%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU187+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:20 AM UTC 2026
% Result : Theorem 5.58s 1.31s
% Output : CNFRefutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 49
% Syntax : Number of formulae : 1020 ( 392 unt; 0 typ; 0 def)
% Number of atoms : 8439 (3452 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 14719 (3284 ~;2796 |; 35 &;8432 @)
% ( 52 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 58 usr; 3 con; 0-3 aty)
% Number of variables : 2554 ( 0 ^;2546 !; 8 ?;2554 :)
% 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_SY116,type,
sK10_SY116: $i > $i > $i ).
thf(tp_sK11_SY122,type,
sK11_SY122: $i > $i > $i > $i ).
thf(tp_sK12_SY120,type,
sK12_SY120: $i > $i > $i ).
thf(tp_sK13_SY116,type,
sK13_SY116: $i > $i > $i > $i ).
thf(tp_sK14_SY120,type,
sK14_SY120: $i > $i > $i > $i ).
thf(tp_sK15_SY142,type,
sK15_SY142: $i > $i ).
thf(tp_sK16_SY139,type,
sK16_SY139: $i > $i ).
thf(tp_sK17_SY182,type,
sK17_SY182: $i > $i ).
thf(tp_sK18_SY173,type,
sK18_SY173: $i > $i > $i ).
thf(tp_sK19_SY179,type,
sK19_SY179: $i > $i > $i ).
thf(tp_sK1_SY67,type,
sK1_SY67: $i > $i ).
thf(tp_sK20_SY167,type,
sK20_SY167: $i > $i > $i ).
thf(tp_sK21_SY183,type,
sK21_SY183: $i > $i > $i > $i ).
thf(tp_sK22_SY187,type,
sK22_SY187: $i > $i > $i > $i ).
thf(tp_sK23_SY193,type,
sK23_SY193: $i > $i > $i ).
thf(tp_sK24_SY186,type,
sK24_SY186: $i > $i > $i ).
thf(tp_sK25_SY192,type,
sK25_SY192: $i > $i > $i > $i ).
thf(tp_sK26_SY190,type,
sK26_SY190: $i > $i > $i ).
thf(tp_sK27_SY186,type,
sK27_SY186: $i > $i > $i > $i ).
thf(tp_sK28_SY190,type,
sK28_SY190: $i > $i > $i > $i ).
thf(tp_sK2_SY112,type,
sK2_SY112: $i > $i ).
thf(tp_sK3_SY80,type,
sK3_SY80: $i > $i ).
thf(tp_sK4_SY103,type,
sK4_SY103: $i > $i > $i ).
thf(tp_sK5_SY109,type,
sK5_SY109: $i > $i > $i ).
thf(tp_sK6_SY96,type,
sK6_SY96: $i > $i > $i ).
thf(tp_sK7_SY113,type,
sK7_SY113: $i > $i > $i > $i ).
thf(tp_sK8_SY117,type,
sK8_SY117: $i > $i > $i > $i ).
thf(tp_sK9_SY123,type,
sK9_SY123: $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(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(7,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(9,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(12,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(14,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(32,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(35,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(42,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(45,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(51,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(52,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(54,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(55,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(57,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(58,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(59,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(60,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(62,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(63,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(64,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(65,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(66,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(67,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(71,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(73,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(76,axiom,
! [A: $i] :
( ( 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(80,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(88,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(90,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(111,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(118,axiom,
! [A: $i] :
( ( 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(120,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(121,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(123,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(124,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(127,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(134,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(139,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(142,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(143,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(144,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(145,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(158,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(161,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(166,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(167,conjecture,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(168,negated_conjecture,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $false ),
inference(negate_conjecture,[status(cth)],[167]) ).
thf(169,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $false ),
inference(unfold_def,[status(thm)],[168]) ).
thf(170,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(171,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(172,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(173,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(174,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(175,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(176,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(177,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(178,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(179,plain,
$true = $true,
inference(unfold_def,[status(thm)],[45]) ).
thf(180,plain,
$true = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(181,plain,
$true = $true,
inference(unfold_def,[status(thm)],[52]) ).
thf(182,plain,
$true = $true,
inference(unfold_def,[status(thm)],[54]) ).
thf(183,plain,
$true = $true,
inference(unfold_def,[status(thm)],[55]) ).
thf(184,plain,
$true = $true,
inference(unfold_def,[status(thm)],[57]) ).
thf(185,plain,
$true = $true,
inference(unfold_def,[status(thm)],[58]) ).
thf(186,plain,
$true = $true,
inference(unfold_def,[status(thm)],[59]) ).
thf(187,plain,
$true = $true,
inference(unfold_def,[status(thm)],[60]) ).
thf(188,plain,
$true = $true,
inference(unfold_def,[status(thm)],[62]) ).
thf(189,plain,
$true = $true,
inference(unfold_def,[status(thm)],[63]) ).
thf(190,plain,
$true = $true,
inference(unfold_def,[status(thm)],[64]) ).
thf(191,plain,
$true = $true,
inference(unfold_def,[status(thm)],[65]) ).
thf(192,plain,
$true = $true,
inference(unfold_def,[status(thm)],[66]) ).
thf(193,plain,
$true = $true,
inference(unfold_def,[status(thm)],[67]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(195,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(196,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)],[76]) ).
thf(197,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)],[80]) ).
thf(198,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(199,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)],[90]) ).
thf(200,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(201,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)],[118]) ).
thf(202,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)],[120]) ).
thf(203,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)],[121]) ).
thf(204,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)],[123]) ).
thf(205,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)],[124]) ).
thf(206,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(207,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(208,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(209,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)],[134]) ).
thf(210,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(211,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)],[142]) ).
thf(212,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(213,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)],[144]) ).
thf(214,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(216,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(217,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(218,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[169]) ).
thf(219,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[169]) ).
thf(220,plain,
( ( ( relation_dom @ empty_set )
!= empty_set )
= $true ),
inference(polarity_switch,[status(thm)],[218]) ).
thf(221,plain,
( ( ( relation_rng @ empty_set )
!= empty_set )
= $true ),
inference(polarity_switch,[status(thm)],[219]) ).
thf(222,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(225,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(226,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(copy,[status(thm)],[213]) ).
thf(227,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(228,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(copy,[status(thm)],[211]) ).
thf(229,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(230,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(233,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(234,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(235,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(236,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)],[203]) ).
thf(237,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)],[202]) ).
thf(238,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)],[201]) ).
thf(239,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(240,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(copy,[status(thm)],[199]) ).
thf(241,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(242,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(copy,[status(thm)],[197]) ).
thf(243,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(copy,[status(thm)],[196]) ).
thf(244,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(246,plain,
$true = $true,
inference(copy,[status(thm)],[193]) ).
thf(247,plain,
$true = $true,
inference(copy,[status(thm)],[192]) ).
thf(248,plain,
$true = $true,
inference(copy,[status(thm)],[191]) ).
thf(249,plain,
$true = $true,
inference(copy,[status(thm)],[190]) ).
thf(250,plain,
$true = $true,
inference(copy,[status(thm)],[189]) ).
thf(251,plain,
$true = $true,
inference(copy,[status(thm)],[188]) ).
thf(252,plain,
$true = $true,
inference(copy,[status(thm)],[187]) ).
thf(253,plain,
$true = $true,
inference(copy,[status(thm)],[186]) ).
thf(254,plain,
$true = $true,
inference(copy,[status(thm)],[185]) ).
thf(255,plain,
$true = $true,
inference(copy,[status(thm)],[184]) ).
thf(256,plain,
$true = $true,
inference(copy,[status(thm)],[183]) ).
thf(257,plain,
$true = $true,
inference(copy,[status(thm)],[182]) ).
thf(258,plain,
$true = $true,
inference(copy,[status(thm)],[181]) ).
thf(259,plain,
$true = $true,
inference(copy,[status(thm)],[180]) ).
thf(260,plain,
$true = $true,
inference(copy,[status(thm)],[179]) ).
thf(261,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(262,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(263,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(264,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(265,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(266,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(267,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(268,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(269,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(270,plain,
( ( ( relation_dom @ empty_set )
!= empty_set )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(271,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX1 ) )
| ( ( relation_rng @ ( relation_composition @ SX1 @ SX0 ) )
= ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(272,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(273,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(274,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(275,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_dom @ SX1 ) )
| ( ( relation_dom @ ( relation_composition @ SX0 @ SX1 ) )
= ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(276,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(277,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(278,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_field @ SX0 )
= ( set_union2 @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(279,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(280,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(281,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( subset @ SX0 @ ( cartesian_product2 @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(282,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ! [SX1: $i,SX2: $i] :
~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(283,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ( ( relation_rng @ SX0 )
!= ( relation_dom @ ( relation_inverse @ SX0 ) ) )
| ( ( relation_dom @ SX0 )
!= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(284,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
| ~ ( ( SX0 != empty_set )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) )
| ~ ( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(285,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(286,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(287,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(288,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(289,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(290,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(291,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(292,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(293,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(294,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(295,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(296,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_rng @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(297,plain,
! [SV1: $i] :
( ( subset @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(298,plain,
! [SV2: $i] :
( ( ( set_union2 @ SV2 @ empty_set )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(299,plain,
! [SV3: $i] :
( ( ( set_intersection2 @ SV3 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(300,plain,
! [SV4: $i] :
( ( ( set_difference @ SV4 @ empty_set )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(301,plain,
! [SV5: $i] :
( ( ( set_difference @ empty_set @ SV5 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(302,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(303,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ! [SY55: $i] :
( ~ ( relation @ SY55 )
| ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_rng @ SY55 ) )
| ( ( relation_rng @ ( relation_composition @ SY55 @ SV6 ) )
= ( relation_rng @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(304,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV7 )
| ~ ( relation @ SV7 ) )
| ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(305,plain,
! [SV8: $i] :
( ( ! [SY56: $i] :
~ ( ~ ( ~ ( subset @ SV8 @ ( singleton @ SY56 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SY56 ) ) )
| ~ ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SY56 ) ) )
| ( subset @ SV8 @ ( singleton @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(306,plain,
! [SV9: $i] :
( ( ! [SY57: $i] :
~ ( ~ ( ( ( set_difference @ SV9 @ SY57 )
!= empty_set )
| ( subset @ SV9 @ SY57 ) )
| ~ ( ~ ( subset @ SV9 @ SY57 )
| ( ( set_difference @ SV9 @ SY57 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(307,plain,
! [SV10: $i] :
( ( ~ ( relation @ SV10 )
| ! [SY58: $i] :
( ~ ( relation @ SY58 )
| ~ ( subset @ ( relation_rng @ SV10 ) @ ( relation_dom @ SY58 ) )
| ( ( relation_dom @ ( relation_composition @ SV10 @ SY58 ) )
= ( relation_dom @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(308,plain,
! [SV11: $i] :
( ( ~ ( subset @ SV11 @ empty_set )
| ( SV11 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(309,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ! [SY59: $i] :
~ ( ~ ( ( SY59
!= ( relation_rng @ SV12 ) )
| ! [SY60: $i] :
~ ( ~ ( ~ ( in @ SY60 @ SY59 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY60 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY60 ) @ SV12 )
| ( in @ SY60 @ SY59 ) ) ) )
| ~ ( ~ ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SY59 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY63 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY63 ) @ SV12 )
| ( in @ SY63 @ SY59 ) ) )
| ( SY59
= ( relation_rng @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(310,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ( ( relation_field @ SV13 )
= ( set_union2 @ ( relation_dom @ SV13 ) @ ( relation_rng @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(311,plain,
! [SV14: $i] :
( ( ~ ( empty @ SV14 )
| ( SV14 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(312,plain,
! [SV15: $i] :
( ( ~ ( relation @ SV15 )
| ! [SY66: $i] :
( ~ ( relation @ SY66 )
| ~ ( subset @ SV15 @ SY66 )
| ~ ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SY66 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SY66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(313,plain,
! [SV16: $i] :
( ( ~ ( relation @ SV16 )
| ( subset @ SV16 @ ( cartesian_product2 @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(314,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ~ ! [SY67: $i,SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( SV17 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(315,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ~ ( ( ( relation_rng @ SV18 )
!= ( relation_dom @ ( relation_inverse @ SV18 ) ) )
| ( ( relation_dom @ SV18 )
!= ( relation_rng @ ( relation_inverse @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(316,plain,
! [SV19: $i] :
( ( ! [SY69: $i] :
~ ( ~ ( ~ ( ( SV19 != empty_set ) )
| ~ ( ~ ( ( SY69
!= ( set_meet @ SV19 ) )
| ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY70 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY70 @ SY72 ) )
| ( in @ SY70 @ SY69 ) ) ) )
| ~ ( ~ ! [SY73: $i] :
~ ( ~ ( ~ ( in @ SY73 @ SY69 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY73 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY73 @ SY75 ) )
| ( in @ SY73 @ SY69 ) ) )
| ( SY69
= ( set_meet @ SV19 ) ) ) ) )
| ~ ( ( SV19 != empty_set )
| ~ ( ~ ( ( SY69
!= ( set_meet @ SV19 ) )
| ( SY69 = empty_set ) )
| ~ ( ( SY69 != empty_set )
| ( SY69
= ( set_meet @ SV19 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(317,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ! [SY76: $i] :
( ~ ( relation @ SY76 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV20 @ SY76 ) ) @ ( relation_dom @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(318,plain,
! [SV21: $i] :
( ( ! [SY77: $i] :
~ ( ~ ( ~ ( disjoint @ SV21 @ SY77 )
| ( ( set_intersection2 @ SV21 @ SY77 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV21 @ SY77 )
!= empty_set )
| ( disjoint @ SV21 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(319,plain,
! [SV22: $i] :
( ( ! [SY78: $i] :
~ ( ~ ( ~ ( subset @ SV22 @ ( singleton @ SY78 ) )
| ( SV22 = empty_set )
| ( SV22
= ( singleton @ SY78 ) ) )
| ~ ( ~ ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SY78 ) ) )
| ( subset @ SV22 @ ( singleton @ SY78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(320,plain,
! [SV23: $i] :
( ( ( singleton @ SV23 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(321,plain,
! [SV24: $i] :
( ( ~ ( ~ ( ( SV24 != empty_set )
| ! [SY79: $i] :
~ ( in @ SY79 @ SV24 ) )
| ~ ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV24 )
| ( SV24 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(322,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(323,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV25 )
| ~ ( relation @ SV25 ) )
| ~ ( empty @ ( relation_rng @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(324,plain,
! [SV26: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ( relation @ SY82 )
| ~ ( in @ ( ordered_pair @ SV26 @ SY81 ) @ SY82 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SY82 ) )
| ~ ( in @ SY81 @ ( relation_rng @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(325,plain,
! [SV27: $i] :
( ( ! [SY83: $i] :
( ~ ( element @ SY83 @ ( powerset @ ( powerset @ SV27 ) ) )
| ~ ~ ( ~ ( ( SY83 != empty_set ) )
| ( ( complements_of_subsets @ SV27 @ SY83 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(326,plain,
! [SV28: $i] :
( ( ! [SY84: $i] :
~ ( ~ ( ( ( set_difference @ SV28 @ SY84 )
!= empty_set )
| ( subset @ SV28 @ SY84 ) )
| ~ ( ~ ( subset @ SV28 @ SY84 )
| ( ( set_difference @ SV28 @ SY84 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(327,plain,
! [SV29: $i] :
( ( ~ ( relation @ SV29 )
| ! [SY85: $i] :
~ ( ~ ( ( SY85
!= ( relation_dom @ SV29 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SY85 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV29 )
| ( in @ SY86 @ SY85 ) ) ) )
| ~ ( ~ ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SY85 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY89 @ SY91 ) @ SV29 )
| ( in @ SY89 @ SY85 ) ) )
| ( SY85
= ( relation_dom @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(328,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ! [SY92: $i] :
( ~ ( relation @ SY92 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY92 ) ) @ ( relation_rng @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(329,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ! [SY55: $i] :
( ~ ( relation @ SY55 )
| ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_rng @ SY55 ) )
| ( ( relation_rng @ ( relation_composition @ SY55 @ SV6 ) )
= ( relation_rng @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(330,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV7 )
| ~ ( relation @ SV7 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(331,plain,
! [SV31: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV8 @ ( singleton @ SV31 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
| ~ ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
| ( subset @ SV8 @ ( singleton @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(332,plain,
! [SV32: $i,SV9: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV9 @ SV32 )
!= empty_set )
| ( subset @ SV9 @ SV32 ) )
| ~ ( ~ ( subset @ SV9 @ SV32 )
| ( ( set_difference @ SV9 @ SV32 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(333,plain,
! [SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( relation @ SY58 )
| ~ ( subset @ ( relation_rng @ SV10 ) @ ( relation_dom @ SY58 ) )
| ( ( relation_dom @ ( relation_composition @ SV10 @ SY58 ) )
= ( relation_dom @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(334,plain,
! [SV11: $i] :
( ( ( ~ ( subset @ SV11 @ empty_set ) )
= $true )
| ( ( SV11 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(335,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( ! [SY59: $i] :
~ ( ~ ( ( SY59
!= ( relation_rng @ SV12 ) )
| ! [SY60: $i] :
~ ( ~ ( ~ ( in @ SY60 @ SY59 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY60 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY60 ) @ SV12 )
| ( in @ SY60 @ SY59 ) ) ) )
| ~ ( ~ ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SY59 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY63 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY63 ) @ SV12 )
| ( in @ SY63 @ SY59 ) ) )
| ( SY59
= ( relation_rng @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(336,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ( relation_field @ SV13 )
= ( set_union2 @ ( relation_dom @ SV13 ) @ ( relation_rng @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(337,plain,
! [SV14: $i] :
( ( ( ~ ( empty @ SV14 ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(338,plain,
! [SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( relation @ SY66 )
| ~ ( subset @ SV15 @ SY66 )
