV176 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(1813,plain,
! [SV309: $i,SV284: $i,SV105: $i] :
( ( ( ! [SY730: $i,SY731: $i] :
( ~ ( in @ SY730 @ SV105 )
| ~ ( in @ SY731 @ SV284 )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SY730 @ SY731 ) ) )
| ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1814,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) ) )
| ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1815,plain,
! [SV310: $i,SV285: $i,SV105: $i] :
( ( ( ~ ! [SY732: $i] :
( ! [SY708: $i,SY709: $i] :
( ~ ( in @ SY708 @ SV105 )
| ~ ( in @ SY709 @ SV285 )
| ( SY732
!= ( ordered_pair @ SY708 @ SY709 ) ) )
| ( in @ SY732 @ SV310 ) ) )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1816,plain,
! [SV105: $i,SV285: $i,SV310: $i] :
( ( ( ~ ! [SY735: $i] :
( ~ ( in @ SY735 @ SV310 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SY735
!= ( ordered_pair @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) ) ) ) ) )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1817,plain,
! [SV378: $i,SV330: $i] :
( ( ( subset @ SV330 @ ( singleton @ SV378 ) )
= $true )
| ( ( SV330 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(1818,plain,
! [SV360: $i,SV331: $i] :
( ( ( SV331
= ( singleton @ SV360 ) )
= $false )
| ( ( subset @ SV331 @ ( singleton @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1819,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) ) ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1820,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV106 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV287 ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1821,plain,
! [SV288: $i,SV106: $i,SV312: $i] :
( ( ( ~ ! [SY736: $i] :
( ~ ( in @ SY736 @ SV312 )
| ( SY736 = SV106 )
| ( SY736 = SV288 ) ) )
= $false )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1822,plain,
! [SV288: $i,SV312: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) )
| ~ ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) ) )
= $false )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1823,plain,
! [SV332: $i,SV177: $i,SV313: $i,SV107: $i] :
( ( ( in @ SV107 @ SV313 )
= $false )
| ( ( ~ ( in @ SV177 @ SV332 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV313 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1824,plain,
! [SV367: $i,SV177: $i,SV107: $i] :
( ( ( ! [SY777: $i] :
~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV367 @ SY777 ) ) )
= $true )
| ( ( in @ SV107 @ SV367 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1825,plain,
! [SV379: $i,SV368: $i,SV177: $i,SV107: $i] :
( ( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV368 @ SV379 ) )
| ( in @ SV177 @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(1826,plain,
! [SV109: $i,SV334: $i] :
( ( ( ~ ( ! [SY754: $i] :
~ ( in @ ( ordered_pair @ SY754 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) ) )
= $false )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1827,plain,
! [SV109: $i,SV334: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SV334 @ SV109 ) @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) ) )
= $false )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1828,plain,
! [SV335: $i,SV109: $i] :
( ( ( ~ ! [SY755: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY755 ) @ SV109 )
| ( in @ SY755 @ SV335 ) )
| ~ ! [SY757: $i] :
( ~ ( in @ SY757 @ SV335 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY757 @ SV335 @ SV109 ) @ SY757 ) @ SV109 ) ) )
= $false )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1829,plain,
! [SV314: $i,SV291: $i,SV110: $i] :
( ( ( in @ ( ordered_pair @ SV110 @ SV291 ) @ SV314 )
= $false )
| ( ( in @ SV110 @ ( relation_dom @ SV314 ) )
= $true )
| ( ( relation @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1830,plain,
! [SV315: $i,SV292: $i,SV110: $i] :
( ( ( in @ ( ordered_pair @ SV110 @ SV292 ) @ SV315 )
= $false )
| ( ( in @ SV292 @ ( relation_rng @ SV315 ) )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1831,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) )
| ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
| ~ ( ! [SY779: $i] :
( ~ ( in @ SY779 @ SV336 )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SY779 ) )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) ) ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(1832,plain,
! [SV337: $i,SV370: $i] :
( ( ( ( SV370
!= ( set_meet @ SV337 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY780: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SY780 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SY780 @ ( sK41_D @ SY780 @ SV370 @ SV337 ) ) )
| ( in @ SY780 @ SV370 ) )
| ~ ! [SY781: $i] :
( ~ ( in @ SY781 @ SV370 )
| ! [SY763: $i] :
( ~ ( in @ SY763 @ SV337 )
| ( in @ SY781 @ SY763 ) ) ) ) )
= $true )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(1833,plain,
! [SV338: $i,SV380: $i] :
( ( ( ( SV380
!= ( set_meet @ SV338 ) )
| ( SV380 = empty_set ) )
= $true )
| ( ( SV338 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(1834,plain,
! [SV339: $i,SV381: $i] :
( ( ( ( SV381 != empty_set )
| ( SV381
= ( set_meet @ SV339 ) ) )
= $true )
| ( ( SV339 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(1835,plain,
! [SV361: $i,SV340: $i] :
( ( ( proper_subset @ SV340 @ SV361 )
= $false )
| ( ( ( SV340 != SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1836,plain,
! [SV362: $i,SV341: $i] :
( ( ( proper_subset @ SV341 @ SV362 )
= $false )
| ( ( subset @ SV341 @ SV362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1837,plain,
! [SV382: $i,SV371: $i,SV239: $i] :
( ( ( ( ( sK46_B @ SV239 )
!= ( ordered_pair @ SV371 @ SV382 ) ) )
= $true )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1838,plain,
! [SV343: $i,SV372: $i] :
( ( ( ~ ( element @ SV372 @ SV343 ) )
= $true )
| ( ( in @ SV372 @ SV343 )
= $true )
| ( ( empty @ SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1839,plain,
! [SV344: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV344 ) )
= $true )
| ( ( element @ SV373 @ SV344 )
= $true )
| ( ( empty @ SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1840,plain,
! [SV345: $i,SV383: $i] :
( ( ( ~ ( element @ SV383 @ SV345 )
| ( empty @ SV383 ) )
= $true )
| ( ( empty @ SV345 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(1841,plain,
! [SV346: $i,SV384: $i] :
( ( ( ~ ( empty @ SV384 )
| ( element @ SV384 @ SV346 ) )
= $true )
| ( ( empty @ SV346 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(1842,plain,
! [SV206: $i,SV249: $i] :
( ( ( ( sK40_C @ SV249 @ SV206 )
= SV206 )
= $false )
| ( ( ~ ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 ) )
= $true )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1843,plain,
! [SV250: $i,SV207: $i,SV385: $i] :
( ( ( ( SV385 != SV207 )
| ( in @ SV385 @ SV250 ) )
= $true )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1844,plain,
! [SV207: $i,SV250: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV250 )
| ( SV386 = SV207 ) )
= $true )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1845,plain,
! [SV90: $i,SV317: $i] :
( ( ( ! [SY740: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SY740 ) @ SV90 )
| ~ ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) )
= $true )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(1846,plain,
! [SV90: $i,SV317: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ ( sK28_SY360 @ SV317 @ SV90 ) ) @ SV90 )
| ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) )
= $true )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1847,plain,
! [SV318: $i,SV90: $i] :
( ( ( ~ ! [SY741: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY741 @ SY463 ) @ SV90 )
| ( in @ SY741 @ SV318 ) ) )
= $false )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1848,plain,
! [SV90: $i,SV318: $i] :
( ( ( ~ ! [SY743: $i] :
( ~ ( in @ SY743 @ SV318 )
| ( in @ ( ordered_pair @ SY743 @ ( sK26_D @ SY743 @ SV318 @ SV90 ) ) @ SV90 ) ) )
= $false )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1849,plain,
! [SV387: $i,SV208: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV387 )
| ~ ( in @ SV387 @ SV208 ) )
= $true )
| ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(1850,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) )
| ~ ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 ) )
= $false )
| ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1851,plain,
! [SV252: $i,SV209: $i,SV388: $i] :
( ( ( ! [SY790: $i] :
( ~ ( in @ SV388 @ SY790 )
| ~ ( in @ SY790 @ SV209 ) )
| ( in @ SV388 @ SV252 ) )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(1852,plain,
! [SV209: $i,SV252: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV252 )
| ~ ( ~ ( in @ SV389 @ ( sK23_D @ SV389 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SV389 @ SV252 @ SV209 ) @ SV209 ) ) )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(1853,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
| ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) )
= $false )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1854,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
= $true )
| ( ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 )
| ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1855,plain,
! [SV254: $i,SV91: $i,SV298: $i] :
( ( ( ! [SY718: $i] :
( ~ ( in @ SY718 @ SV298 )
| ( in @ SY718 @ SV91 )
| ( in @ SY718 @ SV254 ) ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1856,plain,
! [SV254: $i,SV298: $i,SV91: $i] :
( ( ( ~ ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) )
| ~ ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1857,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1858,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) )
= $false )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1859,plain,
! [SV300: $i,SV256: $i,SV92: $i] :
( ( ( ! [SY721: $i] :
( ~ ( in @ SY721 @ SV92 )
| ( in @ SY721 @ SV256 )
| ( in @ SY721 @ SV300 ) ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1860,plain,
! [SV256: $i,SV92: $i,SV300: $i] :
( ( ( ~ ( ~ ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1861,plain,
! [SV363: $i,SV348: $i,SV93: $i] :
( ( ( subset @ ( unordered_pair @ SV93 @ SV348 ) @ SV363 )
= $false )
| ( ( in @ SV93 @ SV363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1862,plain,
! [SV364: $i,SV349: $i,SV93: $i] :
( ( ( subset @ ( unordered_pair @ SV93 @ SV349 ) @ SV364 )
= $false )
| ( ( in @ SV349 @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1863,plain,
! [SV95: $i,SV390: $i] :
( ( ! [SY791: $i] :
( ~ ( in @ SV390 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SY791 @ SV390 )
| ( in @ SY791 @ ( sK7_B @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(1864,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( relation @ SV374 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY784: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SY784 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY784 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) ) )
| ( SV374
= ( relation_composition @ SV96 @ SV216 ) ) )
= $true )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1865,plain,
! [SV216: $i,SV96: $i,SV375: $i] :
( ( ( ~ ( relation @ SV375 ) )
= $true )
| ( ( ( SV375
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY785: $i,SY786: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY785 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY786 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY785 @ SY786 ) @ SV375 ) )
| ~ ! [SY788: $i,SY789: $i] :
( ~ ( in @ ( ordered_pair @ SY788 @ SY789 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SY788 @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) @ SY789 ) @ SV216 ) ) ) ) )
= $true )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(1866,plain,
! [SV319: $i,SV272: $i,SV222: $i] :
( ( ( disjoint @ SV222 @ SV272 )
= $false )
| ( ( in @ SV319 @ SV222 )
= $false )
| ( ( in @ SV319 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1867,plain,
! [SV223: $i,SV273: $i] :
( ( ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
= $false )
| ( ( ~ ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 ) )
= $true )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1868,plain,
! [SV224: $i,SV274: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ SV274 )
| ( subset @ SV391 @ SV224 ) )
= $true )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1869,plain,
! [SV274: $i,SV224: $i,SV392: $i] :
( ( ( ~ ( subset @ SV392 @ SV224 )
| ( in @ SV392 @ SV274 ) )
= $true )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(1870,plain,
! [SV98: $i,SV354: $i,SV175: $i] :
( ( ( ~ ( disjoint @ SV175 @ SV354 ) )
= $true )
| ( ( subset @ SV175 @ ( subset_complement @ SV98 @ SV354 ) )
= $true )
| ( ( element @ SV354 @ ( powerset @ SV98 ) )
= $false )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1871,plain,
! [SV355: $i,SV98: $i,SV175: $i] :
( ( ( ~ ( subset @ SV175 @ ( subset_complement @ SV98 @ SV355 ) ) )
= $true )
| ( ( disjoint @ SV175 @ SV355 )
= $true )
| ( ( element @ SV355 @ ( powerset @ SV98 ) )
= $false )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(1872,plain,
! [SV321: $i,SV99: $i] :
( ( ( subset @ SV99 @ SV321 )
= $false )
| ( ( subset @ ( relation_dom @ SV99 ) @ ( relation_dom @ SV321 ) )
= $true )
| ( ( relation @ SV321 )
= $false )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1873,plain,
! [SV322: $i,SV99: $i] :
( ( ( subset @ SV99 @ SV322 )
= $false )
| ( ( subset @ ( relation_rng @ SV99 ) @ ( relation_rng @ SV322 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(1874,plain,
! [SV100: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) ) )
= $false )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1875,plain,
! [SV100: $i,SV324: $i] :
( ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( ~ ( ~ ! [SY744: $i,SY745: $i] :
( ~ ( in @ ( ordered_pair @ SY744 @ SY745 ) @ SV324 )
| ( in @ ( ordered_pair @ SY745 @ SY744 ) @ SV100 ) )
| ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ ( ordered_pair @ SY747 @ SY746 ) @ SV100 )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV324 ) ) ) )
= $true )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1876,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(1877,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
| ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) )
= $false )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1878,plain,
! [SV305: $i,SV276: $i,SV101: $i] :
( ( ( ! [SY726: $i] :
( ~ ( in @ SY726 @ SV101 )
| ~ ( in @ SY726 @ SV276 )
| ( in @ SY726 @ SV305 ) ) )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1879,plain,
! [SV276: $i,SV101: $i,SV305: $i] :
( ( ( ~ ( ~ ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) ) )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1880,plain,
! [SV103: $i,SV356: $i] :
( ( ( ~ ! [SY774: $i] :
( ~ ( subset @ SY774 @ SV356 )
| ( in @ SY774 @ ( sK9_SY344 @ SV356 @ SV103 ) ) ) )
= $false )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1803]) ).