| ~ ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SY66 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SY66 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(339,plain,
! [SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( subset @ SV16 @ ( cartesian_product2 @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(340,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ! [SY67: $i,SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( SV17 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(341,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( ( ( relation_rng @ SV18 )
!= ( relation_dom @ ( relation_inverse @ SV18 ) ) )
| ( ( relation_dom @ SV18 )
!= ( relation_rng @ ( relation_inverse @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(342,plain,
! [SV33: $i,SV19: $i] :
( ( ~ ( ~ ( ~ ( ( SV19 != empty_set ) )
| ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
| ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
| ~ ( ( SV19 != empty_set )
| ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) )
| ~ ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(343,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ! [SY76: $i] :
( ~ ( relation @ SY76 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV20 @ SY76 ) ) @ ( relation_dom @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(344,plain,
! [SV34: $i,SV21: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV21 @ SV34 )
| ( ( set_intersection2 @ SV21 @ SV34 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV21 @ SV34 )
!= empty_set )
| ( disjoint @ SV21 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(345,plain,
! [SV35: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV22 @ ( singleton @ SV35 ) )
| ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
| ~ ( ~ ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
| ( subset @ SV22 @ ( singleton @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(346,plain,
! [SV23: $i] :
( ( ( singleton @ SV23 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(347,plain,
! [SV24: $i] :
( ( ~ ( ( SV24 != empty_set )
| ! [SY79: $i] :
~ ( in @ SY79 @ SV24 ) )
| ~ ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV24 )
| ( SV24 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(348,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(349,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(350,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV25 )
| ~ ( relation @ SV25 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(351,plain,
! [SV36: $i,SV26: $i] :
( ( ! [SY99: $i] :
( ~ ( relation @ SY99 )
| ~ ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SY99 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SY99 ) )
| ~ ( in @ SV36 @ ( relation_rng @ SY99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(352,plain,
! [SV27: $i,SV37: $i] :
( ( ~ ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) )
| ~ ~ ( ~ ( ( SV37 != empty_set ) )
| ( ( complements_of_subsets @ SV27 @ SV37 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(353,plain,
! [SV38: $i,SV28: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV28 @ SV38 )
!= empty_set )
| ( subset @ SV28 @ SV38 ) )
| ~ ( ~ ( subset @ SV28 @ SV38 )
| ( ( set_difference @ SV28 @ SV38 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(354,plain,
! [SV29: $i] :
( ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ! [SY85: $i] :
~ ( ~ ( ( SY85
!= ( relation_dom @ SV29 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SY85 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV29 )
| ( in @ SY86 @ SY85 ) ) ) )
| ~ ( ~ ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SY85 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY89 @ SY91 ) @ SV29 )
| ( in @ SY89 @ SY85 ) ) )
| ( SY85
= ( relation_dom @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(355,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ! [SY92: $i] :
( ~ ( relation @ SY92 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY92 ) ) @ ( relation_rng @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(356,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ! [SY55: $i] :
( ~ ( relation @ SY55 )
| ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_rng @ SY55 ) )
| ( ( relation_rng @ ( relation_composition @ SY55 @ SV6 ) )
= ( relation_rng @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(357,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV7 )
| ~ ( relation @ SV7 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(358,plain,
! [SV31: $i,SV8: $i] :
( ( ~ ( ~ ( subset @ SV8 @ ( singleton @ SV31 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
| ~ ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
| ( subset @ SV8 @ ( singleton @ SV31 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(359,plain,
! [SV32: $i,SV9: $i] :
( ( ~ ( ( ( set_difference @ SV9 @ SV32 )
!= empty_set )
| ( subset @ SV9 @ SV32 ) )
| ~ ( ~ ( subset @ SV9 @ SV32 )
| ( ( set_difference @ SV9 @ SV32 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(360,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( relation @ SY58 )
| ~ ( subset @ ( relation_rng @ SV10 ) @ ( relation_dom @ SY58 ) )
| ( ( relation_dom @ ( relation_composition @ SV10 @ SY58 ) )
= ( relation_dom @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(361,plain,
! [SV11: $i] :
( ( ( subset @ SV11 @ empty_set )
= $false )
| ( ( SV11 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(362,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( ! [SY59: $i] :
~ ( ~ ( ( SY59
!= ( relation_rng @ SV12 ) )
| ! [SY60: $i] :
~ ( ~ ( ~ ( in @ SY60 @ SY59 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY60 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY60 ) @ SV12 )
| ( in @ SY60 @ SY59 ) ) ) )
| ~ ( ~ ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SY59 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY63 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY63 ) @ SV12 )
| ( in @ SY63 @ SY59 ) ) )
| ( SY59
= ( relation_rng @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(363,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ( relation_field @ SV13 )
= ( set_union2 @ ( relation_dom @ SV13 ) @ ( relation_rng @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(364,plain,
! [SV14: $i] :
( ( ( empty @ SV14 )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(365,plain,
! [SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( relation @ SY66 )
| ~ ( subset @ SV15 @ SY66 )
| ~ ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SY66 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SY66 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(366,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( subset @ SV16 @ ( cartesian_product2 @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(367,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ~ ! [SY67: $i,SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( SV17 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(368,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ( ( ( relation_rng @ SV18 )
!= ( relation_dom @ ( relation_inverse @ SV18 ) ) )
| ( ( relation_dom @ SV18 )
!= ( relation_rng @ ( relation_inverse @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(369,plain,
! [SV33: $i,SV19: $i] :
( ( ~ ( ~ ( ( SV19 != empty_set ) )
| ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
| ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
| ~ ( ( SV19 != empty_set )
| ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) )
| ~ ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(370,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ! [SY76: $i] :
( ~ ( relation @ SY76 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV20 @ SY76 ) ) @ ( relation_dom @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(371,plain,
! [SV34: $i,SV21: $i] :
( ( ~ ( ~ ( disjoint @ SV21 @ SV34 )
| ( ( set_intersection2 @ SV21 @ SV34 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV21 @ SV34 )
!= empty_set )
| ( disjoint @ SV21 @ SV34 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(372,plain,
! [SV35: $i,SV22: $i] :
( ( ~ ( ~ ( subset @ SV22 @ ( singleton @ SV35 ) )
| ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
| ~ ( ~ ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
| ( subset @ SV22 @ ( singleton @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(373,plain,
! [SV24: $i] :
( ( ~ ( ( SV24 != empty_set )
| ! [SY79: $i] :
~ ( in @ SY79 @ SV24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(374,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV24 )
| ( SV24 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(375,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(376,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(377,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV25 )
| ~ ( relation @ SV25 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(378,plain,
! [SV36: $i,SV26: $i,SV39: $i] :
( ( ~ ( relation @ SV39 )
| ~ ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV39 ) )
| ~ ( in @ SV36 @ ( relation_rng @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(379,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV37 != empty_set ) )
| ( ( complements_of_subsets @ SV27 @ SV37 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(380,plain,
! [SV38: $i,SV28: $i] :
( ( ~ ( ( ( set_difference @ SV28 @ SV38 )
!= empty_set )
| ( subset @ SV28 @ SV38 ) )
| ~ ( ~ ( subset @ SV28 @ SV38 )
| ( ( set_difference @ SV28 @ SV38 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(381,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( ! [SY85: $i] :
~ ( ~ ( ( SY85
!= ( relation_dom @ SV29 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SY85 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV29 )
| ( in @ SY86 @ SY85 ) ) ) )
| ~ ( ~ ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SY85 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY89 @ SY91 ) @ SV29 )
| ( in @ SY89 @ SY85 ) ) )
| ( SY85
= ( relation_dom @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(382,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ! [SY92: $i] :
( ~ ( relation @ SY92 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY92 ) ) @ ( relation_rng @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(383,plain,
! [SV6: $i,SV40: $i] :
( ( ( ~ ( relation @ SV40 )
| ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_rng @ SV40 ) )
| ( ( relation_rng @ ( relation_composition @ SV40 @ SV6 ) )
= ( relation_rng @ SV6 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(384,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty @ SV7 )
| ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(385,plain,
! [SV31: $i,SV8: $i] :
( ( ~ ( ~ ( subset @ SV8 @ ( singleton @ SV31 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(386,plain,
! [SV31: $i,SV8: $i] :
( ( ~ ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
| ( subset @ SV8 @ ( singleton @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(387,plain,
! [SV32: $i,SV9: $i] :
( ( ~ ( ( ( set_difference @ SV9 @ SV32 )
!= empty_set )
| ( subset @ SV9 @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(388,plain,
! [SV32: $i,SV9: $i] :
( ( ~ ( ~ ( subset @ SV9 @ SV32 )
| ( ( set_difference @ SV9 @ SV32 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(389,plain,
! [SV10: $i,SV41: $i] :
( ( ( ~ ( relation @ SV41 )
| ~ ( subset @ ( relation_rng @ SV10 ) @ ( relation_dom @ SV41 ) )
| ( ( relation_dom @ ( relation_composition @ SV10 @ SV41 ) )
= ( relation_dom @ SV10 ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(390,plain,
! [SV12: $i,SV42: $i] :
( ( ( ~ ( ~ ( ( SV42
!= ( relation_rng @ SV12 ) )
| ! [SY100: $i] :
~ ( ~ ( ~ ( in @ SY100 @ SV42 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY100 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY100 ) @ SV12 )
| ( in @ SY100 @ SV42 ) ) ) )
| ~ ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV42 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY103 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY103 ) @ SV12 )
| ( in @ SY103 @ SV42 ) ) )
| ( SV42
= ( relation_rng @ SV12 ) ) ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(391,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( relation @ SV43 )
| ~ ( subset @ SV15 @ SV43 )
| ~ ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SV43 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SV43 ) ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(392,plain,
! [SV17: $i] :
( ( ( ~ ! [SY67: $i,SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 ) )
= $true )
| ( ( SV17 = empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(393,plain,
! [SV18: $i] :
( ( ( ( ( relation_rng @ SV18 )
!= ( relation_dom @ ( relation_inverse @ SV18 ) ) )
| ( ( relation_dom @ SV18 )
!= ( relation_rng @ ( relation_inverse @ SV18 ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(394,plain,
! [SV33: $i,SV19: $i] :
( ( ~ ( ~ ( ( SV19 != empty_set ) )
| ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
| ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(395,plain,
! [SV33: $i,SV19: $i] :
( ( ~ ( ( SV19 != empty_set )
| ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) )
| ~ ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(396,plain,
! [SV20: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV20 @ SV44 ) ) @ ( relation_dom @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(397,plain,
! [SV34: $i,SV21: $i] :
( ( ~ ( ~ ( disjoint @ SV21 @ SV34 )
| ( ( set_intersection2 @ SV21 @ SV34 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(398,plain,
! [SV34: $i,SV21: $i] :
( ( ~ ( ( ( set_intersection2 @ SV21 @ SV34 )
!= empty_set )
| ( disjoint @ SV21 @ SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(399,plain,
! [SV35: $i,SV22: $i] :
( ( ~ ( ~ ( subset @ SV22 @ ( singleton @ SV35 ) )
| ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(400,plain,
! [SV35: $i,SV22: $i] :
( ( ~ ( ~ ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
| ( subset @ SV22 @ ( singleton @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(401,plain,
! [SV24: $i] :
( ( ( SV24 != empty_set )
| ! [SY79: $i] :
~ ( in @ SY79 @ SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(402,plain,
! [SV24: $i] :
( ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV24 )
| ( SV24 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(403,plain,
! [SV25: $i] :
( ( ( ~ ~ ( empty @ SV25 )
| ~ ( relation @ SV25 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(404,plain,
! [SV36: $i,SV26: $i,SV39: $i] :
( ( ( ~ ( relation @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV39 ) )
| ~ ( in @ SV36 @ ( relation_rng @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(405,plain,
! [SV27: $i,SV37: $i] :
( ( ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV37 != empty_set ) )
| ( ( complements_of_subsets @ SV27 @ SV37 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(406,plain,
! [SV38: $i,SV28: $i] :
( ( ~ ( ( ( set_difference @ SV28 @ SV38 )
!= empty_set )
| ( subset @ SV28 @ SV38 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(407,plain,
! [SV38: $i,SV28: $i] :
( ( ~ ( ~ ( subset @ SV28 @ SV38 )
| ( ( set_difference @ SV28 @ SV38 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(408,plain,
! [SV29: $i,SV45: $i] :
( ( ( ~ ( ~ ( ( SV45
!= ( relation_dom @ SV29 ) )
| ! [SY106: $i] :
~ ( ~ ( ~ ( in @ SY106 @ SV45 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY88 ) @ SV29 )
| ( in @ SY106 @ SV45 ) ) ) )
| ~ ( ~ ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV45 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY91 ) @ SV29 )
| ( in @ SY109 @ SV45 ) ) )
| ( SV45
= ( relation_dom @ SV29 ) ) ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(409,plain,
! [SV30: $i,SV46: $i] :
( ( ( ~ ( relation @ SV46 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV46 ) ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(410,plain,
! [SV6: $i,SV40: $i] :
( ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_rng @ SV40 ) )
| ( ( relation_rng @ ( relation_composition @ SV40 @ SV6 ) )
= ( relation_rng @ SV6 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(411,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty @ SV7 ) )
= $true )
| ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(412,plain,
! [SV31: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ ( singleton @ SV31 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(413,plain,
! [SV31: $i,SV8: $i] :
( ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
| ( subset @ SV8 @ ( singleton @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(414,plain,
! [SV32: $i,SV9: $i] :
( ( ( ( set_difference @ SV9 @ SV32 )
!= empty_set )
| ( subset @ SV9 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(415,plain,
! [SV32: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV32 )
| ( ( set_difference @ SV9 @ SV32 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(416,plain,
! [SV10: $i,SV41: $i] :
( ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV10 ) @ ( relation_dom @ SV41 ) )
| ( ( relation_dom @ ( relation_composition @ SV10 @ SV41 ) )
= ( relation_dom @ SV10 ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(417,plain,
! [SV12: $i,SV42: $i] :
( ( ( ~ ( ( SV42
!= ( relation_rng @ SV12 ) )
| ! [SY100: $i] :
~ ( ~ ( ~ ( in @ SY100 @ SV42 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY100 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY100 ) @ SV12 )
| ( in @ SY100 @ SV42 ) ) ) )
| ~ ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV42 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY103 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY103 ) @ SV12 )
| ( in @ SY103 @ SV42 ) ) )
| ( SV42
= ( relation_rng @ SV12 ) ) ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(418,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ~ ( subset @ SV15 @ SV43 )
| ~ ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SV43 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SV43 ) ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(419,plain,
! [SV17: $i] :
( ( ( ! [SY67: $i,SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 ) )
= $false )
| ( ( SV17 = empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(420,plain,
! [SV18: $i] :
( ( ( ( relation_rng @ SV18 )
!= ( relation_dom @ ( relation_inverse @ SV18 ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(421,plain,
! [SV18: $i] :
( ( ( ( relation_dom @ SV18 )
!= ( relation_rng @ ( relation_inverse @ SV18 ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(422,plain,
! [SV33: $i,SV19: $i] :
( ( ~ ( ( SV19 != empty_set ) )
| ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
| ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(423,plain,
! [SV33: $i,SV19: $i] :
( ( ( SV19 != empty_set )
| ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) )
| ~ ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(424,plain,
! [SV20: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV20 @ SV44 ) ) @ ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(425,plain,
! [SV34: $i,SV21: $i] :
( ( ~ ( disjoint @ SV21 @ SV34 )
| ( ( set_intersection2 @ SV21 @ SV34 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(426,plain,
! [SV34: $i,SV21: $i] :
( ( ( ( set_intersection2 @ SV21 @ SV34 )
!= empty_set )
| ( disjoint @ SV21 @ SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(427,plain,
! [SV35: $i,SV22: $i] :
( ( ~ ( subset @ SV22 @ ( singleton @ SV35 ) )
| ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(428,plain,
! [SV35: $i,SV22: $i] :
( ( ~ ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
| ( subset @ SV22 @ ( singleton @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(429,plain,
! [SV24: $i] :
( ( ( SV24 != empty_set )
= $true )
| ( ( ! [SY79: $i] :
~ ( in @ SY79 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(430,plain,
! [SV24: $i] :
( ( ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV24 ) )
= $true )
| ( ( SV24 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(431,plain,
! [SV25: $i] :
( ( ( ~ ~ ( empty @ SV25 ) )
= $true )
| ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(432,plain,
! [SV36: $i,SV26: $i,SV39: $i] :
( ( ( relation @ SV39 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV39 ) )
| ~ ( in @ SV36 @ ( relation_rng @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(433,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( ~ ( ( SV37 != empty_set ) )
| ( ( complements_of_subsets @ SV27 @ SV37 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(434,plain,
! [SV38: $i,SV28: $i] :
( ( ( ( set_difference @ SV28 @ SV38 )
!= empty_set )
| ( subset @ SV28 @ SV38 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(435,plain,
! [SV38: $i,SV28: $i] :
( ( ~ ( subset @ SV28 @ SV38 )
| ( ( set_difference @ SV28 @ SV38 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(436,plain,
! [SV29: $i,SV45: $i] :
( ( ( ~ ( ( SV45
!= ( relation_dom @ SV29 ) )
| ! [SY106: $i] :
~ ( ~ ( ~ ( in @ SY106 @ SV45 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY88 ) @ SV29 )
| ( in @ SY106 @ SV45 ) ) ) )
| ~ ( ~ ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV45 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY91 ) @ SV29 )
| ( in @ SY109 @ SV45 ) ) )
| ( SV45
= ( relation_dom @ SV29 ) ) ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(437,plain,
! [SV30: $i,SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV46 ) ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(438,plain,
! [SV6: $i,SV40: $i] :
( ( ( relation @ SV40 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_rng @ SV40 ) )
| ( ( relation_rng @ ( relation_composition @ SV40 @ SV6 ) )
= ( relation_rng @ SV6 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(439,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $false )
| ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(440,plain,
! [SV31: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ ( singleton @ SV31 ) ) )
= $true )
| ( ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(441,plain,
! [SV31: $i,SV8: $i] :
( ( ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) ) )
= $true )
| ( ( subset @ SV8 @ ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(442,plain,
! [SV32: $i,SV9: $i] :
( ( ( ( set_difference @ SV9 @ SV32 )
!= empty_set )
= $true )
| ( ( subset @ SV9 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(443,plain,
! [SV32: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV32 ) )
= $true )
| ( ( ( set_difference @ SV9 @ SV32 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(444,plain,
! [SV10: $i,SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV10 ) @ ( relation_dom @ SV41 ) )
| ( ( relation_dom @ ( relation_composition @ SV10 @ SV41 ) )
= ( relation_dom @ SV10 ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(445,plain,
! [SV12: $i,SV42: $i] :
( ( ( ~ ( ( SV42
!= ( relation_rng @ SV12 ) )
| ! [SY100: $i] :
~ ( ~ ( ~ ( in @ SY100 @ SV42 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY100 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY100 ) @ SV12 )
| ( in @ SY100 @ SV42 ) ) ) ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(446,plain,
! [SV12: $i,SV42: $i] :
( ( ( ~ ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV42 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY103 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY103 ) @ SV12 )
| ( in @ SY103 @ SV42 ) ) )
| ( SV42
= ( relation_rng @ SV12 ) ) ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(447,plain,
! [SV15: $i,SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( ~ ( subset @ SV15 @ SV43 )
| ~ ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SV43 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SV43 ) ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(448,plain,
! [SV17: $i] :
( ( ( ! [SY112: $i] :
~ ( in @ ( ordered_pair @ ( sK1_SY67 @ SV17 ) @ SY112 ) @ SV17 ) )
= $false )
| ( ( SV17 = empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[419]) ).
thf(449,plain,
! [SV18: $i] :
( ( ( ( relation_rng @ SV18 )
= ( relation_dom @ ( relation_inverse @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(450,plain,
! [SV18: $i] :
( ( ( ( relation_dom @ SV18 )
= ( relation_rng @ ( relation_inverse @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(451,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ( ( SV19 != empty_set ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
| ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(452,plain,
! [SV33: $i,SV19: $i] :
( ( ( SV19 != empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) )
| ~ ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(453,plain,
! [SV20: $i,SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV20 @ SV44 ) ) @ ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(454,plain,
! [SV34: $i,SV21: $i] :
( ( ( ~ ( disjoint @ SV21 @ SV34 ) )
= $true )
| ( ( ( set_intersection2 @ SV21 @ SV34 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(455,plain,
! [SV34: $i,SV21: $i] :
( ( ( ( set_intersection2 @ SV21 @ SV34 )
!= empty_set )
= $true )
| ( ( disjoint @ SV21 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(456,plain,
! [SV35: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ ( singleton @ SV35 ) ) )
= $true )
| ( ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(457,plain,
! [SV35: $i,SV22: $i] :
( ( ( ~ ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) ) )
= $true )
| ( ( subset @ SV22 @ ( singleton @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(458,plain,
! [SV24: $i] :
( ( ( SV24 = empty_set )
= $false )
| ( ( ! [SY79: $i] :
~ ( in @ SY79 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(459,plain,
! [SV24: $i] :
( ( ( ! [SY80: $i] :
~ ( in @ SY80 @ SV24 ) )
= $false )
| ( ( SV24 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(460,plain,
! [SV25: $i] :
( ( ( ~ ( empty @ SV25 ) )
= $false )
| ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(461,plain,
! [SV39: $i,SV36: $i,SV26: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV39 ) )
| ~ ( in @ SV36 @ ( relation_rng @ SV39 ) ) ) )
= $true )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(462,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( ( SV37 != empty_set ) )
| ( ( complements_of_subsets @ SV27 @ SV37 )
!= empty_set ) )
= $true )
| ( ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(463,plain,
! [SV38: $i,SV28: $i] :
( ( ( ( set_difference @ SV28 @ SV38 )
!= empty_set )
= $true )
| ( ( subset @ SV28 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(464,plain,
! [SV38: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV38 ) )
= $true )
| ( ( ( set_difference @ SV28 @ SV38 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(465,plain,
! [SV29: $i,SV45: $i] :
( ( ( ~ ( ( SV45
!= ( relation_dom @ SV29 ) )
| ! [SY106: $i] :
~ ( ~ ( ~ ( in @ SY106 @ SV45 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY88 ) @ SV29 )
| ( in @ SY106 @ SV45 ) ) ) ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(466,plain,
! [SV29: $i,SV45: $i] :
( ( ( ~ ( ~ ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV45 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY91 ) @ SV29 )
| ( in @ SY109 @ SV45 ) ) )
| ( SV45
= ( relation_dom @ SV29 ) ) ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(467,plain,
! [SV30: $i,SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV46 ) ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(468,plain,
! [SV40: $i,SV6: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV40 @ SV6 ) )
= ( relation_rng @ SV6 ) )
= $true )
| ( ( relation @ SV40 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(469,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $true )
| ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(470,plain,
! [SV31: $i,SV8: $i] :
( ( ( subset @ SV8 @ ( singleton @ SV31 ) )
= $false )
| ( ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(471,plain,
! [SV31: $i,SV8: $i] :
( ( ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV31 ) ) )
= $false )
| ( ( subset @ SV8 @ ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(472,plain,
! [SV32: $i,SV9: $i] :
( ( ( ( set_difference @ SV9 @ SV32 )
= empty_set )
= $false )
| ( ( subset @ SV9 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(473,plain,
! [SV32: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV32 )
= $false )
| ( ( ( set_difference @ SV9 @ SV32 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(474,plain,
! [SV41: $i,SV10: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV10 ) @ ( relation_dom @ SV41 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV10 @ SV41 ) )
= ( relation_dom @ SV10 ) )
= $true )
| ( ( relation @ SV41 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(475,plain,
! [SV12: $i,SV42: $i] :
( ( ( ( SV42
!= ( relation_rng @ SV12 ) )
| ! [SY100: $i] :
~ ( ~ ( ~ ( in @ SY100 @ SV42 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY100 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY100 ) @ SV12 )
| ( in @ SY100 @ SV42 ) ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(476,plain,
! [SV12: $i,SV42: $i] :
( ( ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV42 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY103 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY103 ) @ SV12 )
| ( in @ SY103 @ SV42 ) ) )
| ( SV42
= ( relation_rng @ SV12 ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(477,plain,
! [SV43: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SV43 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SV43 ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(478,plain,
! [SV17: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK1_SY67 @ SV17 ) @ ( sK2_SY112 @ SV17 ) ) @ SV17 ) )
= $false )
| ( ( SV17 = empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[448]) ).
thf(479,plain,
! [SV33: $i,SV19: $i] :
( ( ( SV19 != empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
| ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(480,plain,
! [SV33: $i,SV19: $i] :
( ( ( SV19 = empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) )
| ~ ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(481,plain,
! [SV34: $i,SV21: $i] :
( ( ( disjoint @ SV21 @ SV34 )
= $false )
| ( ( ( set_intersection2 @ SV21 @ SV34 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(482,plain,
! [SV34: $i,SV21: $i] :
( ( ( ( set_intersection2 @ SV21 @ SV34 )
= empty_set )
= $false )
| ( ( disjoint @ SV21 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(483,plain,
! [SV35: $i,SV22: $i] :
( ( ( subset @ SV22 @ ( singleton @ SV35 ) )
= $false )
| ( ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(484,plain,
! [SV35: $i,SV22: $i] :
( ( ( ( SV22 = empty_set )
| ( SV22
= ( singleton @ SV35 ) ) )
= $false )
| ( ( subset @ SV22 @ ( singleton @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(485,plain,
! [SV24: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV24 ) )
= $true )
| ( ( SV24 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(486,plain,
! [SV24: $i] :
( ( ( ~ ( in @ ( sK3_SY80 @ SV24 ) @ SV24 ) )
= $false )
| ( ( SV24 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[459]) ).
thf(487,plain,
! [SV25: $i] :
( ( ( empty @ SV25 )
= $true )
| ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(488,plain,
! [SV39: $i,SV36: $i,SV26: $i] :
( ( ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
= $false )
| ( ( ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV39 ) )
| ~ ( in @ SV36 @ ( relation_rng @ SV39 ) ) ) )
= $true )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(489,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( ( SV37 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV27 @ SV37 )
!= empty_set )
= $true )
| ( ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(490,plain,
! [SV38: $i,SV28: $i] :
( ( ( ( set_difference @ SV28 @ SV38 )
= empty_set )
= $false )
| ( ( subset @ SV28 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(491,plain,
! [SV38: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV38 )
= $false )
| ( ( ( set_difference @ SV28 @ SV38 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(492,plain,
! [SV29: $i,SV45: $i] :
( ( ( ( SV45
!= ( relation_dom @ SV29 ) )
| ! [SY106: $i] :
~ ( ~ ( ~ ( in @ SY106 @ SV45 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY88 ) @ SV29 )
| ( in @ SY106 @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(493,plain,
! [SV29: $i,SV45: $i] :
( ( ( ~ ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV45 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY91 ) @ SV29 )
| ( in @ SY109 @ SV45 ) ) )
| ( SV45
= ( relation_dom @ SV29 ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(494,plain,
! [SV40: $i,SV6: $i] :
( ( ( subset @ ( relation_dom @ SV6 ) @ ( relation_rng @ SV40 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV40 @ SV6 ) )
= ( relation_rng @ SV6 ) )
= $true )
| ( ( relation @ SV40 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(495,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( empty @ SV7 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(496,plain,
! [SV31: $i,SV8: $i] :
( ( ( SV8 = empty_set )
= $true )
| ( ( SV8
= ( singleton @ SV31 ) )
= $true )
| ( ( subset @ SV8 @ ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(497,plain,
! [SV31: $i,SV8: $i] :
( ( ( SV8 = empty_set )
= $false )
| ( ( subset @ SV8 @ ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(498,plain,
! [SV31: $i,SV8: $i] :
( ( ( SV8
= ( singleton @ SV31 ) )
= $false )
| ( ( subset @ SV8 @ ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(499,plain,
! [SV41: $i,SV10: $i] :
( ( ( subset @ ( relation_rng @ SV10 ) @ ( relation_dom @ SV41 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV10 @ SV41 ) )
= ( relation_dom @ SV10 ) )
= $true )
| ( ( relation @ SV41 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(500,plain,
! [SV12: $i,SV42: $i] :
( ( ( SV42
!= ( relation_rng @ SV12 ) )
= $true )
| ( ( ! [SY100: $i] :
~ ( ~ ( ~ ( in @ SY100 @ SV42 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY100 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY100 ) @ SV12 )
| ( in @ SY100 @ SV42 ) ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(501,plain,
! [SV12: $i,SV42: $i] :
( ( ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV42 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY103 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY103 ) @ SV12 )
| ( in @ SY103 @ SV42 ) ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(502,plain,
! [SV43: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV43 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SV43 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SV43 ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(503,plain,
! [SV17: $i] :
( ( ( in @ ( ordered_pair @ ( sK1_SY67 @ SV17 ) @ ( sK2_SY112 @ SV17 ) ) @ SV17 )
= $true )
| ( ( SV17 = empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(504,plain,
! [SV33: $i,SV19: $i] :
( ( ( SV19 = empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
| ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(505,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) )
| ~ ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) ) )
= $false )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(506,plain,
! [SV35: $i,SV22: $i] :
( ( ( SV22 = empty_set )
= $true )
| ( ( SV22
= ( singleton @ SV35 ) )
= $true )
| ( ( subset @ SV22 @ ( singleton @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(507,plain,
! [SV35: $i,SV22: $i] :
( ( ( SV22 = empty_set )
= $false )
| ( ( subset @ SV22 @ ( singleton @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(508,plain,
! [SV35: $i,SV22: $i] :
( ( ( SV22
= ( singleton @ SV35 ) )
= $false )
| ( ( subset @ SV22 @ ( singleton @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(509,plain,
! [SV24: $i,SV47: $i] :
( ( ( in @ SV47 @ SV24 )
= $false )
| ( ( SV24 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(510,plain,
! [SV24: $i] :
( ( ( in @ ( sK3_SY80 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(511,plain,
! [SV25: $i] :
( ( ( relation @ SV25 )
= $false )
| ( ( empty @ SV25 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(512,plain,
! [SV36: $i,SV39: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( relation_dom @ SV39 ) )
| ~ ( in @ SV36 @ ( relation_rng @ SV39 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(513,plain,
! [SV27: $i,SV37: $i] :
( ( ( SV37 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV27 @ SV37 )
!= empty_set )
= $true )
| ( ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(514,plain,
! [SV29: $i,SV45: $i] :
( ( ( SV45
!= ( relation_dom @ SV29 ) )
= $true )
| ( ( ! [SY106: $i] :
~ ( ~ ( ~ ( in @ SY106 @ SV45 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY88 ) @ SV29 )
| ( in @ SY106 @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(515,plain,
! [SV29: $i,SV45: $i] :
( ( ( ~ ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV45 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY91 ) @ SV29 )
| ( in @ SY109 @ SV45 ) ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(516,plain,
! [SV7: $i] :
( ( ( empty @ ( relation_dom @ SV7 ) )
= $false )
| ( ( empty @ SV7 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(517,plain,
! [SV12: $i,SV42: $i] :
( ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( ! [SY100: $i] :
~ ( ~ ( ~ ( in @ SY100 @ SV42 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY100 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY100 ) @ SV12 )
| ( in @ SY100 @ SV42 ) ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(518,plain,
! [SV12: $i,SV42: $i] :
( ( ( ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV42 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY103 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY103 ) @ SV12 )
| ( in @ SY103 @ SV42 ) ) ) )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(519,plain,
! [SV43: $i,SV15: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SV43 ) )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SV43 ) ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(520,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
| ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(521,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) ) )
= $false )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(522,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) ) )
= $false )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(523,plain,
! [SV25: $i] :
( ( ( empty @ ( relation_rng @ SV25 ) )
= $false )
| ( ( empty @ SV25 )
= $true )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(524,plain,
! [SV36: $i,SV39: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( relation_dom @ SV39 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(525,plain,
! [SV26: $i,SV39: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( relation_rng @ SV39 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(526,plain,
! [SV27: $i,SV37: $i] :
( ( ( SV37 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV27 @ SV37 )
!= empty_set )
= $true )
| ( ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(527,plain,
! [SV29: $i,SV45: $i] :
( ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( ! [SY106: $i] :
~ ( ~ ( ~ ( in @ SY106 @ SV45 )
| ~ ! [SY87: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY87 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ( in @ ( ordered_pair @ SY106 @ SY88 ) @ SV29 )
| ( in @ SY106 @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(528,plain,
! [SV29: $i,SV45: $i] :
( ( ( ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV45 )
| ~ ! [SY90: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY90 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ( in @ ( ordered_pair @ SY109 @ SY91 ) @ SV29 )
| ( in @ SY109 @ SV45 ) ) ) )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(529,plain,
! [SV12: $i,SV42: $i,SV48: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV48 @ SV42 )
| ~ ! [SY113: $i] :
~ ( in @ ( ordered_pair @ SY113 @ SV48 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY114: $i] :
~ ( in @ ( ordered_pair @ SY114 @ SV48 ) @ SV12 )
| ( in @ SV48 @ SV42 ) ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(530,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
| ~ ! [SY115: $i] :
~ ( in @ ( ordered_pair @ SY115 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
| ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) ) )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[518]) ).
thf(531,plain,
! [SV43: $i,SV15: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SV43 ) ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(532,plain,
! [SV43: $i,SV15: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SV43 ) ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(533,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[520]) ).
thf(534,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[520]) ).
thf(535,plain,
! [SV19: $i,SV33: $i] :
( ( ( ( SV33
!= ( set_meet @ SV19 ) )
| ( SV33 = empty_set ) )
= $true )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(536,plain,
! [SV19: $i,SV33: $i] :
( ( ( ( SV33 != empty_set )
| ( SV33
= ( set_meet @ SV19 ) ) )
= $true )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(537,plain,
! [SV36: $i,SV39: $i,SV26: $i] :
( ( ( in @ SV26 @ ( relation_dom @ SV39 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(538,plain,
! [SV26: $i,SV39: $i,SV36: $i] :
( ( ( in @ SV36 @ ( relation_rng @ SV39 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV26 @ SV36 ) @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(539,plain,
! [SV37: $i,SV27: $i] :
( ( ( ( complements_of_subsets @ SV27 @ SV37 )
= empty_set )
= $false )
| ( ( SV37 = empty_set )
= $true )
| ( ( element @ SV37 @ ( powerset @ ( powerset @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(540,plain,
! [SV29: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV49 @ SV45 )
| ~ ! [SY117: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY117 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY118: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY118 ) @ SV29 )
| ( in @ SV49 @ SV45 ) ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(541,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
| ~ ! [SY119: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY119 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) ) )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[528]) ).
thf(542,plain,
! [SV12: $i,SV42: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ SV42 )
| ~ ! [SY113: $i] :
~ ( in @ ( ordered_pair @ SY113 @ SV48 ) @ SV12 ) )
| ~ ( ~ ~ ! [SY114: $i] :
~ ( in @ ( ordered_pair @ SY114 @ SV48 ) @ SV12 )
| ( in @ SV48 @ SV42 ) ) )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(543,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
| ~ ! [SY115: $i] :
~ ( in @ ( ordered_pair @ SY115 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
| ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(544,plain,
! [SV43: $i,SV15: $i] :
( ( ( subset @ ( relation_dom @ SV15 ) @ ( relation_dom @ SV43 ) )
= $true )
| ( ( subset @ SV15 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(545,plain,
! [SV43: $i,SV15: $i] :
( ( ( subset @ ( relation_rng @ SV15 ) @ ( relation_rng @ SV43 ) )
= $true )
| ( ( subset @ SV15 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(546,plain,
! [SV19: $i,SV33: $i] :
( ( ( ( SV33
!= ( set_meet @ SV19 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(547,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) )
| ( SV33
= ( set_meet @ SV19 ) ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(548,plain,
! [SV19: $i,SV33: $i] :
( ( ( SV33
!= ( set_meet @ SV19 ) )
= $true )
| ( ( SV33 = empty_set )
= $true )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(549,plain,
! [SV19: $i,SV33: $i] :
( ( ( SV33 != empty_set )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(550,plain,
! [SV29: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV45 )
| ~ ! [SY117: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY117 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY118: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY118 ) @ SV29 )
| ( in @ SV49 @ SV45 ) ) )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(551,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
| ~ ! [SY119: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY119 ) @ SV29 ) )
| ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(552,plain,
! [SV12: $i,SV42: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ SV42 )
| ~ ! [SY113: $i] :
~ ( in @ ( ordered_pair @ SY113 @ SV48 ) @ SV12 ) ) )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(553,plain,
! [SV42: $i,SV12: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ( in @ ( ordered_pair @ SY114 @ SV48 ) @ SV12 )
| ( in @ SV48 @ SV42 ) ) )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(554,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
| ~ ! [SY115: $i] :
~ ( in @ ( ordered_pair @ SY115 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(555,plain,
! [SV19: $i,SV33: $i] :
( ( ( SV33
!= ( set_meet @ SV19 ) )
= $true )
| ( ( ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(556,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(557,plain,
! [SV19: $i,SV33: $i] :
( ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV33 = empty_set )
= $true )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(558,plain,
! [SV19: $i,SV33: $i] :
( ( ( SV33 = empty_set )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(559,plain,
! [SV29: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV45 )
| ~ ! [SY117: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY117 ) @ SV29 ) ) )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(560,plain,
! [SV45: $i,SV29: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ! [SY118: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY118 ) @ SV29 )
| ( in @ SV49 @ SV45 ) ) )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(561,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
| ~ ! [SY119: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY119 ) @ SV29 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(562,plain,
! [SV12: $i,SV42: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV42 )
| ~ ! [SY113: $i] :
~ ( in @ ( ordered_pair @ SY113 @ SV48 ) @ SV12 ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(563,plain,
! [SV42: $i,SV12: $i,SV48: $i] :
( ( ( ~ ~ ! [SY114: $i] :
~ ( in @ ( ordered_pair @ SY114 @ SV48 ) @ SV12 )
| ( in @ SV48 @ SV42 ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(564,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
| ~ ! [SY115: $i] :
~ ( in @ ( ordered_pair @ SY115 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(565,plain,
! [SV19: $i,SV33: $i] :
( ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SV33 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ SV19 )
| ( in @ SY93 @ SY71 ) ) )
| ~ ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV19 )
| ( in @ SY93 @ SY72 ) )
| ( in @ SY93 @ SV33 ) ) ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(566,plain,
! [SV19: $i,SV33: $i] :
( ( ( ! [SY96: $i] :
~ ( ~ ( ~ ( in @ SY96 @ SV33 )
| ! [SY74: $i] :
( ~ ( in @ SY74 @ SV19 )
| ( in @ SY96 @ SY74 ) ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ( in @ SY96 @ SY75 ) )
| ( in @ SY96 @ SV33 ) ) ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(567,plain,
! [SV29: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV45 )
| ~ ! [SY117: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY117 ) @ SV29 ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(568,plain,
! [SV45: $i,SV29: $i,SV49: $i] :
( ( ( ~ ~ ! [SY118: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY118 ) @ SV29 )
| ( in @ SV49 @ SV45 ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(569,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
| ~ ! [SY119: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY119 ) @ SV29 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(570,plain,
! [SV12: $i,SV42: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV42 ) )
= $true )
| ( ( ~ ! [SY113: $i] :
~ ( in @ ( ordered_pair @ SY113 @ SV48 ) @ SV12 ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(571,plain,
! [SV42: $i,SV12: $i,SV48: $i] :
( ( ( ~ ~ ! [SY114: $i] :
~ ( in @ ( ordered_pair @ SY114 @ SV48 ) @ SV12 ) )
= $true )
| ( ( in @ SV48 @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(572,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(573,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ! [SY115: $i] :
~ ( in @ ( ordered_pair @ SY115 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(574,plain,
! [SV19: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV50 @ SV33 )
| ! [SY121: $i] :
( ~ ( in @ SY121 @ SV19 )
| ( in @ SV50 @ SY121 ) ) )
| ~ ( ~ ! [SY122: $i] :
( ~ ( in @ SY122 @ SV19 )
| ( in @ SV50 @ SY122 ) )
| ( in @ SV50 @ SV33 ) ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(575,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
| ! [SY123: $i] :
( ~ ( in @ SY123 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY123 ) ) )
| ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[566]) ).