thf(1881,plain,
! [SV103: $i,SV356: $i] :
( ( ( ~ ( in @ ( sK9_SY344 @ SV356 @ SV103 ) @ ( sK8_B @ SV103 ) ) )
= $false )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1803]) ).
thf(1882,plain,
! [SV103: $i,SV393: $i] :
( ( ! [SY792: $i] :
( ~ ( in @ SV393 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SY792 @ SV393 )
| ( in @ SY792 @ ( sK8_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(1883,plain,
! [SV308: $i,SV104: $i,SV329: $i,SV176: $i] :
( ( ( in @ SV176 @ SV329 )
= $false )
| ( ( in @ SV104 @ SV308 )
= $false )
| ( ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV308 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1884,plain,
! [SV394: $i,SV365: $i,SV176: $i,SV104: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV365 @ SV394 ) ) )
= $true )
| ( ( in @ SV104 @ SV365 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(1885,plain,
! [SV377: $i,SV366: $i,SV176: $i,SV104: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV366 @ SV377 ) ) )
= $true )
| ( ( in @ SV176 @ SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(1886,plain,
! [SV309: $i,SV284: $i,SV105: $i] :
( ( ( ! [SY730: $i,SY731: $i] :
( ~ ( in @ SY730 @ SV105 )
| ~ ( in @ SY731 @ SV284 )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SY730 @ SY731 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1887,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) ) ) )
= $true )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(1888,plain,
! [SV310: $i,SV285: $i,SV105: $i] :
( ( ( ! [SY732: $i] :
( ! [SY708: $i,SY709: $i] :
( ~ ( in @ SY708 @ SV105 )
| ~ ( in @ SY709 @ SV285 )
| ( SY732
!= ( ordered_pair @ SY708 @ SY709 ) ) )
| ( in @ SY732 @ SV310 ) ) )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1889,plain,
! [SV105: $i,SV285: $i,SV310: $i] :
( ( ( ! [SY735: $i] :
( ~ ( in @ SY735 @ SV310 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SY735
!= ( ordered_pair @ ( sK31_E @ SY735 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SY735 @ SV310 @ SV285 @ SV105 ) ) ) ) ) )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1890,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) ) )
= $false )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1891,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
= $true )
| ( ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV106 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV287 ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1892,plain,
! [SV288: $i,SV106: $i,SV312: $i] :
( ( ( ! [SY736: $i] :
( ~ ( in @ SY736 @ SV312 )
| ( SY736 = SV106 )
| ( SY736 = SV288 ) ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1893,plain,
! [SV288: $i,SV312: $i,SV106: $i] :
( ( ( ~ ( ~ ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) )
| ~ ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1894,plain,
! [SV313: $i,SV107: $i,SV332: $i,SV177: $i] :
( ( ( in @ SV177 @ SV332 )
= $false )
| ( ( in @ SV107 @ SV313 )
= $false )
| ( ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV313 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1895,plain,
! [SV395: $i,SV367: $i,SV177: $i,SV107: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV367 @ SV395 ) ) )
= $true )
| ( ( in @ SV107 @ SV367 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(1896,plain,
! [SV379: $i,SV368: $i,SV177: $i,SV107: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV368 @ SV379 ) ) )
= $true )
| ( ( in @ SV177 @ SV379 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1897,plain,
! [SV109: $i,SV334: $i] :
( ( ( ! [SY754: $i] :
~ ( in @ ( ordered_pair @ SY754 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ~ ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) )
= $true )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1898,plain,
! [SV109: $i,SV334: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SV334 @ SV109 ) @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
| ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) )
= $true )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1899,plain,
! [SV335: $i,SV109: $i] :
( ( ( ~ ! [SY755: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY755 ) @ SV109 )
| ( in @ SY755 @ SV335 ) ) )
= $false )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1900,plain,
! [SV109: $i,SV335: $i] :
( ( ( ~ ! [SY757: $i] :
( ~ ( in @ SY757 @ SV335 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY757 @ SV335 @ SV109 ) @ SY757 ) @ SV109 ) ) )
= $false )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1901,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) )
| ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
| ~ ( ! [SY779: $i] :
( ~ ( in @ SY779 @ SV336 )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SY779 ) )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) ) )
= $false )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1902,plain,
! [SV337: $i,SV370: $i] :
( ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( ~ ( ~ ! [SY780: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SY780 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SY780 @ ( sK41_D @ SY780 @ SV370 @ SV337 ) ) )
| ( in @ SY780 @ SV370 ) )
| ~ ! [SY781: $i] :
( ~ ( in @ SY781 @ SV370 )
| ! [SY763: $i] :
( ~ ( in @ SY763 @ SV337 )
| ( in @ SY781 @ SY763 ) ) ) ) )
= $true )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1903,plain,
! [SV338: $i,SV380: $i] :
( ( ( ( SV380
!= ( set_meet @ SV338 ) ) )
= $true )
| ( ( SV380 = empty_set )
= $true )
| ( ( SV338 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1904,plain,
! [SV339: $i,SV381: $i] :
( ( ( ( SV381 != empty_set ) )
= $true )
| ( ( SV381
= ( set_meet @ SV339 ) )
= $true )
| ( ( SV339 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(1905,plain,
! [SV361: $i,SV340: $i] :
( ( ( SV340 = SV361 )
= $false )
| ( ( proper_subset @ SV340 @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1906,plain,
! [SV382: $i,SV371: $i,SV239: $i] :
( ( ( ( sK46_B @ SV239 )
= ( ordered_pair @ SV371 @ SV382 ) )
= $false )
| ( ( relation @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1907,plain,
! [SV343: $i,SV372: $i] :
( ( ( element @ SV372 @ SV343 )
= $false )
| ( ( in @ SV372 @ SV343 )
= $true )
| ( ( empty @ SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1908,plain,
! [SV344: $i,SV373: $i] :
( ( ( in @ SV373 @ SV344 )
= $false )
| ( ( element @ SV373 @ SV344 )
= $true )
| ( ( empty @ SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1909,plain,
! [SV345: $i,SV383: $i] :
( ( ( ~ ( element @ SV383 @ SV345 ) )
= $true )
| ( ( empty @ SV383 )
= $true )
| ( ( empty @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(1910,plain,
! [SV346: $i,SV384: $i] :
( ( ( ~ ( empty @ SV384 ) )
= $true )
| ( ( element @ SV384 @ SV346 )
= $true )
| ( ( empty @ SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(1911,plain,
! [SV206: $i,SV249: $i] :
( ( ( in @ ( sK40_C @ SV249 @ SV206 ) @ SV249 )
= $false )
| ( ( ( sK40_C @ SV249 @ SV206 )
= SV206 )
= $false )
| ( ( SV249
= ( singleton @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(1912,plain,
! [SV250: $i,SV207: $i,SV385: $i] :
( ( ( ( SV385 != SV207 ) )
= $true )
| ( ( in @ SV385 @ SV250 )
= $true )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(1913,plain,
! [SV207: $i,SV250: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV250 ) )
= $true )
| ( ( SV386 = SV207 )
= $true )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(1914,plain,
! [SV90: $i,SV317: $i] :
( ( ( ! [SY740: $i] :
~ ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SY740 ) @ SV90 ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) )
= $true )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1915,plain,
! [SV90: $i,SV317: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ ( sK28_SY360 @ SV317 @ SV90 ) ) @ SV90 )
= $true )
| ( ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 )
= $true )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1916,plain,
! [SV318: $i,SV90: $i] :
( ( ( ! [SY741: $i] :
( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY741 @ SY463 ) @ SV90 )
| ( in @ SY741 @ SV318 ) ) )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1847]) ).