thf(576,plain,
! [SV29: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV45 ) )
= $true )
| ( ( ~ ! [SY117: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY117 ) @ SV29 ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(577,plain,
! [SV45: $i,SV29: $i,SV49: $i] :
( ( ( ~ ~ ! [SY118: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY118 ) @ SV29 ) )
= $true )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(578,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(579,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ! [SY119: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY119 ) @ SV29 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(580,plain,
! [SV12: $i,SV42: $i,SV48: $i] :
( ( ( in @ SV48 @ SV42 )
= $false )
| ( ( ~ ! [SY113: $i] :
~ ( in @ ( ordered_pair @ SY113 @ SV48 ) @ SV12 ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(581,plain,
! [SV42: $i,SV12: $i,SV48: $i] :
( ( ( ~ ! [SY114: $i] :
~ ( in @ ( ordered_pair @ SY114 @ SV48 ) @ SV12 ) )
= $false )
| ( ( in @ SV48 @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(582,plain,
! [SV42: $i,SV12: $i] :
( ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $true )
| ( ( ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(583,plain,
! [SV42: $i,SV12: $i] :
( ( ( ! [SY115: $i] :
~ ( in @ ( ordered_pair @ SY115 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(584,plain,
! [SV19: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( ~ ( in @ SV50 @ SV33 )
| ! [SY121: $i] :
( ~ ( in @ SY121 @ SV19 )
| ( in @ SV50 @ SY121 ) ) )
| ~ ( ~ ! [SY122: $i] :
( ~ ( in @ SY122 @ SV19 )
| ( in @ SV50 @ SY122 ) )
| ( in @ SV50 @ SV33 ) ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(585,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
| ! [SY123: $i] :
( ~ ( in @ SY123 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY123 ) ) )
| ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(586,plain,
! [SV29: $i,SV45: $i,SV49: $i] :
( ( ( in @ SV49 @ SV45 )
= $false )
| ( ( ~ ! [SY117: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY117 ) @ SV29 ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(587,plain,
! [SV45: $i,SV29: $i,SV49: $i] :
( ( ( ~ ! [SY118: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY118 ) @ SV29 ) )
= $false )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(588,plain,
! [SV45: $i,SV29: $i] :
( ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $true )
| ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(589,plain,
! [SV45: $i,SV29: $i] :
( ( ( ! [SY119: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY119 ) @ SV29 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(590,plain,
! [SV42: $i,SV12: $i,SV48: $i] :
( ( ( ! [SY113: $i] :
~ ( in @ ( ordered_pair @ SY113 @ SV48 ) @ SV12 ) )
= $false )
| ( ( in @ SV48 @ SV42 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(591,plain,
! [SV42: $i,SV12: $i,SV48: $i] :
( ( ( ! [SY114: $i] :
~ ( in @ ( ordered_pair @ SY114 @ SV48 ) @ SV12 ) )
= $true )
| ( ( in @ SV48 @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(592,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(593,plain,
! [SV42: $i,SV12: $i,SV51: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(594,plain,
! [SV19: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( ~ ( in @ SV50 @ SV33 )
| ! [SY121: $i] :
( ~ ( in @ SY121 @ SV19 )
| ( in @ SV50 @ SY121 ) ) ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(595,plain,
! [SV33: $i,SV50: $i,SV19: $i] :
( ( ( ~ ( ~ ! [SY122: $i] :
( ~ ( in @ SY122 @ SV19 )
| ( in @ SV50 @ SY122 ) )
| ( in @ SV50 @ SV33 ) ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(596,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
| ! [SY123: $i] :
( ~ ( in @ SY123 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY123 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(597,plain,
! [SV45: $i,SV29: $i,SV49: $i] :
( ( ( ! [SY117: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY117 ) @ SV29 ) )
= $false )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(598,plain,
! [SV45: $i,SV29: $i,SV49: $i] :
( ( ( ! [SY118: $i] :
~ ( in @ ( ordered_pair @ SV49 @ SY118 ) @ SV29 ) )
= $true )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(599,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) )
= $false )
| ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(600,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(601,plain,
! [SV48: $i,SV12: $i,SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_SY113 @ SV42 @ SV12 @ SV48 ) @ SV48 ) @ SV12 ) )
= $false )
| ( ( in @ SV48 @ SV42 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[590]) ).
thf(602,plain,
! [SV42: $i,SV12: $i,SV48: $i,SV53: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV53 @ SV48 ) @ SV12 ) )
= $true )
| ( ( in @ SV48 @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(603,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $false )
| ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(604,plain,
! [SV42: $i,SV12: $i] :
( ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $false )
| ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(605,plain,
! [SV42: $i,SV12: $i,SV51: $i] :
( ( ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $false )
| ( ( ~ ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(606,plain,
! [SV19: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ SV33 )
| ! [SY121: $i] :
( ~ ( in @ SY121 @ SV19 )
| ( in @ SV50 @ SY121 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(607,plain,
! [SV33: $i,SV50: $i,SV19: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( in @ SY122 @ SV19 )
| ( in @ SV50 @ SY122 ) )
| ( in @ SV50 @ SV33 ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(608,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
| ! [SY123: $i] :
( ~ ( in @ SY123 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY123 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(609,plain,
! [SV29: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV49 @ ( sK8_SY117 @ SV45 @ SV29 @ SV49 ) ) @ SV29 ) )
= $false )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[597]) ).
thf(610,plain,
! [SV45: $i,SV29: $i,SV54: $i,SV49: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV54 ) @ SV29 ) )
= $true )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(611,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 ) )
= $false )
| ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(612,plain,
! [SV45: $i,SV29: $i] :
( ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $false )
| ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(613,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 )
= $false )
| ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(614,plain,
! [SV48: $i,SV12: $i,SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_SY113 @ SV42 @ SV12 @ SV48 ) @ SV48 ) @ SV12 )
= $true )
| ( ( in @ SV48 @ SV42 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(615,plain,
! [SV42: $i,SV12: $i,SV48: $i,SV53: $i] :
( ( ( in @ ( ordered_pair @ SV53 @ SV48 ) @ SV12 )
= $false )
| ( ( in @ SV48 @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $false )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(616,plain,
! [SV42: $i,SV12: $i] :
( ( ( ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $true )
| ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(617,plain,
! [SV51: $i,SV42: $i,SV12: $i] :
( ( ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
| ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(618,plain,
! [SV19: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ SV33 ) )
= $true )
| ( ( ! [SY121: $i] :
( ~ ( in @ SY121 @ SV19 )
| ( in @ SV50 @ SY121 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(619,plain,
! [SV33: $i,SV50: $i,SV19: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( in @ SY122 @ SV19 )
| ( in @ SV50 @ SY122 ) ) )
= $true )
| ( ( in @ SV50 @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(620,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) )
= $false )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(621,plain,
! [SV33: $i,SV19: $i] :
( ( ( ! [SY123: $i] :
( ~ ( in @ SY123 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY123 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(622,plain,
! [SV29: $i,SV45: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ SV49 @ ( sK8_SY117 @ SV45 @ SV29 @ SV49 ) ) @ SV29 )
= $true )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(623,plain,
! [SV45: $i,SV29: $i,SV54: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ SV49 @ SV54 ) @ SV29 )
= $false )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(624,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 ) )
= $true )
| ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(625,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 )
| ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(626,plain,
! [SV42: $i,SV12: $i] :
( ( ( ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $false )
| ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(627,plain,
! [SV51: $i,SV42: $i,SV12: $i] :
( ( ( ~ ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(628,plain,
! [SV51: $i,SV42: $i,SV12: $i] :
( ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $false )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(629,plain,
! [SV19: $i,SV33: $i,SV50: $i] :
( ( ( in @ SV50 @ SV33 )
= $false )
| ( ( ! [SY121: $i] :
( ~ ( in @ SY121 @ SV19 )
| ( in @ SV50 @ SY121 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(630,plain,
! [SV33: $i,SV50: $i,SV19: $i] :
( ( ( ! [SY122: $i] :
( ~ ( in @ SY122 @ SV19 )
| ( in @ SV50 @ SY122 ) ) )
= $false )
| ( ( in @ SV50 @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(631,plain,
! [SV33: $i,SV19: $i] :
( ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(632,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[621]) ).
thf(633,plain,
! [SV45: $i,SV29: $i] :
( ( ( ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 ) )
= $false )
| ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(634,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( ~ ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(635,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(636,plain,
! [SV12: $i,SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_SY116 @ SV42 @ SV12 ) @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $false )
| ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[626]) ).
thf(637,plain,
! [SV51: $i,SV42: $i,SV12: $i] :
( ( ( ~ ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(638,plain,
! [SV33: $i,SV50: $i,SV19: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV19 )
| ( in @ SV50 @ SV55 ) )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(639,plain,
! [SV19: $i,SV50: $i,SV33: $i] :
( ( ( ~ ( in @ ( sK11_SY122 @ SV33 @ SV50 @ SV19 ) @ SV19 )
| ( in @ SV50 @ ( sK11_SY122 @ SV33 @ SV50 @ SV19 ) ) )
= $false )
| ( ( in @ SV50 @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[630]) ).
thf(640,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(641,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 ) )
= $false )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(642,plain,
! [SV33: $i,SV19: $i] :
( ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) )
= $false )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(643,plain,
! [SV45: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ ( sK12_SY120 @ SV45 @ SV29 ) ) @ SV29 ) )
= $false )
| ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[633]) ).
thf(644,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( ~ ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(645,plain,
! [SV12: $i,SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_SY116 @ SV42 @ SV12 ) @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $true )
| ( ( in @ ( sK4_SY103 @ SV12 @ SV42 ) @ SV42 )
= $true )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[636]) ).
thf(646,plain,
! [SV51: $i,SV42: $i,SV12: $i] :
( ( ( ! [SY116: $i] :
~ ( in @ ( ordered_pair @ SY116 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(647,plain,
! [SV33: $i,SV50: $i,SV19: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV19 ) )
= $true )
| ( ( in @ SV50 @ SV55 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(648,plain,
! [SV19: $i,SV50: $i,SV33: $i] :
( ( ( ~ ( in @ ( sK11_SY122 @ SV33 @ SV50 @ SV19 ) @ SV19 ) )
= $false )
| ( ( in @ SV50 @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(649,plain,
! [SV19: $i,SV33: $i,SV50: $i] :
( ( ( in @ SV50 @ ( sK11_SY122 @ SV33 @ SV50 @ SV19 ) )
= $false )
| ( ( in @ SV50 @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(650,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) ) )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(651,plain,
! [SV33: $i,SV19: $i] :
( ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(652,plain,
! [SV19: $i,SV33: $i] :
( ( ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
= $true )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(653,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(654,plain,
! [SV45: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ ( sK12_SY120 @ SV45 @ SV29 ) ) @ SV29 )
= $true )
| ( ( in @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(655,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( ! [SY120: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SY120 ) @ SV29 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(656,plain,
! [SV12: $i,SV42: $i,SV51: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_SY116 @ SV51 @ SV42 @ SV12 ) @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[646]) ).
thf(657,plain,
! [SV33: $i,SV50: $i,SV19: $i,SV55: $i] :
( ( ( in @ SV55 @ SV19 )
= $false )
| ( ( in @ SV50 @ SV55 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(658,plain,
! [SV19: $i,SV50: $i,SV33: $i] :
( ( ( in @ ( sK11_SY122 @ SV33 @ SV50 @ SV19 ) @ SV19 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(659,plain,
! [SV33: $i,SV19: $i] :
( ( ( ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) ) )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(660,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(661,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) ) )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(662,plain,
! [SV33: $i,SV19: $i] :
( ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(663,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ ( sK14_SY120 @ SV52 @ SV45 @ SV29 ) ) @ SV29 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[655]) ).
thf(664,plain,
! [SV12: $i,SV42: $i,SV51: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_SY116 @ SV51 @ SV42 @ SV12 ) @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $true )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK4_SY103 @ SV12 @ SV42 ) ) @ SV12 )
= $false )
| ( ( SV42
= ( relation_rng @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(665,plain,
! [SV33: $i,SV19: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV56 ) )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(666,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) ) )
= $false )
| ( ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(667,plain,
! [SV33: $i,SV19: $i] :
( ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(668,plain,
! [SV33: $i,SV19: $i] :
( ( ( ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) ) )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(669,plain,
! [SV52: $i,SV45: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ ( sK14_SY120 @ SV52 @ SV45 @ SV29 ) ) @ SV29 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK5_SY109 @ SV29 @ SV45 ) @ SV52 ) @ SV29 )
= $false )
| ( ( SV45
= ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(670,plain,
! [SV33: $i,SV19: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV19 ) )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV56 )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(671,plain,
! [SV33: $i,SV19: $i] :
( ( ( ! [SY124: $i] :
( ~ ( in @ SY124 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SY124 ) ) )
= $true )
| ( ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[666]) ).
thf(672,plain,
! [SV33: $i,SV19: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV57 ) )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(673,plain,
! [SV33: $i,SV19: $i,SV56: $i] :
( ( ( in @ SV56 @ SV19 )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV56 )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(674,plain,
! [SV33: $i,SV19: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV19 )
| ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV58 ) )
= $true )
| ( ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(675,plain,
! [SV33: $i,SV19: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV19 ) )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV57 )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(676,plain,
! [SV33: $i,SV19: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV19 ) )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV58 )
= $true )
| ( ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(677,plain,
! [SV33: $i,SV19: $i,SV57: $i] :
( ( ( in @ SV57 @ SV19 )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV57 )
= $true )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ ( sK9_SY123 @ SV33 @ SV19 ) )
= $false )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(678,plain,
! [SV33: $i,SV19: $i,SV58: $i] :
( ( ( in @ SV58 @ SV19 )
= $false )
| ( ( in @ ( sK6_SY96 @ SV19 @ SV33 ) @ SV58 )
= $true )
| ( ( in @ ( sK9_SY123 @ SV33 @ SV19 ) @ SV19 )
= $true )
| ( ( SV33
= ( set_meet @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(679,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[225,678,677,673,669,667,664,662,658,657,654,651,649,645,635,628,623,622,615,614,612,604,558,557,545,544,539,538,537,523,516,510,509,508,507,506,503,499,498,497,496,494,491,490,482,481,473,472,467,453,450,449,376,375,366,364,363,361,346,302,301,300,299,298,297,261,260,259,258,257,256,255,254,253,252,251,250,249,248,247,246]) ).
thf(680,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(681,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(683,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(684,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(copy,[status(thm)],[213]) ).
thf(685,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(686,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(copy,[status(thm)],[211]) ).
thf(687,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(688,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(689,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(690,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(691,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(692,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(693,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(694,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)],[203]) ).
thf(695,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)],[202]) ).
thf(696,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)],[201]) ).
thf(697,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(698,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(copy,[status(thm)],[199]) ).
thf(699,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(700,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(copy,[status(thm)],[197]) ).
thf(701,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(copy,[status(thm)],[196]) ).
thf(702,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(703,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(704,plain,
$true = $true,
inference(copy,[status(thm)],[193]) ).
thf(705,plain,
$true = $true,
inference(copy,[status(thm)],[192]) ).
thf(706,plain,
$true = $true,
inference(copy,[status(thm)],[191]) ).
thf(707,plain,
$true = $true,
inference(copy,[status(thm)],[190]) ).
thf(708,plain,
$true = $true,
inference(copy,[status(thm)],[189]) ).
thf(709,plain,
$true = $true,
inference(copy,[status(thm)],[188]) ).
thf(710,plain,
$true = $true,
inference(copy,[status(thm)],[187]) ).
thf(711,plain,
$true = $true,
inference(copy,[status(thm)],[186]) ).
thf(712,plain,
$true = $true,
inference(copy,[status(thm)],[185]) ).
thf(713,plain,
$true = $true,
inference(copy,[status(thm)],[184]) ).
thf(714,plain,
$true = $true,
inference(copy,[status(thm)],[183]) ).
thf(715,plain,
$true = $true,
inference(copy,[status(thm)],[182]) ).
thf(716,plain,
$true = $true,
inference(copy,[status(thm)],[181]) ).
thf(717,plain,
$true = $true,
inference(copy,[status(thm)],[180]) ).
thf(718,plain,
$true = $true,
inference(copy,[status(thm)],[179]) ).
thf(719,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(720,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(721,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(722,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(723,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(724,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(725,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(726,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(727,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(728,plain,
( ( ( relation_rng @ empty_set )
!= empty_set )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(729,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(730,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(731,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(732,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(733,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(734,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_dom @ SX1 ) )
| ( ( relation_dom @ ( relation_composition @ SX0 @ SX1 ) )
= ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(735,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_rng @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(736,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(737,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(738,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(739,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[721]) ).