thf(1917,plain,
! [SV90: $i,SV318: $i] :
( ( ( ! [SY743: $i] :
( ~ ( in @ SY743 @ SV318 )
| ( in @ ( ordered_pair @ SY743 @ ( sK26_D @ SY743 @ SV318 @ SV90 ) ) @ SV90 ) ) )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1918,plain,
! [SV387: $i,SV208: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV387 ) )
= $true )
| ( ( ~ ( in @ SV387 @ SV208 ) )
= $true )
| ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(1919,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) ) )
= $false )
| ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(1920,plain,
! [SV208: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 ) )
= $false )
| ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(1921,plain,
! [SV252: $i,SV209: $i,SV388: $i] :
( ( ( ! [SY790: $i] :
( ~ ( in @ SV388 @ SY790 )
| ~ ( in @ SY790 @ SV209 ) ) )
= $true )
| ( ( in @ SV388 @ SV252 )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(1922,plain,
! [SV209: $i,SV252: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV252 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV389 @ ( sK23_D @ SV389 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SV389 @ SV252 @ SV209 ) @ SV209 ) ) )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(1923,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) ) )
= $false )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(1924,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) ) )
= $false )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(1925,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 )
= $true )
| ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 )
= $true )
| ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(1926,plain,
! [SV254: $i,SV91: $i,SV298: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV298 )
| ( in @ SV396 @ SV91 )
| ( in @ SV396 @ SV254 ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(1927,plain,
! [SV254: $i,SV298: $i,SV91: $i] :
( ( ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) )
| ~ ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) )
= $false )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1928,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 ) )
= $true )
| ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(1929,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) )
= $false )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1930,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) ) )
= $false )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1931,plain,
! [SV300: $i,SV256: $i,SV92: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV92 )
| ( in @ SV397 @ SV256 )
| ( in @ SV397 @ SV300 ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(1932,plain,
! [SV256: $i,SV92: $i,SV300: $i] :
( ( ( ~ ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) )
= $false )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1933,plain,
! [SV398: $i,SV95: $i,SV390: $i] :
( ( ~ ( in @ SV390 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SV398 @ SV390 )
| ( in @ SV398 @ ( sK7_B @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1934,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( relation @ SV374 )
= $false )
| ( ( ~ ( ~ ( ! [SY784: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SY784 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY784 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) ) )
| ( SV374
= ( relation_composition @ SV96 @ SV216 ) ) )
= $true )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1935,plain,
! [SV216: $i,SV96: $i,SV375: $i] :
( ( ( relation @ SV375 )
= $false )
| ( ( ( SV375
!= ( relation_composition @ SV96 @ SV216 ) )
| ~ ( ~ ! [SY785: $i,SY786: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY785 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY786 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY785 @ SY786 ) @ SV375 ) )
| ~ ! [SY788: $i,SY789: $i] :
( ~ ( in @ ( ordered_pair @ SY788 @ SY789 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SY788 @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) @ SY789 ) @ SV216 ) ) ) ) )
= $true )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1936,plain,
! [SV223: $i,SV273: $i] :
( ( ( subset @ ( sK38_C @ SV273 @ SV223 ) @ SV223 )
= $false )
| ( ( in @ ( sK38_C @ SV273 @ SV223 ) @ SV273 )
= $false )
| ( ( SV273
= ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1937,plain,
! [SV224: $i,SV274: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ SV274 ) )
= $true )
| ( ( subset @ SV391 @ SV224 )
= $true )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(1938,plain,
! [SV274: $i,SV224: $i,SV392: $i] :
( ( ( ~ ( subset @ SV392 @ SV224 ) )
= $true )
| ( ( in @ SV392 @ SV274 )
= $true )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1939,plain,
! [SV98: $i,SV354: $i,SV175: $i] :
( ( ( disjoint @ SV175 @ SV354 )
= $false )
| ( ( subset @ SV175 @ ( subset_complement @ SV98 @ SV354 ) )
= $true )
| ( ( element @ SV354 @ ( powerset @ SV98 ) )
= $false )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1940,plain,
! [SV355: $i,SV98: $i,SV175: $i] :
( ( ( subset @ SV175 @ ( subset_complement @ SV98 @ SV355 ) )
= $false )
| ( ( disjoint @ SV175 @ SV355 )
= $true )
| ( ( element @ SV355 @ ( powerset @ SV98 ) )
= $false )
| ( ( element @ SV175 @ ( powerset @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1941,plain,
! [SV100: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) ) )
= $false )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1942,plain,
! [SV100: $i,SV323: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) ) )
= $false )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1943,plain,
! [SV100: $i,SV324: $i] :
( ( ( ~ ! [SY744: $i,SY745: $i] :
( ~ ( in @ ( ordered_pair @ SY744 @ SY745 ) @ SV324 )
| ( in @ ( ordered_pair @ SY745 @ SY744 ) @ SV100 ) )
| ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ ( ordered_pair @ SY747 @ SY746 ) @ SV100 )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(1944,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 ) )
= $true )
| ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(1945,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) )
= $false )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1946,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ~ ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) ) )
= $false )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1947,plain,
! [SV305: $i,SV276: $i,SV101: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ SV101 )
| ~ ( in @ SV399 @ SV276 )
| ( in @ SV399 @ SV305 ) )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(1948,plain,
! [SV276: $i,SV101: $i,SV305: $i] :
( ( ( ~ ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) )
= $false )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1949,plain,
! [SV103: $i,SV356: $i] :
( ( ( ! [SY774: $i] :
( ~ ( subset @ SY774 @ SV356 )
| ( in @ SY774 @ ( sK9_SY344 @ SV356 @ SV103 ) ) ) )
= $true )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1880]) ).
thf(1950,plain,
! [SV103: $i,SV356: $i] :
( ( ( in @ ( sK9_SY344 @ SV356 @ SV103 ) @ ( sK8_B @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(1951,plain,
! [SV400: $i,SV103: $i,SV393: $i] :
( ( ~ ( in @ SV393 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SV400 @ SV393 )
| ( in @ SV400 @ ( sK8_B @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(1952,plain,
! [SV394: $i,SV365: $i,SV176: $i,SV104: $i] :
( ( ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV365 @ SV394 ) )
= $false )
| ( ( in @ SV104 @ SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1953,plain,
! [SV377: $i,SV366: $i,SV176: $i,SV104: $i] :
( ( ( in @ ( ordered_pair @ SV104 @ SV176 ) @ ( cartesian_product2 @ SV366 @ SV377 ) )
= $false )
| ( ( in @ SV176 @ SV377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1954,plain,
! [SV309: $i,SV284: $i,SV105: $i,SV401: $i] :
( ( ( ! [SY793: $i] :
( ~ ( in @ SV401 @ SV105 )
| ~ ( in @ SY793 @ SV284 )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SV401 @ SY793 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(1955,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) ) )
= $false )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1956,plain,
! [SV310: $i,SV402: $i,SV285: $i,SV105: $i] :
( ( ( ! [SY794: $i,SY795: $i] :
( ~ ( in @ SY794 @ SV105 )
| ~ ( in @ SY795 @ SV285 )
| ( SV402
!= ( ordered_pair @ SY794 @ SY795 ) ) )
| ( in @ SV402 @ SV310 ) )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(1957,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV310 )
| ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SV403
!= ( ordered_pair @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) ) ) ) )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(1958,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) ) )
= $false )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1959,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) ) )
= $false )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1960,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV106 )
= $true )
| ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV287 )
= $true )
| ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(1961,plain,
! [SV288: $i,SV106: $i,SV312: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV312 )
| ( SV404 = SV106 )
| ( SV404 = SV288 ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(1962,plain,
! [SV288: $i,SV312: $i,SV106: $i] :
( ( ( ~ ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) )
| ~ ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) )
= $false )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1963,plain,
! [SV395: $i,SV367: $i,SV177: $i,SV107: $i] :
( ( ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV367 @ SV395 ) )
= $false )
| ( ( in @ SV107 @ SV367 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1964,plain,
! [SV379: $i,SV368: $i,SV177: $i,SV107: $i] :
( ( ( in @ ( ordered_pair @ SV107 @ SV177 ) @ ( cartesian_product2 @ SV368 @ SV379 ) )
= $false )
| ( ( in @ SV177 @ SV379 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1965,plain,
! [SV109: $i,SV334: $i] :
( ( ( ! [SY754: $i] :
~ ( in @ ( ordered_pair @ SY754 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 ) )
= $true )
| ( ( ~ ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) )
= $true )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(1966,plain,
! [SV109: $i,SV334: $i] :
( ( ( in @ ( ordered_pair @ ( sK21_SY356 @ SV334 @ SV109 ) @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
= $true )
| ( ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 )
= $true )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(1967,plain,
! [SV335: $i,SV109: $i] :
( ( ( ! [SY755: $i] :
( ! [SY569: $i] :
~ ( in @ ( ordered_pair @ SY569 @ SY755 ) @ SV109 )
| ( in @ SY755 @ SV335 ) ) )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1968,plain,
! [SV109: $i,SV335: $i] :
( ( ( ! [SY757: $i] :
( ~ ( in @ SY757 @ SV335 )
| ( in @ ( ordered_pair @ ( sK19_D @ SY757 @ SV335 @ SV109 ) @ SY757 ) @ SV109 ) ) )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(1969,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) )
| ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) ) )
= $false )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(1970,plain,
! [SV369: $i,SV336: $i] :
( ( ( ~ ( ! [SY779: $i] :
( ~ ( in @ SY779 @ SV336 )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SY779 ) )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) ) )
= $false )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(1971,plain,
! [SV337: $i,SV370: $i] :
( ( ( ~ ! [SY780: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SY780 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SY780 @ ( sK41_D @ SY780 @ SV370 @ SV337 ) ) )
| ( in @ SY780 @ SV370 ) )
| ~ ! [SY781: $i] :
( ~ ( in @ SY781 @ SV370 )
| ! [SY763: $i] :
( ~ ( in @ SY763 @ SV337 )
| ( in @ SY781 @ SY763 ) ) ) )
= $false )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1972,plain,
! [SV338: $i,SV380: $i] :
( ( ( SV380
= ( set_meet @ SV338 ) )
= $false )
| ( ( SV380 = empty_set )
= $true )
| ( ( SV338 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(1973,plain,
! [SV339: $i,SV381: $i] :
( ( ( SV381 = empty_set )
= $false )
| ( ( SV381
= ( set_meet @ SV339 ) )
= $true )
| ( ( SV339 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1974,plain,
! [SV345: $i,SV383: $i] :
( ( ( element @ SV383 @ SV345 )
= $false )
| ( ( empty @ SV383 )
= $true )
| ( ( empty @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(1975,plain,
! [SV346: $i,SV384: $i] :
( ( ( empty @ SV384 )
= $false )
| ( ( element @ SV384 @ SV346 )
= $true )
| ( ( empty @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1976,plain,
! [SV250: $i,SV207: $i,SV385: $i] :
( ( ( SV385 = SV207 )
= $false )
| ( ( in @ SV385 @ SV250 )
= $true )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(1977,plain,
! [SV207: $i,SV250: $i,SV386: $i] :
( ( ( in @ SV386 @ SV250 )
= $false )
| ( ( SV386 = SV207 )
= $true )
| ( ( SV250
= ( singleton @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1978,plain,
! [SV405: $i,SV90: $i,SV317: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SV405 ) @ SV90 ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) )
= $true )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(1979,plain,
! [SV318: $i,SV90: $i,SV406: $i] :
( ( ( ! [SY796: $i] :
~ ( in @ ( ordered_pair @ SV406 @ SY796 ) @ SV90 )
| ( in @ SV406 @ SV318 ) )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(1980,plain,
! [SV90: $i,SV318: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ SV318 )
| ( in @ ( ordered_pair @ SV407 @ ( sK26_D @ SV407 @ SV318 @ SV90 ) ) @ SV90 ) )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(1981,plain,
! [SV387: $i,SV208: $i,SV251: $i] :
( ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV387 )
= $false )
| ( ( ~ ( in @ SV387 @ SV208 ) )
= $true )
| ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(1982,plain,
! [SV208: $i,SV251: $i] :
( ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ ( sK25_SY358 @ SV251 @ SV208 ) )
= $true )
| ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(1983,plain,
! [SV208: $i,SV251: $i] :
( ( ( in @ ( sK25_SY358 @ SV251 @ SV208 ) @ SV208 )
= $true )
| ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(1984,plain,
! [SV252: $i,SV209: $i,SV408: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV408 )
| ~ ( in @ SV408 @ SV209 ) )
= $true )
| ( ( in @ SV388 @ SV252 )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(1985,plain,
! [SV209: $i,SV252: $i,SV389: $i] :
( ( ( in @ SV389 @ SV252 )
= $false )
| ( ( ~ ( ~ ( in @ SV389 @ ( sK23_D @ SV389 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SV389 @ SV252 @ SV209 ) @ SV209 ) ) )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1986,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(1987,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
| ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(1988,plain,
! [SV254: $i,SV91: $i,SV298: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV298 ) )
= $true )
| ( ( ( in @ SV396 @ SV91 )
| ( in @ SV396 @ SV254 ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(1989,plain,
! [SV254: $i,SV298: $i,SV91: $i] :
( ( ( ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) ) )
= $false )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(1990,plain,
! [SV91: $i,SV298: $i,SV254: $i] :
( ( ( ~ ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) )
= $false )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(1991,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
= $false )
| ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(1992,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(1993,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
| ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(1994,plain,
! [SV300: $i,SV256: $i,SV92: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV92 )
| ( in @ SV397 @ SV256 ) )
= $true )
| ( ( in @ SV397 @ SV300 )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(1995,plain,
! [SV256: $i,SV92: $i,SV300: $i] :
( ( ( ~ ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) ) )
= $false )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(1996,plain,
! [SV92: $i,SV256: $i,SV300: $i] :
( ( ( ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) )
= $false )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(1997,plain,
! [SV398: $i,SV95: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( sK7_B @ SV95 ) )
| ~ ( subset @ SV398 @ SV390 ) )
= $true )
| ( ( in @ SV398 @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(1998,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( ~ ( ! [SY784: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SY784 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY784 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) ) ) )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(1999,plain,
! [SV216: $i,SV96: $i,SV375: $i] :
( ( ( ( SV375
!= ( relation_composition @ SV96 @ SV216 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY785: $i,SY786: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY785 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY786 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY785 @ SY786 ) @ SV375 ) )
| ~ ! [SY788: $i,SY789: $i] :
( ~ ( in @ ( ordered_pair @ SY788 @ SY789 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SY788 @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) @ SY789 ) @ SV216 ) ) ) ) )
= $true )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2000,plain,
! [SV224: $i,SV274: $i,SV391: $i] :
( ( ( in @ SV391 @ SV274 )
= $false )
| ( ( subset @ SV391 @ SV224 )
= $true )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2001,plain,
! [SV274: $i,SV224: $i,SV392: $i] :
( ( ( subset @ SV392 @ SV224 )
= $false )
| ( ( in @ SV392 @ SV274 )
= $true )
| ( ( SV274
= ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2002,plain,
! [SV100: $i,SV323: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
= $true )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1941]) ).
thf(2003,plain,
! [SV100: $i,SV323: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
| ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
= $true )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(2004,plain,
! [SV100: $i,SV324: $i] :
( ( ( ~ ! [SY744: $i,SY745: $i] :
( ~ ( in @ ( ordered_pair @ SY744 @ SY745 ) @ SV324 )
| ( in @ ( ordered_pair @ SY745 @ SY744 ) @ SV100 ) ) )
= $false )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(2005,plain,
! [SV324: $i,SV100: $i] :
( ( ( ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ ( ordered_pair @ SY747 @ SY746 ) @ SV100 )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(2006,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
= $false )
| ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2007,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2008,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
| ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1946]) ).
thf(2009,plain,
! [SV305: $i,SV276: $i,SV101: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ SV101 )
| ~ ( in @ SV399 @ SV276 ) )
= $true )
| ( ( in @ SV399 @ SV305 )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2010,plain,
! [SV276: $i,SV101: $i,SV305: $i] :
( ( ( ~ ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) ) )
= $false )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2011,plain,
! [SV101: $i,SV276: $i,SV305: $i] :
( ( ( ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) )
= $false )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2012,plain,
! [SV103: $i,SV356: $i,SV409: $i] :
( ( ( ~ ( subset @ SV409 @ SV356 )
| ( in @ SV409 @ ( sK9_SY344 @ SV356 @ SV103 ) ) )
= $true )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2013,plain,
! [SV103: $i,SV356: $i] :
( ( ( in @ SV356 @ ( sK8_B @ SV103 ) )
= $false )
| ( ( in @ ( sK9_SY344 @ SV356 @ SV103 ) @ ( sK8_B @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2014,plain,
! [SV400: $i,SV103: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ ( sK8_B @ SV103 ) )
| ~ ( subset @ SV400 @ SV393 ) )
= $true )
| ( ( in @ SV400 @ ( sK8_B @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2015,plain,
! [SV309: $i,SV284: $i,SV410: $i,SV105: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV105 )
| ~ ( in @ SV410 @ SV284 )
| ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SV401 @ SV410 ) ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2016,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) ) )
= $false )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2017,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) ) )
= $false )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2018,plain,
! [SV310: $i,SV402: $i,SV285: $i,SV105: $i] :
( ( ( ! [SY794: $i,SY795: $i] :
( ~ ( in @ SY794 @ SV105 )
| ~ ( in @ SY795 @ SV285 )
| ( SV402
!= ( ordered_pair @ SY794 @ SY795 ) ) ) )
= $true )
| ( ( in @ SV402 @ SV310 )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2019,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV310 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SV403
!= ( ordered_pair @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) ) ) ) )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2020,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1958]) ).
thf(2021,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
| ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2022,plain,
! [SV288: $i,SV106: $i,SV312: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV312 ) )
= $true )
| ( ( ( SV404 = SV106 )
| ( SV404 = SV288 ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2023,plain,
! [SV288: $i,SV312: $i,SV106: $i] :
( ( ( ~ ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) ) )
= $false )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1962]) ).
thf(2024,plain,
! [SV106: $i,SV312: $i,SV288: $i] :
( ( ( ~ ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) )
= $false )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1962]) ).
thf(2025,plain,
! [SV109: $i,SV334: $i,SV411: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV411 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 ) )
= $true )
| ( ( ~ ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) )
= $true )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2026,plain,
! [SV335: $i,SV109: $i,SV412: $i] :
( ( ( ! [SY797: $i] :
~ ( in @ ( ordered_pair @ SY797 @ SV412 ) @ SV109 )
| ( in @ SV412 @ SV335 ) )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2027,plain,
! [SV109: $i,SV335: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV335 )
| ( in @ ( ordered_pair @ ( sK19_D @ SV413 @ SV335 @ SV109 ) @ SV413 ) @ SV109 ) )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2028,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) )
| ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1969]) ).
thf(2029,plain,
! [SV369: $i,SV336: $i] :
( ( ( ! [SY779: $i] :
( ~ ( in @ SY779 @ SV336 )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SY779 ) )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2030,plain,
! [SV337: $i,SV370: $i] :
( ( ( ~ ! [SY780: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SY780 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SY780 @ ( sK41_D @ SY780 @ SV370 @ SV337 ) ) )
| ( in @ SY780 @ SV370 ) ) )
= $false )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2031,plain,
! [SV337: $i,SV370: $i] :
( ( ( ~ ! [SY781: $i] :
( ~ ( in @ SY781 @ SV370 )
| ! [SY763: $i] :
( ~ ( in @ SY763 @ SV337 )
| ( in @ SY781 @ SY763 ) ) ) )
= $false )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2032,plain,
! [SV405: $i,SV90: $i,SV317: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SV405 ) @ SV90 )
= $false )
| ( ( ~ ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 ) )
= $true )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2033,plain,
! [SV318: $i,SV90: $i,SV406: $i] :
( ( ( ! [SY796: $i] :
~ ( in @ ( ordered_pair @ SV406 @ SY796 ) @ SV90 ) )
= $true )
| ( ( in @ SV406 @ SV318 )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2034,plain,
! [SV90: $i,SV318: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ SV318 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV407 @ ( sK26_D @ SV407 @ SV318 @ SV90 ) ) @ SV90 )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2035,plain,
! [SV251: $i,SV208: $i,SV387: $i] :
( ( ( in @ SV387 @ SV208 )
= $false )
| ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV387 )
= $false )
| ( ( ~ ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2036,plain,
! [SV252: $i,SV209: $i,SV408: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV408 ) )
= $true )
| ( ( ~ ( in @ SV408 @ SV209 ) )
= $true )
| ( ( in @ SV388 @ SV252 )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2037,plain,
! [SV209: $i,SV252: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ ( sK23_D @ SV389 @ SV252 @ SV209 ) )
| ~ ( in @ ( sK23_D @ SV389 @ SV252 @ SV209 ) @ SV209 ) )
= $false )
| ( ( in @ SV389 @ SV252 )
= $false )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2038,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 ) )
= $true )
| ( ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2039,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 ) )
= $true )
| ( ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2040,plain,
! [SV254: $i,SV91: $i,SV298: $i,SV396: $i] :
( ( ( in @ SV396 @ SV298 )
= $false )
| ( ( ( in @ SV396 @ SV91 )
| ( in @ SV396 @ SV254 ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2041,plain,
! [SV254: $i,SV298: $i,SV91: $i] :
( ( ( ! [SY719: $i] :
( ~ ( in @ SY719 @ SV91 )
| ( in @ SY719 @ SV298 ) ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1989]) ).
thf(2042,plain,
! [SV91: $i,SV298: $i,SV254: $i] :
( ( ( ! [SY720: $i] :
( ~ ( in @ SY720 @ SV254 )
| ( in @ SY720 @ SV298 ) ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2043,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 )
= $false )
| ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
= $true )
| ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
= $false )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2044,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV92 )
= $true )
| ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2045,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 ) )
= $true )
| ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2046,plain,
! [SV300: $i,SV256: $i,SV92: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV92 ) )
= $true )
| ( ( in @ SV397 @ SV256 )
= $true )
| ( ( in @ SV397 @ SV300 )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2047,plain,
! [SV256: $i,SV92: $i,SV300: $i] :
( ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV300 )
| ( in @ SY722 @ SV92 ) ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2048,plain,
! [SV92: $i,SV256: $i,SV300: $i] :
( ( ( ! [SY723: $i] :
( ~ ( in @ SY723 @ SV300 )
| ~ ( in @ SY723 @ SV256 ) ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1996]) ).