thf(740,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(741,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(742,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ! [SX1: $i,SX2: $i] :
~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(743,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
| ~ ( ( SX0 != empty_set )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) )
| ~ ( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(744,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX1 ) )
| ( ( relation_rng @ ( relation_composition @ SX1 @ SX0 ) )
= ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(745,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ( ( relation_rng @ SX0 )
!= ( relation_dom @ ( relation_inverse @ SX0 ) ) )
| ( ( relation_dom @ SX0 )
!= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(746,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(747,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_field @ SX0 )
= ( set_union2 @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(748,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(749,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(750,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( subset @ SX0 @ ( cartesian_product2 @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(751,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(752,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[727]) ).
thf(753,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(754,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(755,plain,
! [SV59: $i] :
( ( subset @ empty_set @ SV59 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(756,plain,
! [SV60: $i] :
( ( ( set_union2 @ SV60 @ empty_set )
= SV60 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(757,plain,
! [SV61: $i] :
( ( ( set_intersection2 @ SV61 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(758,plain,
! [SV62: $i] :
( ( ( set_difference @ SV62 @ empty_set )
= SV62 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(759,plain,
! [SV63: $i] :
( ( ( set_difference @ empty_set @ SV63 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(760,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(761,plain,
! [SV64: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV64 )
| ~ ( relation @ SV64 ) )
| ~ ( empty @ ( relation_rng @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(762,plain,
! [SV65: $i] :
( ( ~ ( relation @ SV65 )
| ! [SY125: $i] :
( ~ ( relation @ SY125 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV65 @ SY125 ) ) @ ( relation_dom @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(763,plain,
! [SV66: $i] :
( ( ~ ( relation @ SV66 )
| ! [SY126: $i] :
~ ( ~ ( ( SY126
!= ( relation_dom @ SV66 ) )
| ! [SY127: $i] :
~ ( ~ ( ~ ( in @ SY127 @ SY126 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY127 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY127 @ SY129 ) @ SV66 )
| ( in @ SY127 @ SY126 ) ) ) )
| ~ ( ~ ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SY126 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY130 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY130 @ SY132 ) @ SV66 )
| ( in @ SY130 @ SY126 ) ) )
| ( SY126
= ( relation_dom @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(764,plain,
! [SV67: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ( relation @ SY134 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY133 ) @ SY134 )
| ~ ( ~ ( in @ SV67 @ ( relation_dom @ SY134 ) )
| ~ ( in @ SY133 @ ( relation_rng @ SY134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(765,plain,
! [SV68: $i] :
( ( ! [SY135: $i] :
~ ( ~ ( ~ ( subset @ SV68 @ ( singleton @ SY135 ) )
| ( SV68 = empty_set )
| ( SV68
= ( singleton @ SY135 ) ) )
| ~ ( ~ ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SY135 ) ) )
| ( subset @ SV68 @ ( singleton @ SY135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(766,plain,
! [SV69: $i] :
( ( ~ ( relation @ SV69 )
| ! [SY136: $i] :
( ~ ( relation @ SY136 )
| ~ ( subset @ ( relation_rng @ SV69 ) @ ( relation_dom @ SY136 ) )
| ( ( relation_dom @ ( relation_composition @ SV69 @ SY136 ) )
= ( relation_dom @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(767,plain,
! [SV70: $i] :
( ( ~ ( relation @ SV70 )
| ! [SY137: $i] :
( ~ ( relation @ SY137 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV70 @ SY137 ) ) @ ( relation_rng @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(768,plain,
! [SV71: $i] :
( ( ~ ( ~ ( ( SV71 != empty_set )
| ! [SY138: $i] :
~ ( in @ SY138 @ SV71 ) )
| ~ ( ~ ! [SY139: $i] :
~ ( in @ SY139 @ SV71 )
| ( SV71 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(769,plain,
! [SV72: $i] :
( ( ! [SY140: $i] :
( ~ ( element @ SY140 @ ( powerset @ ( powerset @ SV72 ) ) )
| ~ ~ ( ~ ( ( SY140 != empty_set ) )
| ( ( complements_of_subsets @ SV72 @ SY140 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(770,plain,
! [SV73: $i] :
( ( ! [SY141: $i] :
~ ( ~ ( ~ ( disjoint @ SV73 @ SY141 )
| ( ( set_intersection2 @ SV73 @ SY141 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV73 @ SY141 )
!= empty_set )
| ( disjoint @ SV73 @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(771,plain,
! [SV74: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV74 )
| ~ ( relation @ SV74 ) )
| ~ ( empty @ ( relation_dom @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(772,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(773,plain,
! [SV75: $i] :
( ( ( singleton @ SV75 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(774,plain,
! [SV76: $i] :
( ( ~ ( relation @ SV76 )
| ~ ! [SY142: $i,SY143: $i] :
~ ( in @ ( ordered_pair @ SY142 @ SY143 ) @ SV76 )
| ( SV76 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(775,plain,
! [SV77: $i] :
( ( ! [SY144: $i] :
~ ( ~ ( ~ ( ( SV77 != empty_set ) )
| ~ ( ~ ( ( SY144
!= ( set_meet @ SV77 ) )
| ! [SY145: $i] :
~ ( ~ ( ~ ( in @ SY145 @ SY144 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY145 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY145 @ SY147 ) )
| ( in @ SY145 @ SY144 ) ) ) )
| ~ ( ~ ! [SY148: $i] :
~ ( ~ ( ~ ( in @ SY148 @ SY144 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY148 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY148 @ SY150 ) )
| ( in @ SY148 @ SY144 ) ) )
| ( SY144
= ( set_meet @ SV77 ) ) ) ) )
| ~ ( ( SV77 != empty_set )
| ~ ( ~ ( ( SY144
!= ( set_meet @ SV77 ) )
| ( SY144 = empty_set ) )
| ~ ( ( SY144 != empty_set )
| ( SY144
= ( set_meet @ SV77 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(776,plain,
! [SV78: $i] :
( ( ~ ( relation @ SV78 )
| ! [SY151: $i] :
( ~ ( relation @ SY151 )
| ~ ( subset @ ( relation_dom @ SV78 ) @ ( relation_rng @ SY151 ) )
| ( ( relation_rng @ ( relation_composition @ SY151 @ SV78 ) )
= ( relation_rng @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(777,plain,
! [SV79: $i] :
( ( ~ ( relation @ SV79 )
| ~ ( ( ( relation_rng @ SV79 )
!= ( relation_dom @ ( relation_inverse @ SV79 ) ) )
| ( ( relation_dom @ SV79 )
!= ( relation_rng @ ( relation_inverse @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(778,plain,
! [SV80: $i] :
( ( ~ ( relation @ SV80 )
| ! [SY152: $i] :
~ ( ~ ( ( SY152
!= ( relation_rng @ SV80 ) )
| ! [SY153: $i] :
~ ( ~ ( ~ ( in @ SY153 @ SY152 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY153 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY153 ) @ SV80 )
| ( in @ SY153 @ SY152 ) ) ) )
| ~ ( ~ ! [SY156: $i] :
~ ( ~ ( ~ ( in @ SY156 @ SY152 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY156 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY156 ) @ SV80 )
| ( in @ SY156 @ SY152 ) ) )
| ( SY152
= ( relation_rng @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(779,plain,
! [SV81: $i] :
( ( ~ ( relation @ SV81 )
| ( ( relation_field @ SV81 )
= ( set_union2 @ ( relation_dom @ SV81 ) @ ( relation_rng @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(780,plain,
! [SV82: $i] :
( ( ! [SY159: $i] :
~ ( ~ ( ~ ( subset @ SV82 @ ( singleton @ SY159 ) )
| ( SV82 = empty_set )
| ( SV82
= ( singleton @ SY159 ) ) )
| ~ ( ~ ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SY159 ) ) )
| ( subset @ SV82 @ ( singleton @ SY159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(781,plain,
! [SV83: $i] :
( ( ! [SY160: $i] :
~ ( ~ ( ( ( set_difference @ SV83 @ SY160 )
!= empty_set )
| ( subset @ SV83 @ SY160 ) )
| ~ ( ~ ( subset @ SV83 @ SY160 )
| ( ( set_difference @ SV83 @ SY160 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(782,plain,
! [SV84: $i] :
( ( ~ ( relation @ SV84 )
| ( subset @ SV84 @ ( cartesian_product2 @ ( relation_dom @ SV84 ) @ ( relation_rng @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(783,plain,
! [SV85: $i] :
( ( ! [SY161: $i] :
~ ( ~ ( ( ( set_difference @ SV85 @ SY161 )
!= empty_set )
| ( subset @ SV85 @ SY161 ) )
| ~ ( ~ ( subset @ SV85 @ SY161 )
| ( ( set_difference @ SV85 @ SY161 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(784,plain,
! [SV86: $i] :
( ( ~ ( empty @ SV86 )
| ( SV86 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(785,plain,
! [SV87: $i] :
( ( ~ ( relation @ SV87 )
| ! [SY162: $i] :
( ~ ( relation @ SY162 )
| ~ ( subset @ SV87 @ SY162 )
| ~ ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SY162 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(786,plain,
! [SV88: $i] :
( ( ~ ( subset @ SV88 @ empty_set )
| ( SV88 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(787,plain,
! [SV64: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV64 )
| ~ ( relation @ SV64 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(788,plain,
! [SV65: $i] :
( ( ( ~ ( relation @ SV65 ) )
= $true )
| ( ( ! [SY125: $i] :
( ~ ( relation @ SY125 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV65 @ SY125 ) ) @ ( relation_dom @ SV65 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(789,plain,
! [SV66: $i] :
( ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( ! [SY126: $i] :
~ ( ~ ( ( SY126
!= ( relation_dom @ SV66 ) )
| ! [SY127: $i] :
~ ( ~ ( ~ ( in @ SY127 @ SY126 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY127 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY127 @ SY129 ) @ SV66 )
| ( in @ SY127 @ SY126 ) ) ) )
| ~ ( ~ ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SY126 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY130 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY130 @ SY132 ) @ SV66 )
| ( in @ SY130 @ SY126 ) ) )
| ( SY126
= ( relation_dom @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(790,plain,
! [SV89: $i,SV67: $i] :
( ( ! [SY163: $i] :
( ~ ( relation @ SY163 )
| ~ ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SY163 )
| ~ ( ~ ( in @ SV67 @ ( relation_dom @ SY163 ) )
| ~ ( in @ SV89 @ ( relation_rng @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(791,plain,
! [SV90: $i,SV68: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV68 @ ( singleton @ SV90 ) )
| ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
| ~ ( ~ ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
| ( subset @ SV68 @ ( singleton @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(792,plain,
! [SV69: $i] :
( ( ( ~ ( relation @ SV69 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( relation @ SY136 )
| ~ ( subset @ ( relation_rng @ SV69 ) @ ( relation_dom @ SY136 ) )
| ( ( relation_dom @ ( relation_composition @ SV69 @ SY136 ) )
= ( relation_dom @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(793,plain,
! [SV70: $i] :
( ( ( ~ ( relation @ SV70 ) )
= $true )
| ( ( ! [SY137: $i] :
( ~ ( relation @ SY137 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV70 @ SY137 ) ) @ ( relation_rng @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(794,plain,
! [SV71: $i] :
( ( ~ ( ( SV71 != empty_set )
| ! [SY138: $i] :
~ ( in @ SY138 @ SV71 ) )
| ~ ( ~ ! [SY139: $i] :
~ ( in @ SY139 @ SV71 )
| ( SV71 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(795,plain,
! [SV72: $i,SV91: $i] :
( ( ~ ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) )
| ~ ~ ( ~ ( ( SV91 != empty_set ) )
| ( ( complements_of_subsets @ SV72 @ SV91 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(796,plain,
! [SV92: $i,SV73: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV73 @ SV92 )
| ( ( set_intersection2 @ SV73 @ SV92 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV73 @ SV92 )
!= empty_set )
| ( disjoint @ SV73 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(797,plain,
! [SV74: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV74 )
| ~ ( relation @ SV74 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(798,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(799,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(800,plain,
! [SV75: $i] :
( ( ( singleton @ SV75 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(801,plain,
! [SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( ~ ! [SY142: $i,SY143: $i] :
~ ( in @ ( ordered_pair @ SY142 @ SY143 ) @ SV76 )
| ( SV76 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(802,plain,
! [SV93: $i,SV77: $i] :
( ( ~ ( ~ ( ~ ( ( SV77 != empty_set ) )
| ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
| ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
| ~ ( ( SV77 != empty_set )
| ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) )
| ~ ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(803,plain,
! [SV78: $i] :
( ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( relation @ SY151 )
| ~ ( subset @ ( relation_dom @ SV78 ) @ ( relation_rng @ SY151 ) )
| ( ( relation_rng @ ( relation_composition @ SY151 @ SV78 ) )
= ( relation_rng @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(804,plain,
! [SV79: $i] :
( ( ( ~ ( relation @ SV79 ) )
= $true )
| ( ( ~ ( ( ( relation_rng @ SV79 )
!= ( relation_dom @ ( relation_inverse @ SV79 ) ) )
| ( ( relation_dom @ SV79 )
!= ( relation_rng @ ( relation_inverse @ SV79 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(805,plain,
! [SV80: $i] :
( ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( ! [SY152: $i] :
~ ( ~ ( ( SY152
!= ( relation_rng @ SV80 ) )
| ! [SY153: $i] :
~ ( ~ ( ~ ( in @ SY153 @ SY152 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY153 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY153 ) @ SV80 )
| ( in @ SY153 @ SY152 ) ) ) )
| ~ ( ~ ! [SY156: $i] :
~ ( ~ ( ~ ( in @ SY156 @ SY152 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY156 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY156 ) @ SV80 )
| ( in @ SY156 @ SY152 ) ) )
| ( SY152
= ( relation_rng @ SV80 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(806,plain,
! [SV81: $i] :
( ( ( ~ ( relation @ SV81 ) )
= $true )
| ( ( ( relation_field @ SV81 )
= ( set_union2 @ ( relation_dom @ SV81 ) @ ( relation_rng @ SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(807,plain,
! [SV94: $i,SV82: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV82 @ ( singleton @ SV94 ) )
| ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
| ~ ( ~ ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
| ( subset @ SV82 @ ( singleton @ SV94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(808,plain,
! [SV95: $i,SV83: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV83 @ SV95 )
!= empty_set )
| ( subset @ SV83 @ SV95 ) )
| ~ ( ~ ( subset @ SV83 @ SV95 )
| ( ( set_difference @ SV83 @ SV95 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(809,plain,
! [SV84: $i] :
( ( ( ~ ( relation @ SV84 ) )
= $true )
| ( ( subset @ SV84 @ ( cartesian_product2 @ ( relation_dom @ SV84 ) @ ( relation_rng @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(810,plain,
! [SV96: $i,SV85: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV85 @ SV96 )
!= empty_set )
| ( subset @ SV85 @ SV96 ) )
| ~ ( ~ ( subset @ SV85 @ SV96 )
| ( ( set_difference @ SV85 @ SV96 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(811,plain,
! [SV86: $i] :
( ( ( ~ ( empty @ SV86 ) )
= $true )
| ( ( SV86 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(812,plain,
! [SV87: $i] :
( ( ( ~ ( relation @ SV87 ) )
= $true )
| ( ( ! [SY162: $i] :
( ~ ( relation @ SY162 )
| ~ ( subset @ SV87 @ SY162 )
| ~ ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SY162 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SY162 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(813,plain,
! [SV88: $i] :
( ( ( ~ ( subset @ SV88 @ empty_set ) )
= $true )
| ( ( SV88 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(814,plain,
! [SV64: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV64 )
| ~ ( relation @ SV64 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(815,plain,
! [SV65: $i] :
( ( ( relation @ SV65 )
= $false )
| ( ( ! [SY125: $i] :
( ~ ( relation @ SY125 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV65 @ SY125 ) ) @ ( relation_dom @ SV65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(816,plain,
! [SV66: $i] :
( ( ( relation @ SV66 )
= $false )
| ( ( ! [SY126: $i] :
~ ( ~ ( ( SY126
!= ( relation_dom @ SV66 ) )
| ! [SY127: $i] :
~ ( ~ ( ~ ( in @ SY127 @ SY126 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY127 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY127 @ SY129 ) @ SV66 )
| ( in @ SY127 @ SY126 ) ) ) )
| ~ ( ~ ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SY126 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY130 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY130 @ SY132 ) @ SV66 )
| ( in @ SY130 @ SY126 ) ) )
| ( SY126
= ( relation_dom @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(817,plain,
! [SV89: $i,SV67: $i,SV97: $i] :
( ( ~ ( relation @ SV97 )
| ~ ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
| ~ ( ~ ( in @ SV67 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV89 @ ( relation_rng @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(818,plain,
! [SV90: $i,SV68: $i] :
( ( ~ ( ~ ( subset @ SV68 @ ( singleton @ SV90 ) )
| ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
| ~ ( ~ ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
| ( subset @ SV68 @ ( singleton @ SV90 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(819,plain,
! [SV69: $i] :
( ( ( relation @ SV69 )
= $false )
| ( ( ! [SY136: $i] :
( ~ ( relation @ SY136 )
| ~ ( subset @ ( relation_rng @ SV69 ) @ ( relation_dom @ SY136 ) )
| ( ( relation_dom @ ( relation_composition @ SV69 @ SY136 ) )
= ( relation_dom @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(820,plain,
! [SV70: $i] :
( ( ( relation @ SV70 )
= $false )
| ( ( ! [SY137: $i] :
( ~ ( relation @ SY137 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV70 @ SY137 ) ) @ ( relation_rng @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(821,plain,
! [SV71: $i] :
( ( ~ ( ( SV71 != empty_set )
| ! [SY138: $i] :
~ ( in @ SY138 @ SV71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(822,plain,
! [SV71: $i] :
( ( ~ ( ~ ! [SY139: $i] :
~ ( in @ SY139 @ SV71 )
| ( SV71 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(823,plain,
! [SV72: $i,SV91: $i] :
( ( ( ~ ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV91 != empty_set ) )
| ( ( complements_of_subsets @ SV72 @ SV91 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(824,plain,
! [SV92: $i,SV73: $i] :
( ( ~ ( ~ ( disjoint @ SV73 @ SV92 )
| ( ( set_intersection2 @ SV73 @ SV92 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV73 @ SV92 )
!= empty_set )
| ( disjoint @ SV73 @ SV92 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(825,plain,
! [SV74: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV74 )
| ~ ( relation @ SV74 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(826,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(827,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(828,plain,
! [SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( ~ ! [SY142: $i,SY143: $i] :
~ ( in @ ( ordered_pair @ SY142 @ SY143 ) @ SV76 )
| ( SV76 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(829,plain,
! [SV93: $i,SV77: $i] :
( ( ~ ( ~ ( ( SV77 != empty_set ) )
| ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
| ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
| ~ ( ( SV77 != empty_set )
| ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) )
| ~ ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(830,plain,
! [SV78: $i] :
( ( ( relation @ SV78 )
= $false )
| ( ( ! [SY151: $i] :
( ~ ( relation @ SY151 )
| ~ ( subset @ ( relation_dom @ SV78 ) @ ( relation_rng @ SY151 ) )
| ( ( relation_rng @ ( relation_composition @ SY151 @ SV78 ) )
= ( relation_rng @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(831,plain,
! [SV79: $i] :
( ( ( relation @ SV79 )
= $false )
| ( ( ~ ( ( ( relation_rng @ SV79 )
!= ( relation_dom @ ( relation_inverse @ SV79 ) ) )
| ( ( relation_dom @ SV79 )
!= ( relation_rng @ ( relation_inverse @ SV79 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(832,plain,
! [SV80: $i] :
( ( ( relation @ SV80 )
= $false )
| ( ( ! [SY152: $i] :
~ ( ~ ( ( SY152
!= ( relation_rng @ SV80 ) )
| ! [SY153: $i] :
~ ( ~ ( ~ ( in @ SY153 @ SY152 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY153 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY153 ) @ SV80 )
| ( in @ SY153 @ SY152 ) ) ) )
| ~ ( ~ ! [SY156: $i] :
~ ( ~ ( ~ ( in @ SY156 @ SY152 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY156 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY156 ) @ SV80 )
| ( in @ SY156 @ SY152 ) ) )
| ( SY152
= ( relation_rng @ SV80 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(833,plain,
! [SV81: $i] :
( ( ( relation @ SV81 )
= $false )
| ( ( ( relation_field @ SV81 )
= ( set_union2 @ ( relation_dom @ SV81 ) @ ( relation_rng @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(834,plain,
! [SV94: $i,SV82: $i] :
( ( ~ ( ~ ( subset @ SV82 @ ( singleton @ SV94 ) )
| ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
| ~ ( ~ ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
| ( subset @ SV82 @ ( singleton @ SV94 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(835,plain,
! [SV95: $i,SV83: $i] :
( ( ~ ( ( ( set_difference @ SV83 @ SV95 )
!= empty_set )
| ( subset @ SV83 @ SV95 ) )
| ~ ( ~ ( subset @ SV83 @ SV95 )
| ( ( set_difference @ SV83 @ SV95 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(836,plain,
! [SV84: $i] :
( ( ( relation @ SV84 )
= $false )
| ( ( subset @ SV84 @ ( cartesian_product2 @ ( relation_dom @ SV84 ) @ ( relation_rng @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(837,plain,
! [SV96: $i,SV85: $i] :
( ( ~ ( ( ( set_difference @ SV85 @ SV96 )
!= empty_set )
| ( subset @ SV85 @ SV96 ) )
| ~ ( ~ ( subset @ SV85 @ SV96 )
| ( ( set_difference @ SV85 @ SV96 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(838,plain,
! [SV86: $i] :
( ( ( empty @ SV86 )
= $false )
| ( ( SV86 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(839,plain,
! [SV87: $i] :
( ( ( relation @ SV87 )
= $false )
| ( ( ! [SY162: $i] :
( ~ ( relation @ SY162 )
| ~ ( subset @ SV87 @ SY162 )
| ~ ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SY162 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SY162 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(840,plain,
! [SV88: $i] :
( ( ( subset @ SV88 @ empty_set )
= $false )
| ( ( SV88 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(841,plain,
! [SV64: $i] :
( ( ( ~ ~ ( empty @ SV64 )
| ~ ( relation @ SV64 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(842,plain,
! [SV65: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV65 @ SV98 ) ) @ ( relation_dom @ SV65 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(843,plain,
! [SV66: $i,SV99: $i] :
( ( ( ~ ( ~ ( ( SV99
!= ( relation_dom @ SV66 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV99 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY129 ) @ SV66 )
| ( in @ SY170 @ SV99 ) ) ) )
| ~ ( ~ ! [SY173: $i] :
~ ( ~ ( ~ ( in @ SY173 @ SV99 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY132 ) @ SV66 )
| ( in @ SY173 @ SV99 ) ) )
| ( SV99
= ( relation_dom @ SV66 ) ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(844,plain,
! [SV89: $i,SV67: $i,SV97: $i] :
( ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
| ~ ( ~ ( in @ SV67 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV89 @ ( relation_rng @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(845,plain,
! [SV90: $i,SV68: $i] :
( ( ~ ( ~ ( subset @ SV68 @ ( singleton @ SV90 ) )
| ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(846,plain,
! [SV90: $i,SV68: $i] :
( ( ~ ( ~ ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
| ( subset @ SV68 @ ( singleton @ SV90 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(847,plain,
! [SV69: $i,SV100: $i] :
( ( ( ~ ( relation @ SV100 )
| ~ ( subset @ ( relation_rng @ SV69 ) @ ( relation_dom @ SV100 ) )
| ( ( relation_dom @ ( relation_composition @ SV69 @ SV100 ) )
= ( relation_dom @ SV69 ) ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(848,plain,
! [SV70: $i,SV101: $i] :
( ( ( ~ ( relation @ SV101 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV70 @ SV101 ) ) @ ( relation_rng @ SV101 ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(849,plain,
! [SV71: $i] :
( ( ( SV71 != empty_set )
| ! [SY138: $i] :
~ ( in @ SY138 @ SV71 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(850,plain,
! [SV71: $i] :
( ( ~ ! [SY139: $i] :
~ ( in @ SY139 @ SV71 )
| ( SV71 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(851,plain,
! [SV72: $i,SV91: $i] :
( ( ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV91 != empty_set ) )
| ( ( complements_of_subsets @ SV72 @ SV91 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(852,plain,
! [SV92: $i,SV73: $i] :
( ( ~ ( ~ ( disjoint @ SV73 @ SV92 )
| ( ( set_intersection2 @ SV73 @ SV92 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(853,plain,
! [SV92: $i,SV73: $i] :
( ( ~ ( ( ( set_intersection2 @ SV73 @ SV92 )
!= empty_set )
| ( disjoint @ SV73 @ SV92 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(854,plain,
! [SV74: $i] :
( ( ( ~ ~ ( empty @ SV74 )
| ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(855,plain,
! [SV76: $i] :
( ( ( ~ ! [SY142: $i,SY143: $i] :
~ ( in @ ( ordered_pair @ SY142 @ SY143 ) @ SV76 ) )
= $true )
| ( ( SV76 = empty_set )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(856,plain,
! [SV93: $i,SV77: $i] :
( ( ~ ( ~ ( ( SV77 != empty_set ) )
| ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
| ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(857,plain,
! [SV93: $i,SV77: $i] :
( ( ~ ( ( SV77 != empty_set )
| ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) )
| ~ ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(858,plain,
! [SV78: $i,SV102: $i] :
( ( ( ~ ( relation @ SV102 )
| ~ ( subset @ ( relation_dom @ SV78 ) @ ( relation_rng @ SV102 ) )
| ( ( relation_rng @ ( relation_composition @ SV102 @ SV78 ) )
= ( relation_rng @ SV78 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(859,plain,
! [SV79: $i] :
( ( ( ( ( relation_rng @ SV79 )
!= ( relation_dom @ ( relation_inverse @ SV79 ) ) )
| ( ( relation_dom @ SV79 )
!= ( relation_rng @ ( relation_inverse @ SV79 ) ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(860,plain,
! [SV80: $i,SV103: $i] :
( ( ( ~ ( ~ ( ( SV103
!= ( relation_rng @ SV80 ) )
| ! [SY176: $i] :
~ ( ~ ( ~ ( in @ SY176 @ SV103 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY176 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY176 ) @ SV80 )
| ( in @ SY176 @ SV103 ) ) ) )
| ~ ( ~ ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SV103 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY179 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY179 ) @ SV80 )
| ( in @ SY179 @ SV103 ) ) )
| ( SV103
= ( relation_rng @ SV80 ) ) ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(861,plain,
! [SV94: $i,SV82: $i] :
( ( ~ ( ~ ( subset @ SV82 @ ( singleton @ SV94 ) )
| ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(862,plain,
! [SV94: $i,SV82: $i] :
( ( ~ ( ~ ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
| ( subset @ SV82 @ ( singleton @ SV94 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(863,plain,
! [SV95: $i,SV83: $i] :
( ( ~ ( ( ( set_difference @ SV83 @ SV95 )
!= empty_set )
| ( subset @ SV83 @ SV95 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[835]) ).
thf(864,plain,
! [SV95: $i,SV83: $i] :
( ( ~ ( ~ ( subset @ SV83 @ SV95 )
| ( ( set_difference @ SV83 @ SV95 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[835]) ).
thf(865,plain,
! [SV96: $i,SV85: $i] :
( ( ~ ( ( ( set_difference @ SV85 @ SV96 )
!= empty_set )
| ( subset @ SV85 @ SV96 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[837]) ).
thf(866,plain,
! [SV96: $i,SV85: $i] :
( ( ~ ( ~ ( subset @ SV85 @ SV96 )
| ( ( set_difference @ SV85 @ SV96 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[837]) ).
thf(867,plain,
! [SV87: $i,SV104: $i] :
( ( ( ~ ( relation @ SV104 )
| ~ ( subset @ SV87 @ SV104 )
| ~ ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SV104 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(868,plain,
! [SV64: $i] :
( ( ( ~ ~ ( empty @ SV64 ) )
= $true )
| ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(869,plain,
! [SV65: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV65 @ SV98 ) ) @ ( relation_dom @ SV65 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(870,plain,
! [SV66: $i,SV99: $i] :
( ( ( ~ ( ( SV99
!= ( relation_dom @ SV66 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV99 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY129 ) @ SV66 )
| ( in @ SY170 @ SV99 ) ) ) )
| ~ ( ~ ! [SY173: $i] :
~ ( ~ ( ~ ( in @ SY173 @ SV99 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY132 ) @ SV66 )
| ( in @ SY173 @ SV99 ) ) )
| ( SV99
= ( relation_dom @ SV66 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(871,plain,
! [SV89: $i,SV67: $i,SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
| ~ ( ~ ( in @ SV67 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV89 @ ( relation_rng @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(872,plain,
! [SV90: $i,SV68: $i] :
( ( ~ ( subset @ SV68 @ ( singleton @ SV90 ) )
| ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(873,plain,
! [SV90: $i,SV68: $i] :
( ( ~ ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
| ( subset @ SV68 @ ( singleton @ SV90 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(874,plain,
! [SV69: $i,SV100: $i] :
( ( ( ~ ( relation @ SV100 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV69 ) @ ( relation_dom @ SV100 ) )
| ( ( relation_dom @ ( relation_composition @ SV69 @ SV100 ) )
= ( relation_dom @ SV69 ) ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(875,plain,
! [SV70: $i,SV101: $i] :
( ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV70 @ SV101 ) ) @ ( relation_rng @ SV101 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(876,plain,
! [SV71: $i] :
( ( ( SV71 != empty_set )
= $true )
| ( ( ! [SY138: $i] :
~ ( in @ SY138 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(877,plain,
! [SV71: $i] :
( ( ( ~ ! [SY139: $i] :
~ ( in @ SY139 @ SV71 ) )
= $true )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(878,plain,
! [SV72: $i,SV91: $i] :
( ( ( ~ ( ~ ( ( SV91 != empty_set ) )
| ( ( complements_of_subsets @ SV72 @ SV91 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(879,plain,
! [SV92: $i,SV73: $i] :
( ( ~ ( disjoint @ SV73 @ SV92 )
| ( ( set_intersection2 @ SV73 @ SV92 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(880,plain,
! [SV92: $i,SV73: $i] :
( ( ( ( set_intersection2 @ SV73 @ SV92 )
!= empty_set )
| ( disjoint @ SV73 @ SV92 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(881,plain,
! [SV74: $i] :
( ( ( ~ ~ ( empty @ SV74 ) )
= $true )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(882,plain,
! [SV76: $i] :
( ( ( ! [SY142: $i,SY143: $i] :
~ ( in @ ( ordered_pair @ SY142 @ SY143 ) @ SV76 ) )
= $false )
| ( ( SV76 = empty_set )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(883,plain,
! [SV93: $i,SV77: $i] :
( ( ~ ( ( SV77 != empty_set ) )
| ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
| ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(884,plain,
! [SV93: $i,SV77: $i] :
( ( ( SV77 != empty_set )
| ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) )
| ~ ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(885,plain,
! [SV78: $i,SV102: $i] :
( ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV78 ) @ ( relation_rng @ SV102 ) )
| ( ( relation_rng @ ( relation_composition @ SV102 @ SV78 ) )
= ( relation_rng @ SV78 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(886,plain,
! [SV79: $i] :
( ( ( ( relation_rng @ SV79 )
!= ( relation_dom @ ( relation_inverse @ SV79 ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(887,plain,
! [SV79: $i] :
( ( ( ( relation_dom @ SV79 )
!= ( relation_rng @ ( relation_inverse @ SV79 ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(888,plain,
! [SV80: $i,SV103: $i] :
( ( ( ~ ( ( SV103
!= ( relation_rng @ SV80 ) )
| ! [SY176: $i] :
~ ( ~ ( ~ ( in @ SY176 @ SV103 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY176 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY176 ) @ SV80 )
| ( in @ SY176 @ SV103 ) ) ) )
| ~ ( ~ ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SV103 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY179 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY179 ) @ SV80 )
| ( in @ SY179 @ SV103 ) ) )
| ( SV103
= ( relation_rng @ SV80 ) ) ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(889,plain,
! [SV94: $i,SV82: $i] :
( ( ~ ( subset @ SV82 @ ( singleton @ SV94 ) )
| ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(890,plain,
! [SV94: $i,SV82: $i] :
( ( ~ ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
| ( subset @ SV82 @ ( singleton @ SV94 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(891,plain,
! [SV95: $i,SV83: $i] :
( ( ( ( set_difference @ SV83 @ SV95 )
!= empty_set )
| ( subset @ SV83 @ SV95 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(892,plain,
! [SV95: $i,SV83: $i] :
( ( ~ ( subset @ SV83 @ SV95 )
| ( ( set_difference @ SV83 @ SV95 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(893,plain,
! [SV96: $i,SV85: $i] :
( ( ( ( set_difference @ SV85 @ SV96 )
!= empty_set )
| ( subset @ SV85 @ SV96 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(894,plain,
! [SV96: $i,SV85: $i] :
( ( ~ ( subset @ SV85 @ SV96 )
| ( ( set_difference @ SV85 @ SV96 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(895,plain,
! [SV87: $i,SV104: $i] :
( ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( ~ ( subset @ SV87 @ SV104 )
| ~ ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SV104 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(896,plain,
! [SV64: $i] :
( ( ( ~ ( empty @ SV64 ) )
= $false )
| ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(897,plain,
! [SV65: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV65 @ SV98 ) ) @ ( relation_dom @ SV65 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(898,plain,
! [SV66: $i,SV99: $i] :
( ( ( ~ ( ( SV99
!= ( relation_dom @ SV66 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV99 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY129 ) @ SV66 )
| ( in @ SY170 @ SV99 ) ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(899,plain,
! [SV66: $i,SV99: $i] :
( ( ( ~ ( ~ ! [SY173: $i] :
~ ( ~ ( ~ ( in @ SY173 @ SV99 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY132 ) @ SV66 )
| ( in @ SY173 @ SV99 ) ) )
| ( SV99
= ( relation_dom @ SV66 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(900,plain,
! [SV97: $i,SV89: $i,SV67: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV67 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV89 @ ( relation_rng @ SV97 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(901,plain,
! [SV90: $i,SV68: $i] :
( ( ( ~ ( subset @ SV68 @ ( singleton @ SV90 ) ) )
= $true )
| ( ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(902,plain,
! [SV90: $i,SV68: $i] :
( ( ( ~ ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) ) )
= $true )
| ( ( subset @ SV68 @ ( singleton @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(903,plain,
! [SV69: $i,SV100: $i] :
( ( ( relation @ SV100 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV69 ) @ ( relation_dom @ SV100 ) )
| ( ( relation_dom @ ( relation_composition @ SV69 @ SV100 ) )
= ( relation_dom @ SV69 ) ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(904,plain,
! [SV70: $i,SV101: $i] :
( ( ( relation @ SV101 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV70 @ SV101 ) ) @ ( relation_rng @ SV101 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(905,plain,
! [SV71: $i] :
( ( ( SV71 = empty_set )
= $false )
| ( ( ! [SY138: $i] :
~ ( in @ SY138 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(906,plain,
! [SV71: $i] :
( ( ( ! [SY139: $i] :
~ ( in @ SY139 @ SV71 ) )
= $false )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(907,plain,
! [SV72: $i,SV91: $i] :
( ( ( ~ ( ( SV91 != empty_set ) )
| ( ( complements_of_subsets @ SV72 @ SV91 )
!= empty_set ) )
= $true )
| ( ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(908,plain,
! [SV92: $i,SV73: $i] :
( ( ( ~ ( disjoint @ SV73 @ SV92 ) )
= $true )
| ( ( ( set_intersection2 @ SV73 @ SV92 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(909,plain,
! [SV92: $i,SV73: $i] :
( ( ( ( set_intersection2 @ SV73 @ SV92 )
!= empty_set )
= $true )
| ( ( disjoint @ SV73 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(910,plain,
! [SV74: $i] :
( ( ( ~ ( empty @ SV74 ) )
= $false )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(911,plain,
! [SV76: $i] :
( ( ( ! [SY182: $i] :
~ ( in @ ( ordered_pair @ ( sK15_SY142 @ SV76 ) @ SY182 ) @ SV76 ) )
= $false )
| ( ( SV76 = empty_set )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[882]) ).