thf(2049,plain,
! [SV398: $i,SV95: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( sK7_B @ SV95 ) ) )
= $true )
| ( ( ~ ( subset @ SV398 @ SV390 ) )
= $true )
| ( ( in @ SV398 @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2050,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( ! [SY784: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SY784 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY784 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) ) )
= $false )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2051,plain,
! [SV216: $i,SV96: $i,SV375: $i] :
( ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ! [SY785: $i,SY786: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY785 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY786 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY785 @ SY786 ) @ SV375 ) )
| ~ ! [SY788: $i,SY789: $i] :
( ~ ( in @ ( ordered_pair @ SY788 @ SY789 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SY788 @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) @ SY789 ) @ SV216 ) ) ) ) )
= $true )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2052,plain,
! [SV100: $i,SV323: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
= $true )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2053,plain,
! [SV100: $i,SV323: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 )
= $true )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2054,plain,
! [SV100: $i,SV324: $i] :
( ( ( ! [SY744: $i,SY745: $i] :
( ~ ( in @ ( ordered_pair @ SY744 @ SY745 ) @ SV324 )
| ( in @ ( ordered_pair @ SY745 @ SY744 ) @ SV100 ) ) )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2055,plain,
! [SV324: $i,SV100: $i] :
( ( ( ! [SY746: $i,SY747: $i] :
( ~ ( in @ ( ordered_pair @ SY747 @ SY746 ) @ SV100 )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV324 ) ) )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2056,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
= $false )
| ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
= $false )
| ( ( ~ ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 ) )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2057,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
= $true )
| ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2058,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
= $true )
| ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 )
= $true )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2059,plain,
! [SV305: $i,SV276: $i,SV101: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ SV101 ) )
= $true )
| ( ( ~ ( in @ SV399 @ SV276 ) )
= $true )
| ( ( in @ SV399 @ SV305 )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2060,plain,
! [SV276: $i,SV101: $i,SV305: $i] :
( ( ( ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ( in @ SY727 @ SV101 ) ) )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2061,plain,
! [SV101: $i,SV276: $i,SV305: $i] :
( ( ( ! [SY728: $i] :
( ~ ( in @ SY728 @ SV305 )
| ( in @ SY728 @ SV276 ) ) )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2062,plain,
! [SV103: $i,SV356: $i,SV409: $i] :
( ( ( ~ ( subset @ SV409 @ SV356 ) )
= $true )
| ( ( in @ SV409 @ ( sK9_SY344 @ SV356 @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2063,plain,
! [SV400: $i,SV103: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ ( sK8_B @ SV103 ) ) )
= $true )
| ( ( ~ ( subset @ SV400 @ SV393 ) )
= $true )
| ( ( in @ SV400 @ ( sK8_B @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2064,plain,
! [SV309: $i,SV284: $i,SV410: $i,SV105: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV105 )
| ~ ( in @ SV410 @ SV284 ) )
= $true )
| ( ( ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SV401 @ SV410 ) ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2065,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) ) )
= $true )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2016]) ).
thf(2066,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ( sK33_D @ SV309 @ SV284 @ SV105 )
= ( ordered_pair @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) ) )
= $true )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2067,plain,
! [SV310: $i,SV402: $i,SV285: $i,SV105: $i,SV414: $i] :
( ( ( ! [SY798: $i] :
( ~ ( in @ SV414 @ SV105 )
| ~ ( in @ SY798 @ SV285 )
| ( SV402
!= ( ordered_pair @ SV414 @ SY798 ) ) ) )
= $true )
| ( ( in @ SV402 @ SV310 )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2068,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( in @ SV403 @ SV310 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SV403
!= ( ordered_pair @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) ) ) ) )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2069,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 ) )
= $true )
| ( ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2070,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 ) )
= $true )
| ( ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2071,plain,
! [SV288: $i,SV106: $i,SV312: $i,SV404: $i] :
( ( ( in @ SV404 @ SV312 )
= $false )
| ( ( ( SV404 = SV106 )
| ( SV404 = SV288 ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2072,plain,
! [SV288: $i,SV312: $i,SV106: $i] :
( ( ( ! [SY737: $i] :
( ( SY737 != SV106 )
| ( in @ SY737 @ SV312 ) ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2073,plain,
! [SV106: $i,SV312: $i,SV288: $i] :
( ( ( ! [SY738: $i] :
( ( SY738 != SV288 )
| ( in @ SY738 @ SV312 ) ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2074,plain,
! [SV109: $i,SV334: $i,SV411: $i] :
( ( ( in @ ( ordered_pair @ SV411 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
= $false )
| ( ( ~ ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 ) )
= $true )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2075,plain,
! [SV335: $i,SV109: $i,SV412: $i] :
( ( ( ! [SY797: $i] :
~ ( in @ ( ordered_pair @ SY797 @ SV412 ) @ SV109 ) )
= $true )
| ( ( in @ SV412 @ SV335 )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2076,plain,
! [SV109: $i,SV335: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV335 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK19_D @ SV413 @ SV335 @ SV109 ) @ SV413 ) @ SV109 )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2077,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2078,plain,
! [SV369: $i,SV336: $i] :
( ( ( ! [SY779: $i] :
( ~ ( in @ SY779 @ SV336 )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SY779 ) ) )
= $true )
| ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2079,plain,
! [SV337: $i,SV370: $i] :
( ( ( ! [SY780: $i] :
( ~ ( ~ ( in @ ( sK41_D @ SY780 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SY780 @ ( sK41_D @ SY780 @ SV370 @ SV337 ) ) )
| ( in @ SY780 @ SV370 ) ) )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2080,plain,
! [SV337: $i,SV370: $i] :
( ( ( ! [SY781: $i] :
( ~ ( in @ SY781 @ SV370 )
| ! [SY763: $i] :
( ~ ( in @ SY763 @ SV337 )
| ( in @ SY781 @ SY763 ) ) ) )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2081,plain,
! [SV405: $i,SV90: $i,SV317: $i] :
( ( ( in @ ( sK27_C @ SV317 @ SV90 ) @ SV317 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_C @ SV317 @ SV90 ) @ SV405 ) @ SV90 )
= $false )
| ( ( SV317
= ( relation_dom @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2082,plain,
! [SV318: $i,SV90: $i,SV415: $i,SV406: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV406 @ SV415 ) @ SV90 ) )
= $true )
| ( ( in @ SV406 @ SV318 )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2083,plain,
! [SV90: $i,SV318: $i,SV407: $i] :
( ( ( in @ SV407 @ SV318 )
= $false )
| ( ( in @ ( ordered_pair @ SV407 @ ( sK26_D @ SV407 @ SV318 @ SV90 ) ) @ SV90 )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2084,plain,
! [SV387: $i,SV208: $i,SV251: $i] :
( ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV251 )
= $false )
| ( ( in @ ( sK24_C @ SV251 @ SV208 ) @ SV387 )
= $false )
| ( ( in @ SV387 @ SV208 )
= $false )
| ( ( SV251
= ( union @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2085,plain,
! [SV252: $i,SV209: $i,SV408: $i,SV388: $i] :
( ( ( in @ SV388 @ SV408 )
= $false )
| ( ( ~ ( in @ SV408 @ SV209 ) )
= $true )
| ( ( in @ SV388 @ SV252 )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2086,plain,
! [SV209: $i,SV252: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ ( sK23_D @ SV389 @ SV252 @ SV209 ) ) )
= $false )
| ( ( in @ SV389 @ SV252 )
= $false )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2087,plain,
! [SV209: $i,SV252: $i,SV389: $i] :
( ( ( ~ ( in @ ( sK23_D @ SV389 @ SV252 @ SV209 ) @ SV209 ) )
= $false )
| ( ( in @ SV389 @ SV252 )
= $false )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2088,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
= $false )
| ( ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2089,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
= $false )
| ( ( ~ ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 ) )
= $true )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2090,plain,
! [SV298: $i,SV254: $i,SV91: $i,SV396: $i] :
( ( ( in @ SV396 @ SV91 )
= $true )
| ( ( in @ SV396 @ SV254 )
= $true )
| ( ( in @ SV396 @ SV298 )
= $false )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2091,plain,
! [SV254: $i,SV298: $i,SV91: $i,SV416: $i] :
( ( ( ~ ( in @ SV416 @ SV91 )
| ( in @ SV416 @ SV298 ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2092,plain,
! [SV91: $i,SV298: $i,SV254: $i,SV417: $i] :
( ( ( ~ ( in @ SV417 @ SV254 )
| ( in @ SV417 @ SV298 ) )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2093,plain,
! [SV92: $i,SV255: $i,SV299: $i] :
( ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV255 )
= $false )
| ( ( in @ ( sK22_D @ SV299 @ SV255 @ SV92 ) @ SV299 )
= $true )
| ( ( SV299
= ( set_difference @ SV92 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2094,plain,
! [SV300: $i,SV256: $i,SV92: $i,SV397: $i] :
( ( ( in @ SV397 @ SV92 )
= $false )
| ( ( in @ SV397 @ SV256 )
= $true )
| ( ( in @ SV397 @ SV300 )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2095,plain,
! [SV256: $i,SV92: $i,SV300: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ SV300 )
| ( in @ SV418 @ SV92 ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2096,plain,
! [SV92: $i,SV256: $i,SV300: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ SV300 )
| ~ ( in @ SV419 @ SV256 ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2097,plain,
! [SV398: $i,SV95: $i,SV390: $i] :
( ( ( in @ SV390 @ ( sK7_B @ SV95 ) )
= $false )
| ( ( ~ ( subset @ SV398 @ SV390 ) )
= $true )
| ( ( in @ SV398 @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2098,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( ! [SY784: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SY784 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY784 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) ) )
= $false )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2050]) ).
thf(2099,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) ) )
= $false )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2050]) ).