thf(912,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ( ( SV77 != empty_set ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
| ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(913,plain,
! [SV93: $i,SV77: $i] :
( ( ( SV77 != empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) )
| ~ ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(914,plain,
! [SV78: $i,SV102: $i] :
( ( ( relation @ SV102 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV78 ) @ ( relation_rng @ SV102 ) )
| ( ( relation_rng @ ( relation_composition @ SV102 @ SV78 ) )
= ( relation_rng @ SV78 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(915,plain,
! [SV79: $i] :
( ( ( ( relation_rng @ SV79 )
= ( relation_dom @ ( relation_inverse @ SV79 ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(916,plain,
! [SV79: $i] :
( ( ( ( relation_dom @ SV79 )
= ( relation_rng @ ( relation_inverse @ SV79 ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(917,plain,
! [SV80: $i,SV103: $i] :
( ( ( ~ ( ( SV103
!= ( relation_rng @ SV80 ) )
| ! [SY176: $i] :
~ ( ~ ( ~ ( in @ SY176 @ SV103 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY176 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY176 ) @ SV80 )
| ( in @ SY176 @ SV103 ) ) ) ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(918,plain,
! [SV80: $i,SV103: $i] :
( ( ( ~ ( ~ ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SV103 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY179 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY179 ) @ SV80 )
| ( in @ SY179 @ SV103 ) ) )
| ( SV103
= ( relation_rng @ SV80 ) ) ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(919,plain,
! [SV94: $i,SV82: $i] :
( ( ( ~ ( subset @ SV82 @ ( singleton @ SV94 ) ) )
= $true )
| ( ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(920,plain,
! [SV94: $i,SV82: $i] :
( ( ( ~ ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) ) )
= $true )
| ( ( subset @ SV82 @ ( singleton @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(921,plain,
! [SV95: $i,SV83: $i] :
( ( ( ( set_difference @ SV83 @ SV95 )
!= empty_set )
= $true )
| ( ( subset @ SV83 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(922,plain,
! [SV95: $i,SV83: $i] :
( ( ( ~ ( subset @ SV83 @ SV95 ) )
= $true )
| ( ( ( set_difference @ SV83 @ SV95 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(923,plain,
! [SV96: $i,SV85: $i] :
( ( ( ( set_difference @ SV85 @ SV96 )
!= empty_set )
= $true )
| ( ( subset @ SV85 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(924,plain,
! [SV96: $i,SV85: $i] :
( ( ( ~ ( subset @ SV85 @ SV96 ) )
= $true )
| ( ( ( set_difference @ SV85 @ SV96 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(925,plain,
! [SV87: $i,SV104: $i] :
( ( ( relation @ SV104 )
= $false )
| ( ( ~ ( subset @ SV87 @ SV104 )
| ~ ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SV104 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(926,plain,
! [SV64: $i] :
( ( ( empty @ SV64 )
= $true )
| ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(927,plain,
! [SV66: $i,SV99: $i] :
( ( ( ( SV99
!= ( relation_dom @ SV66 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV99 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY129 ) @ SV66 )
| ( in @ SY170 @ SV99 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(928,plain,
! [SV66: $i,SV99: $i] :
( ( ( ~ ! [SY173: $i] :
~ ( ~ ( ~ ( in @ SY173 @ SV99 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY132 ) @ SV66 )
| ( in @ SY173 @ SV99 ) ) )
| ( SV99
= ( relation_dom @ SV66 ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(929,plain,
! [SV97: $i,SV89: $i,SV67: $i] :
( ( ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
= $false )
| ( ( ~ ( ~ ( in @ SV67 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV89 @ ( relation_rng @ SV97 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(930,plain,
! [SV90: $i,SV68: $i] :
( ( ( subset @ SV68 @ ( singleton @ SV90 ) )
= $false )
| ( ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(931,plain,
! [SV90: $i,SV68: $i] :
( ( ( ( SV68 = empty_set )
| ( SV68
= ( singleton @ SV90 ) ) )
= $false )
| ( ( subset @ SV68 @ ( singleton @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(932,plain,
! [SV100: $i,SV69: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV69 ) @ ( relation_dom @ SV100 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV69 @ SV100 ) )
= ( relation_dom @ SV69 ) )
= $true )
| ( ( relation @ SV100 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(933,plain,
! [SV71: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV71 ) )
= $true )
| ( ( SV71 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(934,plain,
! [SV71: $i] :
( ( ( ~ ( in @ ( sK16_SY139 @ SV71 ) @ SV71 ) )
= $false )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[906]) ).
thf(935,plain,
! [SV72: $i,SV91: $i] :
( ( ( ~ ( ( SV91 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV72 @ SV91 )
!= empty_set )
= $true )
| ( ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(936,plain,
! [SV92: $i,SV73: $i] :
( ( ( disjoint @ SV73 @ SV92 )
= $false )
| ( ( ( set_intersection2 @ SV73 @ SV92 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(937,plain,
! [SV92: $i,SV73: $i] :
( ( ( ( set_intersection2 @ SV73 @ SV92 )
= empty_set )
= $false )
| ( ( disjoint @ SV73 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(938,plain,
! [SV74: $i] :
( ( ( empty @ SV74 )
= $true )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(939,plain,
! [SV76: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK15_SY142 @ SV76 ) @ ( sK17_SY182 @ SV76 ) ) @ SV76 ) )
= $false )
| ( ( SV76 = empty_set )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[911]) ).
thf(940,plain,
! [SV93: $i,SV77: $i] :
( ( ( SV77 != empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
| ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(941,plain,
! [SV93: $i,SV77: $i] :
( ( ( SV77 = empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) )
| ~ ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(942,plain,
! [SV102: $i,SV78: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV78 ) @ ( relation_rng @ SV102 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV102 @ SV78 ) )
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(943,plain,
! [SV80: $i,SV103: $i] :
( ( ( ( SV103
!= ( relation_rng @ SV80 ) )
| ! [SY176: $i] :
~ ( ~ ( ~ ( in @ SY176 @ SV103 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY176 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY176 ) @ SV80 )
| ( in @ SY176 @ SV103 ) ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(944,plain,
! [SV80: $i,SV103: $i] :
( ( ( ~ ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SV103 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY179 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY179 ) @ SV80 )
| ( in @ SY179 @ SV103 ) ) )
| ( SV103
= ( relation_rng @ SV80 ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(945,plain,
! [SV94: $i,SV82: $i] :
( ( ( subset @ SV82 @ ( singleton @ SV94 ) )
= $false )
| ( ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(946,plain,
! [SV94: $i,SV82: $i] :
( ( ( ( SV82 = empty_set )
| ( SV82
= ( singleton @ SV94 ) ) )
= $false )
| ( ( subset @ SV82 @ ( singleton @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(947,plain,
! [SV95: $i,SV83: $i] :
( ( ( ( set_difference @ SV83 @ SV95 )
= empty_set )
= $false )
| ( ( subset @ SV83 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(948,plain,
! [SV95: $i,SV83: $i] :
( ( ( subset @ SV83 @ SV95 )
= $false )
| ( ( ( set_difference @ SV83 @ SV95 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(949,plain,
! [SV96: $i,SV85: $i] :
( ( ( ( set_difference @ SV85 @ SV96 )
= empty_set )
= $false )
| ( ( subset @ SV85 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(950,plain,
! [SV96: $i,SV85: $i] :
( ( ( subset @ SV85 @ SV96 )
= $false )
| ( ( ( set_difference @ SV85 @ SV96 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(951,plain,
! [SV104: $i,SV87: $i] :
( ( ( ~ ( subset @ SV87 @ SV104 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SV104 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV104 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(952,plain,
! [SV64: $i] :
( ( ( relation @ SV64 )
= $false )
| ( ( empty @ SV64 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(953,plain,
! [SV66: $i,SV99: $i] :
( ( ( SV99
!= ( relation_dom @ SV66 ) )
= $true )
| ( ( ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV99 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY129 ) @ SV66 )
| ( in @ SY170 @ SV99 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(954,plain,
! [SV66: $i,SV99: $i] :
( ( ( ~ ! [SY173: $i] :
~ ( ~ ( ~ ( in @ SY173 @ SV99 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY132 ) @ SV66 )
| ( in @ SY173 @ SV99 ) ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(955,plain,
! [SV89: $i,SV97: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV89 @ ( relation_rng @ SV97 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(956,plain,
! [SV90: $i,SV68: $i] :
( ( ( SV68 = empty_set )
= $true )
| ( ( SV68
= ( singleton @ SV90 ) )
= $true )
| ( ( subset @ SV68 @ ( singleton @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(957,plain,
! [SV90: $i,SV68: $i] :
( ( ( SV68 = empty_set )
= $false )
| ( ( subset @ SV68 @ ( singleton @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(958,plain,
! [SV90: $i,SV68: $i] :
( ( ( SV68
= ( singleton @ SV90 ) )
= $false )
| ( ( subset @ SV68 @ ( singleton @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(959,plain,
! [SV100: $i,SV69: $i] :
( ( ( subset @ ( relation_rng @ SV69 ) @ ( relation_dom @ SV100 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV69 @ SV100 ) )
= ( relation_dom @ SV69 ) )
= $true )
| ( ( relation @ SV100 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(960,plain,
! [SV71: $i,SV105: $i] :
( ( ( in @ SV105 @ SV71 )
= $false )
| ( ( SV71 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(961,plain,
! [SV71: $i] :
( ( ( in @ ( sK16_SY139 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(962,plain,
! [SV72: $i,SV91: $i] :
( ( ( SV91 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV72 @ SV91 )
!= empty_set )
= $true )
| ( ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(963,plain,
! [SV74: $i] :
( ( ( relation @ SV74 )
= $false )
| ( ( empty @ SV74 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(964,plain,
! [SV76: $i] :
( ( ( in @ ( ordered_pair @ ( sK15_SY142 @ SV76 ) @ ( sK17_SY182 @ SV76 ) ) @ SV76 )
= $true )
| ( ( SV76 = empty_set )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(965,plain,
! [SV93: $i,SV77: $i] :
( ( ( SV77 = empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
| ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(966,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) )
| ~ ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) ) )
= $false )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(967,plain,
! [SV102: $i,SV78: $i] :
( ( ( subset @ ( relation_dom @ SV78 ) @ ( relation_rng @ SV102 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV102 @ SV78 ) )
= ( relation_rng @ SV78 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(968,plain,
! [SV80: $i,SV103: $i] :
( ( ( SV103
!= ( relation_rng @ SV80 ) )
= $true )
| ( ( ! [SY176: $i] :
~ ( ~ ( ~ ( in @ SY176 @ SV103 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY176 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY176 ) @ SV80 )
| ( in @ SY176 @ SV103 ) ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(969,plain,
! [SV80: $i,SV103: $i] :
( ( ( ~ ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SV103 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY179 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY179 ) @ SV80 )
| ( in @ SY179 @ SV103 ) ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(970,plain,
! [SV94: $i,SV82: $i] :
( ( ( SV82 = empty_set )
= $true )
| ( ( SV82
= ( singleton @ SV94 ) )
= $true )
| ( ( subset @ SV82 @ ( singleton @ SV94 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(971,plain,
! [SV94: $i,SV82: $i] :
( ( ( SV82 = empty_set )
= $false )
| ( ( subset @ SV82 @ ( singleton @ SV94 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(972,plain,
! [SV94: $i,SV82: $i] :
( ( ( SV82
= ( singleton @ SV94 ) )
= $false )
| ( ( subset @ SV82 @ ( singleton @ SV94 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(973,plain,
! [SV104: $i,SV87: $i] :
( ( ( subset @ SV87 @ SV104 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SV104 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV104 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(974,plain,
! [SV64: $i] :
( ( ( empty @ ( relation_rng @ SV64 ) )
= $false )
| ( ( empty @ SV64 )
= $true )
| ( ( relation @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(975,plain,
! [SV66: $i,SV99: $i] :
( ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV99 )
| ~ ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY128 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ( in @ ( ordered_pair @ SY170 @ SY129 ) @ SV66 )
| ( in @ SY170 @ SV99 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(976,plain,
! [SV66: $i,SV99: $i] :
( ( ( ! [SY173: $i] :
~ ( ~ ( ~ ( in @ SY173 @ SV99 )
| ~ ! [SY131: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY131 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY173 @ SY132 ) @ SV66 )
| ( in @ SY173 @ SV99 ) ) ) )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(977,plain,
! [SV89: $i,SV97: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ ( relation_dom @ SV97 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[955]) ).
thf(978,plain,
! [SV67: $i,SV97: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ ( relation_rng @ SV97 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[955]) ).
thf(979,plain,
! [SV72: $i,SV91: $i] :
( ( ( SV91 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV72 @ SV91 )
!= empty_set )
= $true )
| ( ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(980,plain,
! [SV74: $i] :
( ( ( empty @ ( relation_dom @ SV74 ) )
= $false )
| ( ( empty @ SV74 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(981,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
| ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(982,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) ) )
= $false )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(983,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) ) )
= $false )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(984,plain,
! [SV80: $i,SV103: $i] :
( ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( ! [SY176: $i] :
~ ( ~ ( ~ ( in @ SY176 @ SV103 )
| ~ ! [SY154: $i] :
~ ( in @ ( ordered_pair @ SY154 @ SY176 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY155: $i] :
~ ( in @ ( ordered_pair @ SY155 @ SY176 ) @ SV80 )
| ( in @ SY176 @ SV103 ) ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(985,plain,
! [SV80: $i,SV103: $i] :
( ( ( ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SV103 )
| ~ ! [SY157: $i] :
~ ( in @ ( ordered_pair @ SY157 @ SY179 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ( in @ ( ordered_pair @ SY158 @ SY179 ) @ SV80 )
| ( in @ SY179 @ SV103 ) ) ) )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(986,plain,
! [SV104: $i,SV87: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SV104 ) )
| ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SV104 ) ) )
= $false )
| ( ( subset @ SV87 @ SV104 )
= $false )
| ( ( relation @ SV104 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(987,plain,
! [SV66: $i,SV99: $i,SV106: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV106 @ SV99 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY183 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY184 ) @ SV66 )
| ( in @ SV106 @ SV99 ) ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(988,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
| ~ ! [SY185: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY185 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) ) )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[976]) ).
thf(989,plain,
! [SV89: $i,SV97: $i,SV67: $i] :
( ( ( in @ SV67 @ ( relation_dom @ SV97 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(990,plain,
! [SV67: $i,SV97: $i,SV89: $i] :
( ( ( in @ SV89 @ ( relation_rng @ SV97 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV89 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(991,plain,
! [SV91: $i,SV72: $i] :
( ( ( ( complements_of_subsets @ SV72 @ SV91 )
= empty_set )
= $false )
| ( ( SV91 = empty_set )
= $true )
| ( ( element @ SV91 @ ( powerset @ ( powerset @ SV72 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(992,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(993,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(994,plain,
! [SV77: $i,SV93: $i] :
( ( ( ( SV93
!= ( set_meet @ SV77 ) )
| ( SV93 = empty_set ) )
= $true )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(995,plain,
! [SV77: $i,SV93: $i] :
( ( ( ( SV93 != empty_set )
| ( SV93
= ( set_meet @ SV77 ) ) )
= $true )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(996,plain,
! [SV80: $i,SV103: $i,SV107: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV107 @ SV103 )
| ~ ! [SY187: $i] :
~ ( in @ ( ordered_pair @ SY187 @ SV107 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY188: $i] :
~ ( in @ ( ordered_pair @ SY188 @ SV107 ) @ SV80 )
| ( in @ SV107 @ SV103 ) ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(997,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
| ~ ! [SY189: $i] :
~ ( in @ ( ordered_pair @ SY189 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
| ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) ) )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[985]) ).
thf(998,plain,
! [SV104: $i,SV87: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SV104 ) ) )
= $false )
| ( ( subset @ SV87 @ SV104 )
= $false )
| ( ( relation @ SV104 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(999,plain,
! [SV104: $i,SV87: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SV104 ) ) )
= $false )
| ( ( subset @ SV87 @ SV104 )
= $false )
| ( ( relation @ SV104 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1000,plain,
! [SV66: $i,SV99: $i,SV106: $i] :
( ( ( ~ ( ~ ( in @ SV106 @ SV99 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY183 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY184 ) @ SV66 )
| ( in @ SV106 @ SV99 ) ) )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1001,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
| ~ ! [SY185: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY185 ) @ SV66 ) )
| ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1002,plain,
! [SV77: $i,SV93: $i] :
( ( ( ( SV93
!= ( set_meet @ SV77 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1003,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) )
| ( SV93
= ( set_meet @ SV77 ) ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1004,plain,
! [SV77: $i,SV93: $i] :
( ( ( SV93
!= ( set_meet @ SV77 ) )
= $true )
| ( ( SV93 = empty_set )
= $true )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1005,plain,
! [SV77: $i,SV93: $i] :
( ( ( SV93 != empty_set )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1006,plain,
! [SV80: $i,SV103: $i,SV107: $i] :
( ( ( ~ ( ~ ( in @ SV107 @ SV103 )
| ~ ! [SY187: $i] :
~ ( in @ ( ordered_pair @ SY187 @ SV107 ) @ SV80 ) )
| ~ ( ~ ~ ! [SY188: $i] :
~ ( in @ ( ordered_pair @ SY188 @ SV107 ) @ SV80 )
| ( in @ SV107 @ SV103 ) ) )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1007,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
| ~ ! [SY189: $i] :
~ ( in @ ( ordered_pair @ SY189 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
| ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1008,plain,
! [SV104: $i,SV87: $i] :
( ( ( subset @ ( relation_dom @ SV87 ) @ ( relation_dom @ SV104 ) )
= $true )
| ( ( subset @ SV87 @ SV104 )
= $false )
| ( ( relation @ SV104 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1009,plain,
! [SV104: $i,SV87: $i] :
( ( ( subset @ ( relation_rng @ SV87 ) @ ( relation_rng @ SV104 ) )
= $true )
| ( ( subset @ SV87 @ SV104 )
= $false )
| ( ( relation @ SV104 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1010,plain,
! [SV66: $i,SV99: $i,SV106: $i] :
( ( ( ~ ( ~ ( in @ SV106 @ SV99 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY183 ) @ SV66 ) ) )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1011,plain,
! [SV99: $i,SV66: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY184 ) @ SV66 )
| ( in @ SV106 @ SV99 ) ) )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1012,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
| ~ ! [SY185: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY185 ) @ SV66 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1013,plain,
! [SV77: $i,SV93: $i] :
( ( ( SV93
!= ( set_meet @ SV77 ) )
= $true )
| ( ( ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1014,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1015,plain,
! [SV77: $i,SV93: $i] :
( ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV93 = empty_set )
= $true )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1016,plain,
! [SV77: $i,SV93: $i] :
( ( ( SV93 = empty_set )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1017,plain,
! [SV80: $i,SV103: $i,SV107: $i] :
( ( ( ~ ( ~ ( in @ SV107 @ SV103 )
| ~ ! [SY187: $i] :
~ ( in @ ( ordered_pair @ SY187 @ SV107 ) @ SV80 ) ) )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1018,plain,
! [SV103: $i,SV80: $i,SV107: $i] :
( ( ( ~ ( ~ ~ ! [SY188: $i] :
~ ( in @ ( ordered_pair @ SY188 @ SV107 ) @ SV80 )
| ( in @ SV107 @ SV103 ) ) )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1019,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
| ~ ! [SY189: $i] :
~ ( in @ ( ordered_pair @ SY189 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1020,plain,
! [SV66: $i,SV99: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ SV99 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY183 ) @ SV66 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1021,plain,
! [SV99: $i,SV66: $i,SV106: $i] :
( ( ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY184 ) @ SV66 )
| ( in @ SV106 @ SV99 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1022,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
| ~ ! [SY185: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY185 ) @ SV66 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1023,plain,
! [SV77: $i,SV93: $i] :
( ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV93 )
| ! [SY146: $i] :
( ~ ( in @ SY146 @ SV77 )
| ( in @ SY164 @ SY146 ) ) )
| ~ ( ~ ! [SY147: $i] :
( ~ ( in @ SY147 @ SV77 )
| ( in @ SY164 @ SY147 ) )
| ( in @ SY164 @ SV93 ) ) ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1024,plain,
! [SV77: $i,SV93: $i] :
( ( ( ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ SV93 )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV77 )
| ( in @ SY167 @ SY149 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( in @ SY150 @ SV77 )
| ( in @ SY167 @ SY150 ) )
| ( in @ SY167 @ SV93 ) ) ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1025,plain,
! [SV80: $i,SV103: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV103 )
| ~ ! [SY187: $i] :
~ ( in @ ( ordered_pair @ SY187 @ SV107 ) @ SV80 ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1026,plain,
! [SV103: $i,SV80: $i,SV107: $i] :
( ( ( ~ ~ ! [SY188: $i] :
~ ( in @ ( ordered_pair @ SY188 @ SV107 ) @ SV80 )
| ( in @ SV107 @ SV103 ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1027,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
| ~ ! [SY189: $i] :
~ ( in @ ( ordered_pair @ SY189 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1028,plain,
! [SV66: $i,SV99: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ SV99 ) )
= $true )
| ( ( ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY183 ) @ SV66 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1029,plain,
! [SV99: $i,SV66: $i,SV106: $i] :
( ( ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY184 ) @ SV66 ) )
= $true )
| ( ( in @ SV106 @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1030,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1031,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ! [SY185: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY185 ) @ SV66 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1032,plain,
! [SV77: $i,SV93: $i,SV108: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV108 @ SV93 )
| ! [SY191: $i] :
( ~ ( in @ SY191 @ SV77 )
| ( in @ SV108 @ SY191 ) ) )
| ~ ( ~ ! [SY192: $i] :
( ~ ( in @ SY192 @ SV77 )
| ( in @ SV108 @ SY192 ) )
| ( in @ SV108 @ SV93 ) ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1033,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
| ! [SY193: $i] :
( ~ ( in @ SY193 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY193 ) ) )
| ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1024]) ).
thf(1034,plain,
! [SV80: $i,SV103: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV103 ) )
= $true )
| ( ( ~ ! [SY187: $i] :
~ ( in @ ( ordered_pair @ SY187 @ SV107 ) @ SV80 ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1035,plain,
! [SV103: $i,SV80: $i,SV107: $i] :
( ( ( ~ ~ ! [SY188: $i] :
~ ( in @ ( ordered_pair @ SY188 @ SV107 ) @ SV80 ) )
= $true )
| ( ( in @ SV107 @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1036,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1027]) ).
thf(1037,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ! [SY189: $i] :
~ ( in @ ( ordered_pair @ SY189 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1027]) ).
thf(1038,plain,
! [SV66: $i,SV99: $i,SV106: $i] :
( ( ( in @ SV106 @ SV99 )
= $false )
| ( ( ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY183 ) @ SV66 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1039,plain,
! [SV99: $i,SV66: $i,SV106: $i] :
( ( ( ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY184 ) @ SV66 ) )
= $false )
| ( ( in @ SV106 @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1040,plain,
! [SV99: $i,SV66: $i] :
( ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $true )
| ( ( ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1041,plain,
! [SV99: $i,SV66: $i] :
( ( ( ! [SY185: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY185 ) @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1042,plain,
! [SV77: $i,SV93: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ SV93 )
| ! [SY191: $i] :
( ~ ( in @ SY191 @ SV77 )
| ( in @ SV108 @ SY191 ) ) )
| ~ ( ~ ! [SY192: $i] :
( ~ ( in @ SY192 @ SV77 )
| ( in @ SV108 @ SY192 ) )
| ( in @ SV108 @ SV93 ) ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1043,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
| ! [SY193: $i] :
( ~ ( in @ SY193 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY193 ) ) )
| ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1044,plain,
! [SV80: $i,SV103: $i,SV107: $i] :
( ( ( in @ SV107 @ SV103 )
= $false )
| ( ( ~ ! [SY187: $i] :
~ ( in @ ( ordered_pair @ SY187 @ SV107 ) @ SV80 ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1045,plain,
! [SV103: $i,SV80: $i,SV107: $i] :
( ( ( ~ ! [SY188: $i] :
~ ( in @ ( ordered_pair @ SY188 @ SV107 ) @ SV80 ) )
= $false )
| ( ( in @ SV107 @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1046,plain,
! [SV103: $i,SV80: $i] :
( ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $true )
| ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1047,plain,
! [SV103: $i,SV80: $i] :
( ( ( ! [SY189: $i] :
~ ( in @ ( ordered_pair @ SY189 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1048,plain,
! [SV99: $i,SV66: $i,SV106: $i] :
( ( ( ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY183 ) @ SV66 ) )
= $false )
| ( ( in @ SV106 @ SV99 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1049,plain,
! [SV99: $i,SV66: $i,SV106: $i] :
( ( ( ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY184 ) @ SV66 ) )
= $true )
| ( ( in @ SV106 @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1050,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) )
= $false )
| ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1051,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1052,plain,
! [SV77: $i,SV93: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ SV93 )
| ! [SY191: $i] :
( ~ ( in @ SY191 @ SV77 )
| ( in @ SV108 @ SY191 ) ) ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1053,plain,
! [SV93: $i,SV108: $i,SV77: $i] :
( ( ( ~ ( ~ ! [SY192: $i] :
( ~ ( in @ SY192 @ SV77 )
| ( in @ SV108 @ SY192 ) )
| ( in @ SV108 @ SV93 ) ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1054,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
| ! [SY193: $i] :
( ~ ( in @ SY193 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY193 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1055,plain,
! [SV103: $i,SV80: $i,SV107: $i] :
( ( ( ! [SY187: $i] :
~ ( in @ ( ordered_pair @ SY187 @ SV107 ) @ SV80 ) )
= $false )
| ( ( in @ SV107 @ SV103 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1056,plain,
! [SV103: $i,SV80: $i,SV107: $i] :
( ( ( ! [SY188: $i] :
~ ( in @ ( ordered_pair @ SY188 @ SV107 ) @ SV80 ) )
= $true )
| ( ( in @ SV107 @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1057,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) )
= $false )
| ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1058,plain,
! [SV103: $i,SV80: $i,SV110: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1059,plain,
! [SV66: $i,SV99: $i,SV106: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV106 @ ( sK21_SY183 @ SV99 @ SV66 @ SV106 ) ) @ SV66 ) )
= $false )
| ( ( in @ SV106 @ SV99 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1048]) ).
thf(1060,plain,
! [SV99: $i,SV66: $i,SV111: $i,SV106: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV106 @ SV111 ) @ SV66 ) )
= $true )
| ( ( in @ SV106 @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1061,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1062,plain,
! [SV99: $i,SV66: $i] :
( ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $false )
| ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1063,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 )
= $false )
| ( ( ~ ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1064,plain,
! [SV77: $i,SV93: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV93 )
| ! [SY191: $i] :
( ~ ( in @ SY191 @ SV77 )
| ( in @ SV108 @ SY191 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1065,plain,
! [SV93: $i,SV108: $i,SV77: $i] :
( ( ( ~ ! [SY192: $i] :
( ~ ( in @ SY192 @ SV77 )
| ( in @ SV108 @ SY192 ) )
| ( in @ SV108 @ SV93 ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1066,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
| ! [SY193: $i] :
( ~ ( in @ SY193 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY193 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1067,plain,
! [SV107: $i,SV80: $i,SV103: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_SY187 @ SV103 @ SV80 @ SV107 ) @ SV107 ) @ SV80 ) )
= $false )
| ( ( in @ SV107 @ SV103 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1055]) ).
thf(1068,plain,
! [SV103: $i,SV80: $i,SV107: $i,SV112: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV112 @ SV107 ) @ SV80 ) )
= $true )
| ( ( in @ SV107 @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1069,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $false )
| ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1070,plain,
! [SV103: $i,SV80: $i] :
( ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $false )
| ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1071,plain,
! [SV103: $i,SV80: $i,SV110: $i] :
( ( ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $false )
| ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1072,plain,
! [SV66: $i,SV99: $i,SV106: $i] :
( ( ( in @ ( ordered_pair @ SV106 @ ( sK21_SY183 @ SV99 @ SV66 @ SV106 ) ) @ SV66 )
= $true )
| ( ( in @ SV106 @ SV99 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1073,plain,
! [SV99: $i,SV66: $i,SV111: $i,SV106: $i] :
( ( ( in @ ( ordered_pair @ SV106 @ SV111 ) @ SV66 )
= $false )
| ( ( in @ SV106 @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1074,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 ) )
= $true )
| ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1075,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 )
| ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1076,plain,
! [SV77: $i,SV93: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV93 ) )
= $true )
| ( ( ! [SY191: $i] :
( ~ ( in @ SY191 @ SV77 )
| ( in @ SV108 @ SY191 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1077,plain,
! [SV93: $i,SV108: $i,SV77: $i] :
( ( ( ~ ! [SY192: $i] :
( ~ ( in @ SY192 @ SV77 )
| ( in @ SV108 @ SY192 ) ) )
= $true )
| ( ( in @ SV108 @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1078,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) )
= $false )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1079,plain,
! [SV93: $i,SV77: $i] :
( ( ( ! [SY193: $i] :
( ~ ( in @ SY193 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY193 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1080,plain,
! [SV107: $i,SV80: $i,SV103: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY187 @ SV103 @ SV80 @ SV107 ) @ SV107 ) @ SV80 )
= $true )
| ( ( in @ SV107 @ SV103 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1081,plain,
! [SV103: $i,SV80: $i,SV107: $i,SV112: $i] :
( ( ( in @ ( ordered_pair @ SV112 @ SV107 ) @ SV80 )
= $false )
| ( ( in @ SV107 @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1082,plain,
! [SV103: $i,SV80: $i] :
( ( ( ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $true )
| ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1083,plain,
! [SV110: $i,SV103: $i,SV80: $i] :
( ( ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
| ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1084,plain,
! [SV99: $i,SV66: $i] :
( ( ( ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1085,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( ~ ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1086,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1087,plain,
! [SV77: $i,SV93: $i,SV108: $i] :
( ( ( in @ SV108 @ SV93 )
= $false )
| ( ( ! [SY191: $i] :
( ~ ( in @ SY191 @ SV77 )
| ( in @ SV108 @ SY191 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1088,plain,
! [SV93: $i,SV108: $i,SV77: $i] :
( ( ( ! [SY192: $i] :
( ~ ( in @ SY192 @ SV77 )
| ( in @ SV108 @ SY192 ) ) )
= $false )
| ( ( in @ SV108 @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1089,plain,
! [SV93: $i,SV77: $i] :
( ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $true )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1090,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1079]) ).
thf(1091,plain,
! [SV103: $i,SV80: $i] :
( ( ( ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $false )
| ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1092,plain,
! [SV110: $i,SV103: $i,SV80: $i] :
( ( ( ~ ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1093,plain,
! [SV110: $i,SV103: $i,SV80: $i] :
( ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $false )
| ( ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1094,plain,
! [SV99: $i,SV66: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ ( sK24_SY186 @ SV99 @ SV66 ) ) @ SV66 ) )
= $false )
| ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1084]) ).
thf(1095,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( ~ ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1096,plain,
! [SV93: $i,SV108: $i,SV77: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ SV77 )
| ( in @ SV108 @ SV113 ) )
= $true )
| ( ( in @ SV108 @ SV93 )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1097,plain,
! [SV77: $i,SV108: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK25_SY192 @ SV93 @ SV108 @ SV77 ) @ SV77 )
| ( in @ SV108 @ ( sK25_SY192 @ SV93 @ SV108 @ SV77 ) ) )
= $false )
| ( ( in @ SV108 @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1088]) ).
thf(1098,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1099,plain,
! [SV77: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 ) )
= $false )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1100,plain,
! [SV93: $i,SV77: $i] :
( ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) )
= $false )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1101,plain,
! [SV80: $i,SV103: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK26_SY190 @ SV103 @ SV80 ) @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $false )
| ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1091]) ).
thf(1102,plain,
! [SV110: $i,SV103: $i,SV80: $i] :
( ( ( ~ ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1103,plain,
! [SV99: $i,SV66: $i] :
( ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ ( sK24_SY186 @ SV99 @ SV66 ) ) @ SV66 )
= $true )
| ( ( in @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1104,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( ! [SY186: $i] :
~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SY186 ) @ SV66 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1105,plain,
! [SV93: $i,SV108: $i,SV77: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ SV77 ) )
= $true )
| ( ( in @ SV108 @ SV113 )
= $true )
| ( ( in @ SV108 @ SV93 )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1106,plain,
! [SV77: $i,SV108: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK25_SY192 @ SV93 @ SV108 @ SV77 ) @ SV77 ) )
= $false )
| ( ( in @ SV108 @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1107,plain,
! [SV77: $i,SV93: $i,SV108: $i] :
( ( ( in @ SV108 @ ( sK25_SY192 @ SV93 @ SV108 @ SV77 ) )
= $false )
| ( ( in @ SV108 @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1108,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) ) )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1109,plain,
! [SV93: $i,SV77: $i] :
( ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1110,plain,
! [SV77: $i,SV93: $i] :
( ( ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
= $true )
| ( ( ~ ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1111,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1112,plain,
! [SV80: $i,SV103: $i] :
( ( ( in @ ( ordered_pair @ ( sK26_SY190 @ SV103 @ SV80 ) @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $true )
| ( ( in @ ( sK19_SY179 @ SV80 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1113,plain,
! [SV110: $i,SV103: $i,SV80: $i] :
( ( ( ! [SY190: $i] :
~ ( in @ ( ordered_pair @ SY190 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1114,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ ( sK27_SY186 @ SV109 @ SV99 @ SV66 ) ) @ SV66 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1104]) ).
thf(1115,plain,
! [SV93: $i,SV108: $i,SV77: $i,SV113: $i] :
( ( ( in @ SV113 @ SV77 )
= $false )
| ( ( in @ SV108 @ SV113 )
= $true )
| ( ( in @ SV108 @ SV93 )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1116,plain,
! [SV77: $i,SV108: $i,SV93: $i] :
( ( ( in @ ( sK25_SY192 @ SV93 @ SV108 @ SV77 ) @ SV77 )
= $true )
| ( ( in @ SV108 @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $false )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1117,plain,
! [SV93: $i,SV77: $i] :
( ( ( ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) ) )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1118,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 ) )
= $false )
| ( ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1119,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) ) )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1111]) ).
thf(1120,plain,
! [SV93: $i,SV77: $i] :
( ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1111]) ).
thf(1121,plain,
! [SV80: $i,SV103: $i,SV110: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK28_SY190 @ SV110 @ SV103 @ SV80 ) @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1113]) ).
thf(1122,plain,
! [SV109: $i,SV99: $i,SV66: $i] :
( ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ ( sK27_SY186 @ SV109 @ SV99 @ SV66 ) ) @ SV66 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK18_SY173 @ SV66 @ SV99 ) @ SV109 ) @ SV66 )
= $false )
| ( ( SV99
= ( relation_dom @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1123,plain,
! [SV93: $i,SV77: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV114 ) )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1124,plain,
! [SV93: $i,SV77: $i] :
( ( ( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) ) )
= $false )
| ( ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1125,plain,
! [SV93: $i,SV77: $i] :
( ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $false )
| ( ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1126,plain,
! [SV93: $i,SV77: $i] :
( ( ( ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) ) )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1127,plain,
! [SV80: $i,SV103: $i,SV110: $i] :
( ( ( in @ ( ordered_pair @ ( sK28_SY190 @ SV110 @ SV103 @ SV80 ) @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $true )
| ( ( in @ ( ordered_pair @ SV110 @ ( sK19_SY179 @ SV80 @ SV103 ) ) @ SV80 )
= $false )
| ( ( SV103
= ( relation_rng @ SV80 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1128,plain,
! [SV93: $i,SV77: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV77 ) )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV114 )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1129,plain,
! [SV93: $i,SV77: $i] :
( ( ( ! [SY194: $i] :
( ~ ( in @ SY194 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SY194 ) ) )
= $true )
| ( ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1130,plain,
! [SV93: $i,SV77: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV115 ) )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1131,plain,
! [SV93: $i,SV77: $i,SV114: $i] :
( ( ( in @ SV114 @ SV77 )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV114 )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1132,plain,
! [SV93: $i,SV77: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV77 )
| ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV116 ) )
= $true )
| ( ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1133,plain,
! [SV93: $i,SV77: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV77 ) )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV115 )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1134,plain,
! [SV93: $i,SV77: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV77 ) )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV116 )
= $true )
| ( ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1135,plain,
! [SV93: $i,SV77: $i,SV115: $i] :
( ( ( in @ SV115 @ SV77 )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV115 )
= $true )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ ( sK23_SY193 @ SV93 @ SV77 ) )
= $false )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1136,plain,
! [SV93: $i,SV77: $i,SV116: $i] :
( ( ( in @ SV116 @ SV77 )
= $false )
| ( ( in @ ( sK20_SY167 @ SV77 @ SV93 ) @ SV116 )
= $true )
| ( ( in @ ( sK23_SY193 @ SV93 @ SV77 ) @ SV77 )
= $true )
| ( ( SV93
= ( set_meet @ SV77 ) )
= $true )
| ( ( SV77 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1137,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[683,1136,1135,1131,1127,1125,1122,1120,1116,1115,1112,1109,1107,1103,1093,1086,1081,1080,1073,1072,1070,1062,1016,1015,1009,1008,991,990,989,980,974,972,971,970,967,964,961,960,959,958,957,956,950,949,948,947,937,936,916,915,904,897,840,838,836,833,827,826,800,760,759,758,757,756,755,719,718,717,716,715,714,713,712,711,710,709,708,707,706,705,704]) ).
thf(1138,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1137,679]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU187+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:06:47 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.58/1.31 .
% 5.58/1.31
% 5.58/1.31 No.of.Axioms: 48
% 5.58/1.31
% 5.58/1.31 Length.of.Defs: 0
% 5.58/1.31
% 5.58/1.31 Contains.Choice.Funs: false
% 5.58/1.31 .................................
% 5.58/1.31
% 5.58/1.31 ********************************
% 5.58/1.31 * All subproblems solved! *
% 5.58/1.31 ********************************
% 5.58/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:48,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1137,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.58/1.31
% 5.58/1.31 %**** Beginning of derivation protocol ****
% 5.58/1.31 % SZS output start CNFRefutation
% See solution above
% 5.58/1.32
% 5.58/1.32 %**** End of derivation protocol ****
% 5.58/1.32 %**** no. of clauses in derivation: 1020 ****
% 5.58/1.32 %**** clause counter: 1137 ****
% 5.58/1.32
% 5.58/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:48,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1137,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------