thf(2100,plain,
! [SV375: $i,SV216: $i,SV96: $i] :
( ( ( ~ ! [SY785: $i,SY786: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY785 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY786 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY785 @ SY786 ) @ SV375 ) )
| ~ ! [SY788: $i,SY789: $i] :
( ~ ( in @ ( ordered_pair @ SY788 @ SY789 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SY788 @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) @ SY789 ) @ SV216 ) ) ) )
= $false )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2101,plain,
! [SV100: $i,SV323: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 ) )
= $true )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2102,plain,
! [SV100: $i,SV324: $i,SV420: $i] :
( ( ( ! [SY799: $i] :
( ~ ( in @ ( ordered_pair @ SV420 @ SY799 ) @ SV324 )
| ( in @ ( ordered_pair @ SY799 @ SV420 ) @ SV100 ) ) )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2103,plain,
! [SV324: $i,SV100: $i,SV421: $i] :
( ( ( ! [SY800: $i] :
( ~ ( in @ ( ordered_pair @ SY800 @ SV421 ) @ SV100 )
| ( in @ ( ordered_pair @ SV421 @ SY800 ) @ SV324 ) ) )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2104,plain,
! [SV101: $i,SV275: $i,SV304: $i] :
( ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV304 )
= $false )
| ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV101 )
= $false )
| ( ( in @ ( sK29_D @ SV304 @ SV275 @ SV101 ) @ SV275 )
= $false )
| ( ( SV304
= ( set_intersection2 @ SV101 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2105,plain,
! [SV305: $i,SV276: $i,SV101: $i,SV399: $i] :
( ( ( in @ SV399 @ SV101 )
= $false )
| ( ( ~ ( in @ SV399 @ SV276 ) )
= $true )
| ( ( in @ SV399 @ SV305 )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2106,plain,
! [SV276: $i,SV101: $i,SV305: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV305 )
| ( in @ SV422 @ SV101 ) )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2107,plain,
! [SV101: $i,SV276: $i,SV305: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV305 )
| ( in @ SV423 @ SV276 ) )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2108,plain,
! [SV103: $i,SV356: $i,SV409: $i] :
( ( ( subset @ SV409 @ SV356 )
= $false )
| ( ( in @ SV409 @ ( sK9_SY344 @ SV356 @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV356 @ ( sK8_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2109,plain,
! [SV400: $i,SV103: $i,SV393: $i] :
( ( ( in @ SV393 @ ( sK8_B @ SV103 ) )
= $false )
| ( ( ~ ( subset @ SV400 @ SV393 ) )
= $true )
| ( ( in @ SV400 @ ( sK8_B @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2110,plain,
! [SV309: $i,SV284: $i,SV410: $i,SV105: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV105 ) )
= $true )
| ( ( ~ ( in @ SV410 @ SV284 ) )
= $true )
| ( ( ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SV401 @ SV410 ) ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2111,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
= $false )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2112,plain,
! [SV310: $i,SV402: $i,SV285: $i,SV424: $i,SV105: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV105 )
| ~ ( in @ SV424 @ SV285 )
| ( SV402
!= ( ordered_pair @ SV414 @ SV424 ) ) )
= $true )
| ( ( in @ SV402 @ SV310 )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2113,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
| ( SV403
!= ( ordered_pair @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) ) ) )
= $false )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2114,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
= $false )
| ( ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV106 ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2115,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
= $false )
| ( ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
!= SV287 ) )
= $true )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2116,plain,
! [SV312: $i,SV288: $i,SV106: $i,SV404: $i] :
( ( ( SV404 = SV106 )
= $true )
| ( ( SV404 = SV288 )
= $true )
| ( ( in @ SV404 @ SV312 )
= $false )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2117,plain,
! [SV288: $i,SV312: $i,SV106: $i,SV425: $i] :
( ( ( ( SV425 != SV106 )
| ( in @ SV425 @ SV312 ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2118,plain,
! [SV106: $i,SV312: $i,SV288: $i,SV426: $i] :
( ( ( ( SV426 != SV288 )
| ( in @ SV426 @ SV312 ) )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2119,plain,
! [SV411: $i,SV109: $i,SV334: $i] :
( ( ( in @ ( sK20_C @ SV334 @ SV109 ) @ SV334 )
= $false )
| ( ( in @ ( ordered_pair @ SV411 @ ( sK20_C @ SV334 @ SV109 ) ) @ SV109 )
= $false )
| ( ( SV334
= ( relation_rng @ SV109 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2120,plain,
! [SV335: $i,SV109: $i,SV412: $i,SV427: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV427 @ SV412 ) @ SV109 ) )
= $true )
| ( ( in @ SV412 @ SV335 )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2121,plain,
! [SV109: $i,SV335: $i,SV413: $i] :
( ( ( in @ SV413 @ SV335 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK19_D @ SV413 @ SV335 @ SV109 ) @ SV413 ) @ SV109 )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2122,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
| ~ ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) )
= $false )
| ( ( ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2123,plain,
! [SV369: $i,SV336: $i,SV428: $i] :
( ( ( ~ ( in @ SV428 @ SV336 )
| ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV428 ) )
= $true )
| ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2124,plain,
! [SV337: $i,SV370: $i,SV429: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_D @ SV429 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SV429 @ ( sK41_D @ SV429 @ SV370 @ SV337 ) ) )
| ( in @ SV429 @ SV370 ) )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2125,plain,
! [SV337: $i,SV370: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV370 )
| ! [SY801: $i] :
( ~ ( in @ SY801 @ SV337 )
| ( in @ SV430 @ SY801 ) ) )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2126,plain,
! [SV318: $i,SV90: $i,SV415: $i,SV406: $i] :
( ( ( in @ ( ordered_pair @ SV406 @ SV415 ) @ SV90 )
= $false )
| ( ( in @ SV406 @ SV318 )
= $true )
| ( ( SV318
= ( relation_dom @ SV90 ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2127,plain,
! [SV252: $i,SV388: $i,SV209: $i,SV408: $i] :
( ( ( in @ SV408 @ SV209 )
= $false )
| ( ( in @ SV388 @ SV408 )
= $false )
| ( ( in @ SV388 @ SV252 )
= $true )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2128,plain,
! [SV209: $i,SV252: $i,SV389: $i] :
( ( ( in @ SV389 @ ( sK23_D @ SV389 @ SV252 @ SV209 ) )
= $true )
| ( ( in @ SV389 @ SV252 )
= $false )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2086]) ).
thf(2129,plain,
! [SV209: $i,SV252: $i,SV389: $i] :
( ( ( in @ ( sK23_D @ SV389 @ SV252 @ SV209 ) @ SV209 )
= $true )
| ( ( in @ SV389 @ SV252 )
= $false )
| ( ( SV252
= ( union @ SV209 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2087]) ).
thf(2130,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV91 )
= $false )
| ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
= $false )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2131,plain,
! [SV91: $i,SV253: $i,SV297: $i] :
( ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV253 )
= $false )
| ( ( in @ ( sK36_D @ SV297 @ SV253 @ SV91 ) @ SV297 )
= $false )
| ( ( SV297
= ( set_union2 @ SV91 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2132,plain,
! [SV254: $i,SV298: $i,SV91: $i,SV416: $i] :
( ( ( ~ ( in @ SV416 @ SV91 ) )
= $true )
| ( ( in @ SV416 @ SV298 )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2133,plain,
! [SV91: $i,SV298: $i,SV254: $i,SV417: $i] :
( ( ( ~ ( in @ SV417 @ SV254 ) )
= $true )
| ( ( in @ SV417 @ SV298 )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2134,plain,
! [SV256: $i,SV92: $i,SV300: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ SV300 ) )
= $true )
| ( ( in @ SV418 @ SV92 )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2135,plain,
! [SV92: $i,SV256: $i,SV300: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ SV300 ) )
= $true )
| ( ( ~ ( in @ SV419 @ SV256 ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2136,plain,
! [SV95: $i,SV390: $i,SV398: $i] :
( ( ( subset @ SV398 @ SV390 )
= $false )
| ( ( in @ SV390 @ ( sK7_B @ SV95 ) )
= $false )
| ( ( in @ SV398 @ ( sK7_B @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2137,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ! [SY784: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SY784 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY784 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2138,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2099]) ).
thf(2139,plain,
! [SV375: $i,SV216: $i,SV96: $i] :
( ( ( ~ ! [SY785: $i,SY786: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY785 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY786 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY785 @ SY786 ) @ SV375 ) ) )
= $false )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2140,plain,
! [SV96: $i,SV216: $i,SV375: $i] :
( ( ( ~ ! [SY788: $i,SY789: $i] :
( ~ ( in @ ( ordered_pair @ SY788 @ SY789 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SY788 @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) @ SY789 ) @ SV216 ) ) ) )
= $false )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2141,plain,
! [SV100: $i,SV323: $i] :
( ( ( in @ ( ordered_pair @ ( sK18_SY354 @ SV323 @ SV100 ) @ ( sK17_C @ SV323 @ SV100 ) ) @ SV100 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_C @ SV323 @ SV100 ) @ ( sK18_SY354 @ SV323 @ SV100 ) ) @ SV323 )
= $false )
| ( ( SV323
= ( relation_inverse @ SV100 ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2142,plain,
! [SV100: $i,SV324: $i,SV431: $i,SV420: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV420 @ SV431 ) @ SV324 )
| ( in @ ( ordered_pair @ SV431 @ SV420 ) @ SV100 ) )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2143,plain,
! [SV324: $i,SV100: $i,SV421: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV432 @ SV421 ) @ SV100 )
| ( in @ ( ordered_pair @ SV421 @ SV432 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2144,plain,
! [SV305: $i,SV101: $i,SV276: $i,SV399: $i] :
( ( ( in @ SV399 @ SV276 )
= $false )
| ( ( in @ SV399 @ SV101 )
= $false )
| ( ( in @ SV399 @ SV305 )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2145,plain,
! [SV276: $i,SV101: $i,SV305: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV305 ) )
= $true )
| ( ( in @ SV422 @ SV101 )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2146,plain,
! [SV101: $i,SV276: $i,SV305: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV305 ) )
= $true )
| ( ( in @ SV423 @ SV276 )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2107]) ).
thf(2147,plain,
! [SV409: $i,SV103: $i,SV356: $i] :
( ( ( in @ SV356 @ ( sK8_B @ SV103 ) )
= $false )
| ( ( in @ SV409 @ ( sK9_SY344 @ SV356 @ SV103 ) )
= $true )
| ( ( subset @ SV409 @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2148,plain,
! [SV103: $i,SV393: $i,SV400: $i] :
( ( ( subset @ SV400 @ SV393 )
= $false )
| ( ( in @ SV393 @ ( sK8_B @ SV103 ) )
= $false )
| ( ( in @ SV400 @ ( sK8_B @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2149,plain,
! [SV309: $i,SV284: $i,SV410: $i,SV105: $i,SV401: $i] :
( ( ( in @ SV401 @ SV105 )
= $false )
| ( ( ~ ( in @ SV410 @ SV284 ) )
= $true )
| ( ( ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SV401 @ SV410 ) ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2150,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 ) )
= $false )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2151,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( ~ ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 ) )
= $false )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2152,plain,
! [SV310: $i,SV402: $i,SV285: $i,SV424: $i,SV105: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV105 )
| ~ ( in @ SV424 @ SV285 ) )
= $true )
| ( ( ( SV402
!= ( ordered_pair @ SV414 @ SV424 ) ) )
= $true )
| ( ( in @ SV402 @ SV310 )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2153,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 ) ) )
= $false )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2154,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ( SV403
!= ( ordered_pair @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) ) ) )
= $false )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2155,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV106 )
= $false )
| ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
= $false )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2156,plain,
! [SV106: $i,SV287: $i,SV311: $i] :
( ( ( ( sK37_D @ SV311 @ SV287 @ SV106 )
= SV287 )
= $false )
| ( ( in @ ( sK37_D @ SV311 @ SV287 @ SV106 ) @ SV311 )
= $false )
| ( ( SV311
= ( unordered_pair @ SV106 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2157,plain,
! [SV288: $i,SV312: $i,SV106: $i,SV425: $i] :
( ( ( ( SV425 != SV106 ) )
= $true )
| ( ( in @ SV425 @ SV312 )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2158,plain,
! [SV106: $i,SV312: $i,SV288: $i,SV426: $i] :
( ( ( ( SV426 != SV288 ) )
= $true )
| ( ( in @ SV426 @ SV312 )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2159,plain,
! [SV335: $i,SV109: $i,SV412: $i,SV427: $i] :
( ( ( in @ ( ordered_pair @ SV427 @ SV412 ) @ SV109 )
= $false )
| ( ( in @ SV412 @ SV335 )
= $true )
| ( ( SV335
= ( relation_rng @ SV109 ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2160,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 ) )
= $false )
| ( ( ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2161,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) )
= $false )
| ( ( ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2162,plain,
! [SV369: $i,SV336: $i,SV428: $i] :
( ( ( ~ ( in @ SV428 @ SV336 ) )
= $true )
| ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV428 )
= $true )
| ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2163,plain,
! [SV337: $i,SV370: $i,SV429: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_D @ SV429 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SV429 @ ( sK41_D @ SV429 @ SV370 @ SV337 ) ) ) )
= $true )
| ( ( in @ SV429 @ SV370 )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2164,plain,
! [SV337: $i,SV370: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV370 ) )
= $true )
| ( ( ! [SY801: $i] :
( ~ ( in @ SY801 @ SV337 )
| ( in @ SV430 @ SY801 ) ) )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2165,plain,
! [SV254: $i,SV298: $i,SV91: $i,SV416: $i] :
( ( ( in @ SV416 @ SV91 )
= $false )
| ( ( in @ SV416 @ SV298 )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2166,plain,
! [SV91: $i,SV298: $i,SV254: $i,SV417: $i] :
( ( ( in @ SV417 @ SV254 )
= $false )
| ( ( in @ SV417 @ SV298 )
= $true )
| ( ( SV298
= ( set_union2 @ SV91 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2167,plain,
! [SV256: $i,SV92: $i,SV300: $i,SV418: $i] :
( ( ( in @ SV418 @ SV300 )
= $false )
| ( ( in @ SV418 @ SV92 )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2168,plain,
! [SV92: $i,SV256: $i,SV300: $i,SV419: $i] :
( ( ( in @ SV419 @ SV300 )
= $false )
| ( ( ~ ( in @ SV419 @ SV256 ) )
= $true )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2169,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ! [SY784: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SY784 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY784 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2170,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2171,plain,
! [SV375: $i,SV216: $i,SV96: $i] :
( ( ( ! [SY785: $i,SY786: $i] :
( ! [SY644: $i] :
( ~ ( in @ ( ordered_pair @ SY785 @ SY644 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY786 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SY785 @ SY786 ) @ SV375 ) ) )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2172,plain,
! [SV96: $i,SV216: $i,SV375: $i] :
( ( ( ! [SY788: $i,SY789: $i] :
( ~ ( in @ ( ordered_pair @ SY788 @ SY789 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SY788 @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY789 @ SY788 @ SV375 @ SV216 @ SV96 ) @ SY789 ) @ SV216 ) ) ) )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2173,plain,
! [SV100: $i,SV324: $i,SV431: $i,SV420: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV420 @ SV431 ) @ SV324 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV420 ) @ SV100 )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2174,plain,
! [SV324: $i,SV100: $i,SV421: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV432 @ SV421 ) @ SV100 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV421 @ SV432 ) @ SV324 )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2175,plain,
! [SV276: $i,SV101: $i,SV305: $i,SV422: $i] :
( ( ( in @ SV422 @ SV305 )
= $false )
| ( ( in @ SV422 @ SV101 )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2176,plain,
! [SV101: $i,SV276: $i,SV305: $i,SV423: $i] :
( ( ( in @ SV423 @ SV305 )
= $false )
| ( ( in @ SV423 @ SV276 )
= $true )
| ( ( SV305
= ( set_intersection2 @ SV101 @ SV276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2177,plain,
! [SV309: $i,SV105: $i,SV401: $i,SV284: $i,SV410: $i] :
( ( ( in @ SV410 @ SV284 )
= $false )
| ( ( in @ SV401 @ SV105 )
= $false )
| ( ( ( ( sK33_D @ SV309 @ SV284 @ SV105 )
!= ( ordered_pair @ SV401 @ SV410 ) ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2178,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( in @ ( sK34_SY364 @ SV309 @ SV284 @ SV105 ) @ SV105 )
= $true )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2179,plain,
! [SV105: $i,SV284: $i,SV309: $i] :
( ( ( in @ ( sK35_SY366 @ SV309 @ SV284 @ SV105 ) @ SV284 )
= $true )
| ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2180,plain,
! [SV310: $i,SV402: $i,SV285: $i,SV424: $i,SV105: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV105 ) )
= $true )
| ( ( ~ ( in @ SV424 @ SV285 ) )
= $true )
| ( ( ( SV402
!= ( ordered_pair @ SV414 @ SV424 ) ) )
= $true )
| ( ( in @ SV402 @ SV310 )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2181,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 ) ) )
= $true )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2153]) ).
thf(2182,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( SV403
= ( ordered_pair @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) ) )
= $true )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2154]) ).
thf(2183,plain,
! [SV288: $i,SV312: $i,SV106: $i,SV425: $i] :
( ( ( SV425 = SV106 )
= $false )
| ( ( in @ SV425 @ SV312 )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2184,plain,
! [SV106: $i,SV312: $i,SV288: $i,SV426: $i] :
( ( ( SV426 = SV288 )
= $false )
| ( ( in @ SV426 @ SV312 )
= $true )
| ( ( SV312
= ( unordered_pair @ SV106 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2185,plain,
! [SV336: $i,SV369: $i] :
( ( ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
= $true )
| ( ( ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2186,plain,
! [SV336: $i,SV369: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) ) )
= $true )
| ( ( ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2187,plain,
! [SV369: $i,SV336: $i,SV428: $i] :
( ( ( in @ SV428 @ SV336 )
= $false )
| ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV428 )
= $true )
| ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2188,plain,
! [SV337: $i,SV370: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK41_D @ SV429 @ SV370 @ SV337 ) @ SV337 )
| ~ ~ ( in @ SV429 @ ( sK41_D @ SV429 @ SV370 @ SV337 ) ) )
= $false )
| ( ( in @ SV429 @ SV370 )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2189,plain,
! [SV337: $i,SV370: $i,SV430: $i] :
( ( ( in @ SV430 @ SV370 )
= $false )
| ( ( ! [SY801: $i] :
( ~ ( in @ SY801 @ SV337 )
| ( in @ SV430 @ SY801 ) ) )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2190,plain,
! [SV92: $i,SV300: $i,SV256: $i,SV419: $i] :
( ( ( in @ SV419 @ SV256 )
= $false )
| ( ( in @ SV419 @ SV300 )
= $false )
| ( ( SV300
= ( set_difference @ SV92 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2191,plain,
! [SV433: $i,SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SV433 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SV433 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2192,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2193,plain,
! [SV375: $i,SV216: $i,SV96: $i,SV434: $i] :
( ( ( ! [SY802: $i] :
( ! [SY803: $i] :
( ~ ( in @ ( ordered_pair @ SV434 @ SY803 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY803 @ SY802 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SV434 @ SY802 ) @ SV375 ) ) )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2194,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV435: $i] :
( ( ( ! [SY804: $i] :
( ~ ( in @ ( ordered_pair @ SV435 @ SY804 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SV435 @ ( sK13_F @ SY804 @ SV435 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY804 @ SV435 @ SV375 @ SV216 @ SV96 ) @ SY804 ) @ SV216 ) ) ) )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2195,plain,
! [SV100: $i,SV324: $i,SV431: $i,SV420: $i] :
( ( ( in @ ( ordered_pair @ SV420 @ SV431 ) @ SV324 )
= $false )
| ( ( in @ ( ordered_pair @ SV431 @ SV420 ) @ SV100 )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2196,plain,
! [SV324: $i,SV100: $i,SV421: $i,SV432: $i] :
( ( ( in @ ( ordered_pair @ SV432 @ SV421 ) @ SV100 )
= $false )
| ( ( in @ ( ordered_pair @ SV421 @ SV432 ) @ SV324 )
= $true )
| ( ( SV324
= ( relation_inverse @ SV100 ) )
= $false )
| ( ( relation @ SV324 )
= $false )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2197,plain,
! [SV410: $i,SV401: $i,SV105: $i,SV284: $i,SV309: $i] :
( ( ( ( sK33_D @ SV309 @ SV284 @ SV105 )
= ( ordered_pair @ SV401 @ SV410 ) )
= $false )
| ( ( in @ SV401 @ SV105 )
= $false )
| ( ( in @ SV410 @ SV284 )
= $false )
| ( ( ~ ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2198,plain,
! [SV310: $i,SV402: $i,SV285: $i,SV424: $i,SV105: $i,SV414: $i] :
( ( ( in @ SV414 @ SV105 )
= $false )
| ( ( ~ ( in @ SV424 @ SV285 ) )
= $true )
| ( ( ( SV402
!= ( ordered_pair @ SV414 @ SV424 ) ) )
= $true )
| ( ( in @ SV402 @ SV310 )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2199,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ~ ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 )
| ~ ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
= $false )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2200,plain,
! [SV336: $i,SV369: $i] :
( ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 )
= $false )
| ( ( in @ ( sK43_SY367 @ SV369 @ SV336 ) @ SV336 )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2201,plain,
! [SV336: $i,SV369: $i] :
( ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) )
= $false )
| ( ( ~ ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 ) )
= $true )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2202,plain,
! [SV337: $i,SV370: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK41_D @ SV429 @ SV370 @ SV337 ) @ SV337 ) )
= $false )
| ( ( in @ SV429 @ SV370 )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2203,plain,
! [SV337: $i,SV370: $i,SV429: $i] :
( ( ( ~ ~ ( in @ SV429 @ ( sK41_D @ SV429 @ SV370 @ SV337 ) ) )
= $false )
| ( ( in @ SV429 @ SV370 )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2204,plain,
! [SV370: $i,SV430: $i,SV337: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ SV337 )
| ( in @ SV430 @ SV436 ) )
= $true )
| ( ( in @ SV430 @ SV370 )
= $false )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2205,plain,
! [SV433: $i,SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SV433 ) @ SV96 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV433 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2206,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2192]) ).
thf(2207,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2192]) ).
thf(2208,plain,
! [SV375: $i,SV216: $i,SV437: $i,SV96: $i,SV434: $i] :
( ( ( ! [SY805: $i] :
( ~ ( in @ ( ordered_pair @ SV434 @ SY805 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY805 @ SV437 ) @ SV216 ) )
| ( in @ ( ordered_pair @ SV434 @ SV437 ) @ SV375 ) )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2209,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV438: $i,SV435: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV435 @ SV438 ) @ SV375 )
| ~ ( ~ ( in @ ( ordered_pair @ SV435 @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) @ SV438 ) @ SV216 ) ) )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2210,plain,
! [SV401: $i,SV410: $i,SV105: $i,SV284: $i,SV309: $i] :
( ( ( in @ ( sK33_D @ SV309 @ SV284 @ SV105 ) @ SV309 )
= $false )
| ( ( in @ SV410 @ SV284 )
= $false )
| ( ( in @ SV401 @ SV105 )
= $false )
| ( ( ( sK33_D @ SV309 @ SV284 @ SV105 )
= ( ordered_pair @ SV401 @ SV410 ) )
= $false )
| ( ( SV309
= ( cartesian_product2 @ SV105 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2211,plain,
! [SV310: $i,SV402: $i,SV105: $i,SV414: $i,SV285: $i,SV424: $i] :
( ( ( in @ SV424 @ SV285 )
= $false )
| ( ( in @ SV414 @ SV105 )
= $false )
| ( ( ( SV402
!= ( ordered_pair @ SV414 @ SV424 ) ) )
= $true )
| ( ( in @ SV402 @ SV310 )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2212,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ~ ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 ) )
= $false )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2213,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( ~ ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 ) )
= $false )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2214,plain,
! [SV336: $i,SV369: $i] :
( ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ SV369 )
= $false )
| ( ( in @ ( sK42_C @ SV369 @ SV336 ) @ ( sK43_SY367 @ SV369 @ SV336 ) )
= $false )
| ( ( SV369
= ( set_meet @ SV336 ) )
= $true )
| ( ( SV336 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2215,plain,
! [SV337: $i,SV370: $i,SV429: $i] :
( ( ( in @ ( sK41_D @ SV429 @ SV370 @ SV337 ) @ SV337 )
= $true )
| ( ( in @ SV429 @ SV370 )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2216,plain,
! [SV337: $i,SV370: $i,SV429: $i] :
( ( ( ~ ( in @ SV429 @ ( sK41_D @ SV429 @ SV370 @ SV337 ) ) )
= $true )
| ( ( in @ SV429 @ SV370 )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2203]) ).
thf(2217,plain,
! [SV370: $i,SV430: $i,SV337: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ SV337 ) )
= $true )
| ( ( in @ SV430 @ SV436 )
= $true )
| ( ( in @ SV430 @ SV370 )
= $false )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2218,plain,
! [SV433: $i,SV96: $i,SV216: $i,SV374: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SV433 ) @ SV96 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV433 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2219,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) ) @ SV96 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2206]) ).
thf(2220,plain,
! [SV96: $i,SV216: $i,SV374: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY353 @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2221,plain,
! [SV375: $i,SV216: $i,SV437: $i,SV96: $i,SV434: $i] :
( ( ( ! [SY805: $i] :
( ~ ( in @ ( ordered_pair @ SV434 @ SY805 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SY805 @ SV437 ) @ SV216 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV434 @ SV437 ) @ SV375 )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2222,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV438: $i,SV435: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV435 @ SV438 ) @ SV375 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV435 @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) @ SV438 ) @ SV216 ) ) )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2223,plain,
! [SV310: $i,SV285: $i,SV105: $i,SV424: $i,SV414: $i,SV402: $i] :
( ( ( SV402
= ( ordered_pair @ SV414 @ SV424 ) )
= $false )
| ( ( in @ SV414 @ SV105 )
= $false )
| ( ( in @ SV424 @ SV285 )
= $false )
| ( ( in @ SV402 @ SV310 )
= $true )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2224,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( in @ ( sK31_E @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV105 )
= $true )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2225,plain,
! [SV105: $i,SV285: $i,SV310: $i,SV403: $i] :
( ( ( in @ ( sK32_SY361 @ SV403 @ SV310 @ SV285 @ SV105 ) @ SV285 )
= $true )
| ( ( in @ SV403 @ SV310 )
= $false )
| ( ( SV310
= ( cartesian_product2 @ SV105 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2226,plain,
! [SV337: $i,SV370: $i,SV429: $i] :
( ( ( in @ SV429 @ ( sK41_D @ SV429 @ SV370 @ SV337 ) )
= $false )
| ( ( in @ SV429 @ SV370 )
= $true )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2227,plain,
! [SV370: $i,SV430: $i,SV337: $i,SV436: $i] :
( ( ( in @ SV436 @ SV337 )
= $false )
| ( ( in @ SV430 @ SV436 )
= $true )
| ( ( in @ SV430 @ SV370 )
= $false )
| ( ( SV370
= ( set_meet @ SV337 ) )
= $false )
| ( ( SV337 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2228,plain,
! [SV96: $i,SV216: $i,SV374: $i,SV433: $i] :
( ( ( in @ ( ordered_pair @ SV433 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SV433 ) @ SV96 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2229,plain,
! [SV375: $i,SV216: $i,SV437: $i,SV96: $i,SV439: $i,SV434: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV434 @ SV439 ) @ SV96 )
| ~ ( in @ ( ordered_pair @ SV439 @ SV437 ) @ SV216 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV434 @ SV437 ) @ SV375 )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2230,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV438: $i,SV435: $i] :
( ( ( in @ ( ordered_pair @ SV435 @ SV438 ) @ SV375 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV435 @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) @ SV438 ) @ SV216 ) ) )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2231,plain,
! [SV433: $i,SV96: $i,SV216: $i,SV374: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV374 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV374 @ SV216 @ SV96 ) @ SV433 ) @ SV96 )
= $false )
| ( ( in @ ( ordered_pair @ SV433 @ ( sK15_SY349 @ SV374 @ SV216 @ SV96 ) ) @ SV216 )
= $false )
| ( ( SV374
= ( relation_composition @ SV96 @ SV216 ) )
= $true )
| ( ( relation @ SV374 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2232,plain,
! [SV375: $i,SV216: $i,SV437: $i,SV96: $i,SV439: $i,SV434: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV434 @ SV439 ) @ SV96 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV439 @ SV437 ) @ SV216 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV434 @ SV437 ) @ SV375 )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2233,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV438: $i,SV435: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV435 @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) @ SV438 ) @ SV216 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV435 @ SV438 ) @ SV375 )
= $false )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2234,plain,
! [SV375: $i,SV216: $i,SV437: $i,SV96: $i,SV439: $i,SV434: $i] :
( ( ( in @ ( ordered_pair @ SV434 @ SV439 ) @ SV96 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV439 @ SV437 ) @ SV216 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV434 @ SV437 ) @ SV375 )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2235,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV438: $i,SV435: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV435 @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) ) @ SV96 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV435 @ SV438 ) @ SV375 )
= $false )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2233]) ).
thf(2236,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV435: $i,SV438: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) @ SV438 ) @ SV216 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV435 @ SV438 ) @ SV375 )
= $false )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2233]) ).
thf(2237,plain,
! [SV375: $i,SV96: $i,SV434: $i,SV216: $i,SV437: $i,SV439: $i] :
( ( ( in @ ( ordered_pair @ SV439 @ SV437 ) @ SV216 )
= $false )
| ( ( in @ ( ordered_pair @ SV434 @ SV439 ) @ SV96 )
= $false )
| ( ( in @ ( ordered_pair @ SV434 @ SV437 ) @ SV375 )
= $true )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2238,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV438: $i,SV435: $i] :
( ( ( in @ ( ordered_pair @ SV435 @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) ) @ SV96 )
= $true )
| ( ( in @ ( ordered_pair @ SV435 @ SV438 ) @ SV375 )
= $false )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2235]) ).
thf(2239,plain,
! [SV96: $i,SV216: $i,SV375: $i,SV435: $i,SV438: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_F @ SV438 @ SV435 @ SV375 @ SV216 @ SV96 ) @ SV438 ) @ SV216 )
= $true )
| ( ( in @ ( ordered_pair @ SV435 @ SV438 ) @ SV375 )
= $false )
| ( ( SV375
= ( relation_composition @ SV96 @ SV216 ) )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2236]) ).
thf(2240,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[443,2239,2238,2237,2231,2227,2226,2225,2224,2223,2220,2219,2215,2214,2210,2200,2196,2195,2190,2187,2184,2183,2182,2179,2178,2176,2175,2167,2166,2165,2159,2156,2155,2148,2147,2144,2141,2136,2131,2130,2129,2128,2127,2126,2121,2119,2116,2104,2094,2093,2090,2084,2083,2081,2066,2058,2057,2053,2044,2043,2013,2001,2000,1983,1982,1977,1976,1975,1974,1973,1972,1966,1964,1963,1960,1953,1952,1940,1939,1936,1925,1915,1911,1908,1907,1906,1905,1894,1883,1873,1872,1866,1862,1861,1836,1830,1829,1818,1817,1809,1808,1807,1806,1805,1802,1801,1788,1783,1781,1778,1760,1758,1757,1752,1750,1721,1706,1705,1699,1698,1673,1670,1669,1663,1658,1649,1645,1640,1632,1626,1603,1602,1601,1581,1580,1578,1577,1576,1568,1567,1558,1557,1534,1533,1510,1509,1508,1507,1502,1501,1500,1499,1496,1495,1477,1476,1475,1474,1469,1468,1466,1465,1464,1456,1439,1438,1437,1434,1366,1363,1354,1352,1351,1346,1344,1343,1317,1315,1240,1238,1237,1234,1226,1225,1219,1217,1214,1212,1209,1208,1203,1122,1120,1119,1118,1117,1115,1114,1113,1111,1110,1109,1108,1104,1096,1092,1088,1081,1077,1076,1075,1072,1069,1068,1061,987,986,983,972,965,946,938,934,932,930,929,925,922,830,829,821,820,819,815,809,802,801,800,793,778,767,716,711,707,704,703,696,690,683,678,649,648,646,644,632,574,562,481]) ).
thf(2241,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU186+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 03:06:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.41 ....
% 0.20/0.47
% 0.20/0.47 No.of.Axioms: 163
% 0.20/0.47
% 0.20/0.47 Length.of.Defs: 0
% 0.20/0.47
% 0.20/0.47 Contains.Choice.Funs: false
% 0.20/0.51 ..........
% 0.20/0.55 (rf:2,axioms:142,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:165,loop_count:0,foatp_calls:0,translation:fof_full)........................................................................................................................................................................
% 9.91/10.09
% 9.91/10.09 ********************************
% 9.91/10.09 * All subproblems solved! *
% 9.91/10.09 ********************************
% 9.91/10.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:144,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2240,loop_count:0,foatp_calls:1,translation:fof_full)
% 11.42/11.63
% 11.42/11.63 %**** Beginning of derivation protocol ****
% 11.42/11.63 % SZS output start CNFRefutation
% See solution above
% 11.46/11.64
% 11.46/11.64 %**** End of derivation protocol ****
% 11.46/11.64 %**** no. of clauses in derivation: 2220 ****
% 11.46/11.64 %**** clause counter: 2240 ****
% 11.46/11.64
% 11.46/11.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:144,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2240,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------